Ln Definition and 177 Threads

How would I evaluate $$\int_0^\infty \frac{\ln(x)}{1+x^2} dx$$?

Hello I am struggling with this integral: \[\int \ln\left(\sqrt{x}+1 \right)\,dx\]I tried integrating by parts (multiplying the integral by 1), however I got stuck with another integral I couldn't solve on the way \[\int \frac{1}{\sqrt{x}+1}dx\]Thanks !

i tried to solve this and I got stuck somewhere in my solution. I need help. $\displaystyle \int\frac{3x^5-2x^3+5x^2-2}{x^3+1}dx$ splitting the integrand i get, $\displaystyle \int\frac{3x^5}{x^3+1}dx-\int\frac{2x^3}{x^3+1}dx+\int\frac{5x^2}{x^3+1}dx-\int\frac{2}{x^3+1}dx$ by letting...

can someone give me hints how to solve this.(Coffee) $\displaystyle \int\frac{ln^2\,3x}{x}dx$

Hello I am trying to solve the integral of the function: 3x/(4x-1) Need some help with it, I am stuck... Thanks !

T= ln x/k divided by (x-k) I need to rearrange this equation to solve for x. any suggestions?

hi every one .. i have some question 1 - why the value of exp = 2.71 ?? were from they get this value ? any derive or rule ? 2 - who i can fiend the value of ln and exp and sin or cos without using calculator ? like cos 56 sin 28 ?? or ln 24 ? exp 33 ? without using...

Hi, We know that if x=2, and y=4 for example, i.e that x is directly proportional to y. What i am wondering about is when to say that x is proportional to lny? As in the case of Entropy in Statistical Physics where S proportional to lnW?

We were working with L'hospital's rule and my teacher said that the teacher before him told him that this was true: lim (x→∞) [ln u] = ln ( lim (x→∞) u), where u is a continuous function. My teacher has never found a proof for this, although it works every time. Does anyone know how to...

Homework Statement Radioactive decay is: N = N0e-λt N can also be used to describe count rate after a time, (t) where N0 is intial count rate and λ is decay constant... Half life, t1/2 od radioactive isotope is t1/2 = 1n2 λ The λ should be under the ln2 but it won't let...

I need to find the limit of. Ln (sinx) as x approaches pi-, that is, as x approaches pi from the left. I thought I should use the squeeze theorem, but I am not sure how to apply it. My teacher is not requiring us to use the delta/Epsilon method, so I am sure it is a squeeze method. But how do I...

Anyone heard of a book titled "S=k ln W"? Hi, An old prof. of mine suggested an SM book he read in grad school that was titled "S=k ln W". He didn't remember the author, but said it was pretty short (~100 pages) and was a really good read for a grad class in SM. I've been trying to find this...

Homework Statement I'm doing a lab where I'm trying to find the emissivity of a tungsten filament. I measured voltage and current of a bulb with a tungsten filament and found the power. Then I plotted Power vs Temperature^4 and used the slope along with surface area and Boltzman's constant...

$$ \int (\ln x)^pdx, \quad p > 0 $$ How do I go about integrating this?

Homework Statement This is from an online answer, and I don't understand the steps that it took. How did they go from the first red box to the second red box? Homework Equations L'Hopital's rule Laws of exponents The Attempt at a Solution I am really really confused. It...

How do you solve ln x=1/2x-1/2? Please show every step. Thanks.

Homework Statement Hi guys, I've got : y= ln ( (1 + √x) / x^{3}) 2. The attempt at a solution I honestly don't know where to go from here, I tried getting the ln of each of them. y = ln 1 +ln√x - ln x^{3} Am I doing it write? If not, how am I suppose to work this problem...

So we have the two ODE solutions are the cosine/sine and $r^n$ since it was a Cauchy Euler type. For the steady state, the solution is just a constant since it has to have period 2pi. But with $r^n$, how with lambda equal to zero does $\ln r$ come into play? If my question is hard to follow...

Hello Im solving a problem with calculator to find the zeta in this equation but as i see some persons they solved this equation with different numbers(1.63 ) without calculator.now i want to know how can fine zeta in this equation without calculator and fast?

