# Integration by parts? help plz

• October 22nd 2010, 08:17 PM
ddcamp
Integration by parts? help plz
integral 0 to infinite (x^ 3)(e^-8x) cos(5x) dx

should I do integrate by part?
help me (Worried)
• October 22nd 2010, 08:49 PM
Educated

Is it: $\displaystyle \int_{0}^{\infty} x^3 \cdot e^{-8x} \cdot \cos (5x) dx$

Or is it: $\displaystyle \int_{0}^{\infty} x^{3e^{-8x}} \cdot \cos (5x) dx$
• October 22nd 2010, 10:47 PM
ddcamp
1st one. ! thanks. how did you do it?
• October 23rd 2010, 12:00 AM
Educated
To type equations like I did, you use LaTeX to do it. LaTeX Tutorial.

Yes, you would use integration by parts. For the $\cos (5x)$ part you would also need to use integration by u-substitution as well as integration by parts.

$\displaystyle \int f'(x)g(x)h(x)dx = f(x)g(x)h(x) - \int f(x)g'(x)h(x)dx - \int f(x)g(x)h'(x)dx$
• October 23rd 2010, 04:25 AM
skeeter
Quote:

Originally Posted by ddcamp
integral 0 to infinite (x^ 3)(e^-8x) cos(5x) dx

should I do integrate by part?

do you have to find the actual value of the improper definite integral, or do you just have to show that it converges?
• October 23rd 2010, 11:41 AM
ddcamp
I have to find the actual value :S :S thanks!