Homework Statement
∫(2x+1)/(x²+2x+1)(x²+x+1)
Homework Equations
none
The Attempt at a Solution
I've foiled this out to look like:
∫(2x+1)/(x^4+3x³+4x²+3x+1)
I'm trying long division here but it's getting really ugly really fast. Should I foil this out in the first place or...
Homework Statement
for the following integrals, am I allowed to break them up like so:
1. ∫(1)/(sqrt(16-9x²)³) dx
= ∫(1)/(√16)³ · ∫(1)/(√-9x²)³ dx
2. ∫(x²)/(sqrt(x²-9)) dx
= ∫(x²)/(√x²) · ∫(x²)/(√-9) dx
3. ∫(1)/(x²(sqrt(a²+x²))) dx
= ∫(1)/(x²) · ∫(1)/(√a²) · ∫(1)/(√x²) dx...
Homework Statement
How do I know for sure when to use the power rule instead of the chain rule and vice versa?
Homework Equations
The Attempt at a Solution
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...
Homework Statement
derivative of: (14x^2)/sqrt(1-x)
Homework Equations
The Attempt at a Solution
I am at this point at finding the derivative:
(28x(sqrt(1-x))+((7x^2)/sqrt(1-x))/(1-x)
I am confused about the next step because don't know how it's derived from the previous...
Homework Statement
see title.
Homework Equations
no
The Attempt at a Solution
Ok so the solution is 16cos(2x) but I'm not sure how it is derived to that. I've tried the product rule but it's not working for me. What rule or rules do I use to get this solution?
Homework Statement
a) S(4 is higher limit, 0 is lower limit) (x^4 - x^2 + 1)dx
b) S(pi is higher limit, -pi is lower limit) (cosx + sinx)dx
Homework Equations
The S is the integration sign
The Attempt at a Solution
a) = ((x^5)/5)-((x^3)/3)+x I(4 high, 0 low)
=...
Homework Statement
S e^7x
Homework Equations
no
The Attempt at a Solution
Ok so I am using U-substitution for this problem but I don't know what to do next.
u = 7x, du = 7dx
How do I integrate e^u*du?
Homework Statement
a) S 13(4^x + 3^x)dx
b) S (cosx + sec^2x)dx
c) S (3-(1/x))dx
d) S e^(7x)dx
Homework Equations
The S is supposed to be the integration sign
The Attempt at a Solution
Are these correct or at least close?
a) = 13((4^x)/(ln(4) + (3^x)/(ln(3))) + C
b) =...
Homework Statement
a) d^2/(dx^2): ln(x+1)
b) d^3/(dx^3): x^7 + 4x^6 - x^2
c) d^2/(dx^2): 1/(x + 1)
d) d^4/(dx^4): cos(2x)
Homework Equations
none
The Attempt at a Solution
Can someone tell me if these are right?
a)= -(1/(x + 1)^2)
b)=210x^4 + 480x^3
c)= (2/(x + 1)^3)
d)=...
I think I know how to do the first one by applying the chain rule:
limit to infinity
((lnx)^5)/(x)=
(5(lnx)^4)*(1/x)/(x)=
5(lnx)^4*0/(x)= 0
Is that valid?
Homework Statement
What is the derivative of 14x^2?
Homework Equations
The Attempt at a Solution
Do i bring the 2 in front to get 28x? Or do I use the chain rule?
Homework Statement
I'm having trouble calculating these limits.
Homework Equations
none
The Attempt at a Solution
1. lim.......((lnx)^5)/(x)=
x->infinity
(((lnx)^5)/x)/(x/x)=
(((lnx)^5)/x)/1=
How do I calculate from here?
2.lim .......(14lnx^2)/(6lnx^3)=...