Homework Statement Find dy/dx when y=\sqrt{ln x} Homework Equations d/dx of ln x is equal to 1/x times d/dx of x. The Attempt at a Solution I tried to raise the ln x to the 1/2 power instead of keeping it under a square root sign, but I had no luck. I'm struggling with Calculus. I...

Homework Statement It is stated in "Mathematical methods of Physics" by J. Mathews, 2nd ed, p274, that the Bessel function of the second kind and of order zero, i.e. Y_0(x) can be approximated by \frac{2}{\pi}\ln(x)+constant as x \to 0, but no more details are given in the same text.Homework...

this time it relates to the chain rule and trig functions. for example: $$y=ln(sinx)\Rightarrow y'=cot(x)$$ via the chain rule, including the following steps $$\frac{d}{dx}ln(sinx)$$ $$=cos(x).\frac{1}{sin(x)}$$ $$=\frac{cos(x)}{sin(x)}$$ $=cot(x)$ but I would have expected that, following the...

Hi, I have a hard time understanding why ln (x) and e cancel out, when, for example, we have something like: eln(2x+3) I tried an internet search but I did not get any good explanation, just statements of the rule. Could anyone help me please? Thanks!

Homework Statement Find the series expansion of ln(x + sqrt(1+x2)) Homework Equations ln(1+x) = x - x2 /2 + x3/3 - x4/4 + ... The Attempt at a Solution I don't know how to solve this. If it was ln(1+f(x) ) I know I could substitute the x's for f(x) in the ln(1+x) series...

The integral of sec x is ln|sec x + tan x| + c. That's what the internet is telling me. Now, I am having trouble understanding the modulus sign. I understand that the ln operator gives real numbers for positive values of the argument and complex numbers for negative values of the argument...

Homework Statement Simplify ln [(e^1-3ln2)/(2∏/e)] Homework Equations I was using the equation e^lnx = x to try and simplify the numerator, but I am unsure if that is correct. The Attempt at a Solution I am very rusty with my calculus and when it comes to using ln, I tend to get stumped...

Homework Statement ∫ 1/x arctan (lnx) dx Homework Equations The Attempt at a Solution 1.U substitution. SO u = ln x, du= 1/x dx ∫ arctan u du 2.by parts: u = arctan u du = 1/ 1+u^2 v = 1 dv = du 3. uv - ∫vdu = artan u - ∫ 1/ 1+u^2 =...

Homework Statement Integrate z'' + (1/z)(z'^2) = 0 to find an equation of motion This is a GR problem, using geodesic equations of motion, so I have derivatives of coordinate z wrt some parameter λ, where z is a function of λ, and z'(λ) is the first derivative wrt λ Homework Equations...

Homework Statement integrate:13((4^x)+(3^x))dx Homework Equations The Attempt at a Solution I know the solution is 13((4^x)/ln(4) + (3^x)/ln(3)) + C Can someone explain to me how this works? I don't know where the ln's are coming from. How would I differentiate this back to...

If I had a value of 6V and then found the log which is 1.79 (3.s.f) what are the units of this quantitiy? or is it dimensionless? why?

Homework Statement lim (lnx)^2/x x-->infinity Homework Equations none The Attempt at a Solution =5lnx/x * (1/lnx)/(1/lnx) =5/(x/lnx) How do I calculate x/lnx?

once i get ln on both sides, I'm then supposed to differentiate both sides...but I won't be able to properly differentiate if ln is not applied. Does ln get applied to the 976, (-1) and 176t? How?

Homework Statement Show that lim (x,y) → (a,0) e^(x ln y) = 0 \foralla > 0 Homework Equations The Attempt at a Solution I've tried looking at lim (x,y) → (a,0) x ln y seperately. lim(x,y) → (a,0) x ln y = lim(x,y) -> (a,0) x * lim(x,y) → (a,0) ln y...

∫Homework Statement Use the integration tables to find the exact arc length of the curve f(x)=ln x 1≤x≤e Reference the table number formula used Then approx. your answer and compare that to the approx. "straight line distance" between 2 points coordinates of two points...

