Integration by parts problem.?

Question

Integrate by parts: integral( x^2 * cos(mx) dx). i get that the m is just a constant but i'm still having some trouble with it, please help! thanks!

Answer 1

the formula is: integral(v * u' * dx)=uv-integral(v' * u * dx)

v=x^2 v'=2x

u'=cos(mx) u=sin(mx)/m

integral(x^2 *cos(mx)*dx)=

x^2*sin(mx)/m

-integral(2x*sin(mx)/m *dx)

and again by parts

v=2x v'=2

u'=sin(mx)/m u=-cos(mx)/m^2

=x^2*sin(mx)/m-(-2xcos(mx)/m^2

-integral(-2*cos(mx)/m^2))=

=x^2*sin(mx)/m+2xcos(mx)/m^2

-2/m^3sin(mx)

i compared with http://integrals.wolfram.com/index.jsp and it's all cool.

Answer 2

u=x^2

du =2x dx

dv= cos(mx) dx

v= 1/m sin(mx)

x^2/m sin(mx) - S 1/m sin(mx) 2x dx

x^2/m sin(mx) -2/m S sin(mx) x dx.........

Answer 3

try the following page

http://rbmix.com/problem/ip/tp.php