Integrating Definition and 940 Threads

i'm having trouble rewriting this integral:\int\frac{e^x}{e^{2x} + 1} so that it will be in the arctan formula: should i use long divison here? if it were not for the e^x in the numerator i'd be fine.

Q. Motivate the Integrating factor strategy for U ( "Mew" ) of y I know how to prove it for "Mew" of x but how to do for "mew" of y Maybe something like this. Mdx (x.y) + Ndy ( x, y ) = 0 Assume this is differentiable so let us multiply by "mew" of x on both sides to make it...

Hi there, (I hope this post is in the right forum) I'm trying to integrate a 3x3 orientation matrix using a vector representing rotational velocity (in 3d) This is the formula I'm using: newOrientation = orientation + (dt)(~w)(orientation) where w is the vector rotational velocity...

the question is "evaluate \iiint z \,dv, of a solid tetrahedron bounded by the four planes x=0,y=0,z=0, and x+y+z=1" I can set up the problem correctly but i can't seem to integrate it right \int_{0}^1 \int_{0}^{1-x} \int_{0}^{1-x-y} z dzdydx (1/2) \int_{0}^1 \int_{0}^{1-x} (1-x-y)^2dydx...

I have this population differential equation dP/dt=k1(P)-k2(P) where k1 and k2 are proportionality constants. I need to integrate and analyze where k1>k2, k1=k2, and k1<k2. Trouble is, I don't think I'm integrating this right. I get P=e^(t+C)(k1-k2). I know this should be easy but I don't think...

Does anyone know how to intergrate \frac{1}{\sqrt{2\beta x-\alpha x^2}} I went to wolfram and type it in, but it gave me a weird number.

Hey. I am pretty confident i have solve this problem. I just solve the integral of the given wave function, with the given limits... However, I am having a difficult time integrating it. The sqrt(2/L) can be brought outside of the integral, but what can i with the sin function? The wave...

We just started this and I mostly understand it except when it comes to using A, B, C, etc substitution. What I mean is this, here is an exampe. (6x^2+x+1)/(x^2+1)(x-1) = (Ax+B)/(x^2+1) + (C)/(x-1) You then multiply by denominators so you end up with (Ax+B)*(x-1) + (C)*(x^2+1). You...

I need help with two questions. Find a divergent improper integral whose value is neither infinity nor -infinity. 2. Find the volume of an ellipsoid (a^2*x^2) + (b^2*8y^2) + (c^2*z^2) = a^2*b^2*c^2 using integration.

Can anyone point me to some online resources on how to integrate polar equations? Thanks.

I need to know how to integrate this function: sin(sqrt(x)) I did this: u = sqrt(x) du/dx = 1/(2sqrt(x)) S(sin(sqrt(x))dx) = S(sin(u)*dx*du/dx/(2sqrt(x)) = S(Sin(u)/u du) But then I got stuck: integration by parts won't work, trig substitution is out... The one thing I did come up...

In calculus, my work has recently involved integrating and differentiating the numer e, of which I am very unsure of how to do. I set up some examples for myself to try to figure out, could anyone tell me if they are correct? Please correct me if I am wrong, or tell me where I have made a...

I am able to proove to myself, through generalised substitution, that the integral of f'(x)/f(x) is lnf(x)+c, but where do the modulus signs come from? ie - The accepted integral is ln|f(x)|+c, not lnf(x)+c Thanks in advance. :smile:

Here's the problem: y\left( 2x-y-1 \right) dx + x\left( 2y-x-1 \right) dy = 0 So rewrite it as: \left( 2xy-y^2-y \right) dx + \left( 2xy-x^2-x \right) dy = 0 Now it's in the form,…P(x,y) dx + Q(x,y) dy = 0 \frac{\partial P(x,y)}{\partial y} = 2x-2y-1 \frac {\partial...

whats the integral of tan^2(u)(sec(u))du? i was trying to integrate (x^2)/sqrt(x^2+1)dx, and came into that. it turns out pretty messy though, is there a clean way to do it?

does the integration of Force equal negative potential energy? \int{F}={-U} Also, what is the difference between \oint and \int?

haven't found a way of doing it so far. I have a feeling that it's extremely easy, and I'm missing how to do it somehow :/

Yeah, this questions may be a little elementary for some, but I don't seem to have any sources which would be able to tell me how do i integrate a function 1/x. Any help would be great. : )

how can i integrate the equation presenting the ALLEE EFFect ds/dt = - a s ln(bs) where a and b are constants

here's the problem, i am supposed to take the integral from 1 to 2 of this: (dx)/[(X+3)^2 (x+1)^2] I decided that the easiest way to compute it is by integrating by partial fractions so what i did was set up the equation: A/(x+3) + B/[(x+3)^2] + C/(x+1) + D/[(X+1)^2] = 1 After this I...