Homework Statement the question is for plane curves. find T N and k for the plane curves 1. r(t) = ti + ln (cos t) the derivative of ln x is 1/|x|, so why isn't the derivative of ln cos x, 1/cos x or sec x? My book says the answer is - tan x

Can the natural logarithm in the statistical mechanics formulation of entropy , S = k ln W be based on both multiplicity and an integral ? The extensive property and multiplicity explanation : That for any given macrostate , the total entropy of two interacting systems is the sum of their...

Is the derivation of this relationship ln x/y = ln x - ln y exclusively from, and originating from the evaluation of the Integral from 1 --> x 1/t dt = ln x ? To say another way can ln x/y = ln x - ln y always be considered to apply to this integral ?

Homework Statement I am trying to prove that the following equations are the same for a client, but keep getting different answers using a calculator. Homework Equations 1- Cadmium concentration = e^0.86[In(hardness)]-3.2 μg/L 2 - Cadmium concentration =...

Homework Statement Homework Equations I'm looking over in old midterm to prepare for a final and can't figure out what the correct answer is. No answers were ever given. I'm not cheating on anything, would just like to know what the correct answer is and why :) The Attempt at a...

1. From a lab experiment, I measured the volume of trapped air at various temperatures. I know I did calculations correctly up to the point that I drew the linear relationship between ln (p of H2O in atm) to 1/T (in Kelvin). My textbook says the slope of this graph is supposed to equal -ΔHvap/R...

Homework Statement Determine the domain and find the derivative f(x) = ln|(x+2)/(x3 - 1)| Homework Equations The Attempt at a Solution We can factor x3 - 1 = (x-1)(x2) + x + 1) From this we know that x ≠ 1 or -2 because 1 would be undefined at -2 would cause the function to...

Homework Statement I'm just not sure what the answer to this is. I think it's an identity for e^x and ln, but I've never had a course that dealt with e^x or logs. So I don't know. What is the answer to e^14ln(x)? It's part of a larger problem, but I can't get the rest of it done until I...

Homework Statement How do you find the domain of y=ln(6-x) ? The Attempt at a Solution do i have to set 6-x greater than or equal to 0 to then get that x is less than or equal to 6, or is there more to it than that? I'm confused on where the ln part comes in. Please assist.

If V = Pe-LQ Where P and L are constants, Describe the form that a graph of lnV against Q should take and explain how P and L can be deduced? Very very stuck, please help!

Homework Statement Find the integral of: [a*ln(b/(b -cx)) - kx] dx Where all a,b,c,k are constants and x is the variable. Homework Equations The Attempt at a Solution Rewrote is: a*INT(ln(b/(b-cx)) dx) - k*INT(x dx) I don't know how to solve the first part, (the second...

Homework Statement Problem: find t in the following equationHomework Equations 64000e^{-1600t}+4000e^{-400t}=50000e^{-1000t} The Attempt at a Solution I know the answer: t=6.17\cdot\;10^{-4}s. But I'm struggling with how to get there. This is my attempt: Factorizing down to...

Hey guys, not touched any mathematics in almost 5 years and I am just getting back into it, been going well so far but hit a hurdle with this, I presume its some gaps in my knowledge. So been at this for about an hour, got the first one, no clue on the second, can anyone offer assistance?K(-2...

Homework Statement Let f(x) = x3ln(1+x2), and let the summation (from n=0 to infinity) anxn be the Taylor series for f about 0. Then what is a3? Homework Equations The Attempt at a Solution What?! I definitely don't expect the answer, but does anyone know how I could go about...

Homework Statement find Taylor polynomial for ln x of degree n, at 2 (Pn,2(x)) Homework Equations Pn,1(x)= (x-1) - (x-1)2/2 + ... + (-1)n-1(x-1)n/n The Attempt at a Solution there doesn't seem to be an obvious pattern to this. the coefficients for n=1 to n=4 are 2, -8, 24, -64...

Homework Statement what is the time derivative of the following expression: ln(\frac{ct+\sqrt{(c^2t^2-s^2)}}{s}) Homework Equations \frac{d}{dx} ln x = \frac{1}{x} chain rule log rules eg ln (x/y) = ln x - ln y The Attempt at a Solution ln(ct+\sqrt{(c^2t^2 -s^2)})-ln...