# Math Help - Intergrals ( u SUB ) ... Part to part

1. ## Intergrals ( u SUB ) ... Part to part

hey guys i recently joined, after seeing how helpful this site is =]
i have a test tommorow and i cant figure out these review problems
hope you guys can help thanks in advance

integral cos(5x)cos(sin(5x)dx
u- Sin(5x)

teacher gave U.

Integral 2x^2 sin (3x) DX

teacher said this one is part to part.. and we use a table method?
i was absent for this part of the lesson.. its said to make the problem easier to do or something?

intergral Sin^2(x)DX

intergral e^x sin(x)Dx

2. on integral Sin^2(x)DX, use the half angle trig equation
sin^2 u= (1/2)(1-cos(2u))

For integral e^x sin(x)Dx do PARTs twice
The trick is to keep the u and dv the same for both integrations
and then add the integral to the other side and solve for it.

3. thanks i sort of understand it..
ive been absent to the class due to a broken hip from football and i feel like its piling up on me and cant seem to catch up on my work.

integral cos(5x)cos(sin(5x)dx
u- Sin(5x)

any idea on this that one?

thanks guys, its 3:30am here and my head is like dead.. im lookin thur all my notes and it doesnt seem to go anywhere.. sigh. fml =[

4. you have the substitution right in front of you

integral cos(5x)cos(sin(5x))dx
u- Sin(5x)

let u=Sin(5x) then du =5cos(5x)dx
and the integral becomes [cos(u)](1/5)du

5. What about the othe cos
There is two

6. can any1 tell me the answer? i cant seem to get it.

7. $\int cos(5x)(cos(sin(5x)))dx$
Let u=sin(5x) $\implies$ du=5cos(5x)dx $\implies$ (1/5)du=cos(5x)dx
cos(5x)dx will be replaced by (1/5)du, so it will look like
$\int (cos(sin(5x))) \frac{1}{5} du$
Since you let u=sin(5x), the sin(5x) inside that cos(sin(5x)) will become cos(u). Bring the 1/5 into the front.
$\frac{1}{5} \int (cos(u)) du$
The integral of cos(u) is sin(u)+C
$\int cos(5x)(cos(sin(5x)))dx$ = $\frac{1}{5} sin(sin(5x))+C$