Hi Y'all, I was trying to integrate a function in two dimesions. after integrating it in one dimesion and substituting the limits I got two terms. I am unable to integrate the second term. That is because it had a sqare root in the denominator which contained another one within it. I took...

how do you integrate x^x dx? Thx

how do i integrate sqrt(3-(x^2))/sqrt(3)? i put the sqrt(3) outside the integral and tried using the substitution method to integrate it but there is still an x in there? same thing with integrating sqrt(3-3*(x^2)) Thanks! This thing is due tomorrow.. :eek:

correct me if I am wrong... By integrating gravity(g)= -9.8m/s...you get the motion equations with constant acceleration I didnt know how to set the limits of the integral...LATEX IS TUFF d\vec{a}=(-g)dt 1 \int_{\vec{V}_0}^{\vec{V}}dv=\int_{t_0}^{t_1}{-g}dt 2 \Delta{\vec{v}}=(-g)t...

sorry i didnt use latex..I tried...its annoying V=V(initial) + at...when you integrate both sides you get x=x(initial) + ..? I had a little trouble trying to integrate the (at) do you use the uv-integral(v DV) theorm...well i used that and it and it didnt give me the second equation for...

i'm told to use the method of cylindrical shells to find the volume gnerated by rotating the region bounded these curves about the y axis: y=e^(-x^2) y=0 x=0 x=1 Couple questions. What does the graph of y=e^(-x^2) look like? Also, i know the integral is =integral(a,b) 2(pi)x*e^(-x^2) how...

\int 96cos^4(6x) * dx ok first i take out the 96 cause it's constant! 96 \int cos^4(6x) * dx 96 \int (cos^2(6x)^2) * dx ok now with that setup, i can know use the half-angel formula! 96 \int (\frac{1+cos(12x)}{2})^2 squared the problem... 24 \int (1+ 2cos(12x) +...

Today I was reading my favorite calculus textbook, that saw the integration formula for tan(x). It was : Integral of tan(x) = -ln|cosx| + C . I know that when we say integral of tanx we mean, what is the function whose derivative is tanx. So started to take the derivative of -ln |cosx|, in...

Hi, I have to integrate this: \int e^{2x}sinx I've tried by parts, but e^{2x} never goes away and sinx just keeps going back and forth to cosx. Is there some kind of substitution I should use? The original question was the differential: (-e^xsinx+y)dx+dy = 0 and I'm trying to...

I am trying to solve a linear equation and getting stuck. y' + 2xy = x^2 I am using e^{x^2} as my integrating factor and multiplying that to both sides. Afterwards, I am able to wrap up the LHS as [y e^{x^2}]' and I have [y e^{x^2}]' = x^2 e^{x^2} Now all I need to do is...

Int(cosec x)dx Let: u=cos x then: x=arcos u and: dx=-du/sqrt(1-u^2) Int(cosec x)dx = -Int{1/sqrt(1-u^2)}^2}du = -Int {du/(1-u^2)} = -(1/2)ln(1-u^2) + C =...

I need help with these problems: (1) STan^-1(y)dy and (2) Ssin^-1(x)dx (S=integral) I can't seem to figure out the trigonometric formula for integration. A little help or hint would be nice. Thanks!

I noticed than in the chapters I am studying now that while they give us a formula for taking the derivative of log base a of x, I can't find a correspoding formula for finding the integral of log base a of x. We have a table of integrals in the back of the book, but I only see integrals...

Hi, ive got a really simple question, but I am just slightly confused, im trying to integrate 1/x^3 , now i take x^3 to the top and i get x^-3, and now when i intergrate that i get: x^-2/-2 (i think) now when i put it back into fractional form do i get: -2/x^2 or -1/2x^2 ?

integrating sinx/x between (0,infinty)? hey ppl! Can you help me by giving me a method or how you would go around to prove that this \mid\int\frac{sinx}{x}dx\mid exists. Thanx Saint_n

Given P(x)= \frac{1}{\sigma \sqrt{2\pi}} e ^ \frac { -(x - \mu )^2}{2 \sigma ^2 } This is of course the normal distribution curve. When \mu = 0 and \sigma = 1 I can integrate this from minus infinity to positive infinity no problem using polar coordinates and a bit of multivariable...

Need a kickstart with this one: f(t)=t^(3/2)log(of 2)Sqrt(t+1) Integral of (3-x)7^[(3-x)^2] dx 7^[(3-x)2] = e^[(3-x)2ln 7] u=(3-x)^2 du/dx = -2(3-x) (3-x)dx = -1/2 du not even sure what so far is right..

In school, I'm doing this thing called moment of inertia given by the formula I = \int y^2 dA If the object being solved for is a rectangle where the base of it is parallel to the x axis, dA is equal to xdy. From there, the integration is easy. If the object to solve the integration for is...

I've just finished reading the section on partial fraction integration from my text. The book describes how all rational functions can be integrated by performing a partial fraction decomposition and subsequently integrating the partial fractions using methods that are already known. I tried to...

Integrating 1/(1+e^x): I am currently substituting 1+e^x = u, S (u*e^x)^-1 du since du/dx = e^x S (u*(u-1))^-1 du (S represents the integral symbol) But i looked up the answer and got Ln (e^x(1+e^x)) +c i need to understand how this is done, thanks in advance everyone.