integration by parts problem: integral of (x^5)cos(x^3)

[tessec]

problem: integral of (x^5)cos(x^3)

work:

f(x)=cos(x^3) g'(x)=x^5
f'(x)=-3(x^2)sin(x^3) g(x)=(1/6)(x^6)

=> (1/6)(x^6)(cos(x^3))+(1/2)int[(x^8)(sin(x^3)]

 

[skeeter]

problem: integral of (x^5)cos(x^3)

\(\displaystyle \L u = x^3 ...... dv = x^2 cos(x^3) dx\)

\(\displaystyle \L du = 3x^2 dx ...... v = \frac{1}{3}sin(x^3)\)

\(\displaystyle \L uv - \int v du\)

\(\displaystyle \L \frac{x^3}{3}sin(x^3) - \int x^2 sin(x^3) dx =\)

\(\displaystyle \L \frac{x^3}{3}sin(x^3) + \frac{1}{3}cos(x^3) + C\)