# Problems with an Integral

• Aug 29th 2009, 01:52 AM
coobe
Problems with an Integral
$\displaystyle \int x^2 cos(mx) dx$

I have trouble solving this. I know that i have to integrate by parts, but somehow i always get the wrong answer.... I put it into Wolframalpha, but im having a hard time following its solution

any help would be appreciated
• Aug 29th 2009, 02:09 AM
skeeter
Quote:

Originally Posted by coobe
$\displaystyle \int x^2 cos(mx) dx$

I have trouble solving this. I know that i have to integrate by parts, but somehow i always get the wrong answer.... I put it into Wolframalpha, but im having a hard time following its solution

any help would be appreciated

tabular integration ...

Code:

.............. u ........... dv + .............x^2 ........ cos(mx) - ............ 2x ..........(1/m)sin(mx) + ............. 2 ......... -(1/m^2)cos(mx) - ............. 0 ...........-(1/m^3)sin(mx) 
$\displaystyle \textcolor{red}{\frac{x^2}{m} \sin(mx)} + \textcolor{green}{\frac{2x}{m^2}\cos(mx)} \textcolor{blue}{- \frac{2}{m^3}\sin(mx)} + C$