# integrate

1. ### integrate( x^2) arc (sin x )^3

how to do this ?
2. ### integrate (e^x )arc sec x

i gt stucked here , how to proceed ?
3. ### integrate 1 / (4 +9x2)

my ans is 1/27π , but the correct ans is 1/18π
4. ### integrate x / sqrt rt (4- (3x^4) )

the ans is π/6√3 , but my ans is π/3√3... which part is wrong ?
5. ### integrate 1/ \sqrt{x} (x+1)

how to integrate the 1/ ( \surd{1} (x+1) ) ?
6. ### Integrate power of -3/2

\int \frac{dx}{(x^2+a^2)^{\frac{3}{2}}} Elaboration on how to approach the problem will be greatly appreciated! Thank you!
7. ### integrate x(e^ax)

is my working correct ?the book (1/a^2) instead of 1/a ....
8. ### calc 2... how to integrate the following function?

integrate x^4/(1-x^4). im stuck. do i need to do partial factions after doing long division? idk how to do long division for this problem... because you are dividing something with 1 term by something with 2 terms.
9. ### integrate sin(2*f(x)) dx for some integrable and differentiable function f(x)

Hey guys, How would I integrate sin(2*f(x)) dx with the general function f(x) being both integrable and differentiable? Is this even possible?
10. ### Integrate function

I have that f(x)=\int_{0}^{x}exp(-t^2)dt where f(x) is the primitive function to \exp(-x^2) whose graph passes through (0,0) How is this possible?
11. ### integrate ((sin(x))^2)/(1+cos(x))

I'm stuck.. can't remember how to integrate this (I'm sure I used to know) How do I evaluate \int \dfrac{sin^{2}(x)}{1 + cos(x)}~dx I tried to do that z substitution thingy where z = tan(\dfrac{1}{2}x), sin(x) = \frac{2z}{1+z^{2}}, cos(x) = \frac{1-z^{2}}{1+z^{2}}, dx = \frac{2dz}{1+z^{2}}...
12. ### How do I integrate (sec x + tan x)^2 ?

Hi all, This one is twisting my mind I need to find a volume of the solid of revolution for the function f(x) = sec x + tan x, from x=-pi/3 to x=pi/4. Ok so I did all the work trough and forgot that the formula for volume the function f is squared, and got to do everything again(Crying). But...
13. ### integrate 1/[(1+x)*x^(1/2)]

[SOLVED] integrate 1/[(1+x)*x^(1/2)] $$\int{ \frac{1}{(1+x)\sqrt{x}} dx}$$ //edit well, this is awkward, I've made a stupid mistake, a now I'm able to solve it.
14. ### how to integrate

Hi, How to integrate x^2/(xsinx + cosx)^2. I am clueless. It does not fit into any formula straight away. If I want to try integration by parts, it appears to be lengthy and i do not know whether it will lead to the answer. How to go about this? do we have any particular method for solving...
15. ### Integrate x^(x)

What is the definite integral of x^(x) from 0 to 1?
16. ### Can't integrate the surface area of revolving curve the normal way

Here's the problem I was given: Find the area of the surface generated by revolving the curve x=\frac{e^y + e^{-y} }{2} from 0 \leq y \leq ln(2) about the y-axis. I tried the normal route first... g(y) = x = \frac{1}{2} (e^y + e^{-y}) g'(y) = dx/dy = \frac{1}{2} (e^y - e^{-y}) S =...
17. ### integrate this

Find S(2x+1)^2 /x dx * S is the integrate sign thank you!
18. ### How to integrate double exponential and gaussian?

Hi, I encountered this integration, where the integrand is the multiplication of double exponential and a gaussion... \int^{\infty}_{0}e^{-x^2}e^{e^{-x}}dx. By doing the change of variable y=e^{-x} seems not to do the job... Anyone knows how to integrate it? Thanks a lot!!

ds/(2s+1)^3
20. ### partial fractions, long division

hey everyone, i had a question on partial fractions: integrate (t^2 + 8) / (t^2 - 5t + 6) my problem is with the long division i keep on ending with 2-5t and then i integrate it again and i get a weird answer. i even checked wolfram but the steps don't show long divison. please help, thanks alot