Solve Integration: x^5cos(x^3) dx

[mckallin]

Please Help! Integration!

can anyone help me solve the following integration? thanks a lot.

\int x^5cos(x^3) dx

 

[mjsd]

you really should show some more effort. ie. show us what you have tried, what you know and tell us what you have problems with.hint: try look for a substitution to make the integrand look nicer, then you can try by parts.

 

[mckallin]

I have tried to do it by part.

If I make u=cos(x^3), dv=x^5 dx, the grade of x, which is in the cos(x^3), won't be reduce.

If I make u=x^5, dv=cos(x^3) dx, I can't solve the \int cos(x^3) dx.

I have thought if there is some way to make it look nicer (like u=x^3 ),but I still can't work out a better substitution.

Could you give me some more advice?

 

[hanskuo]

try
u=x^3,dv=x^2\cos(x^3)dx

have you learned partial substitution ?

 

[mjsd]

hint: try look for a substitution to make the integrand look nicer, then you can try by parts.

here I suggested a two-step process,
substitiion: u = x^3 seems ok
then by parts in new variable

then put answer back in x.