# Substitution and Integration by Parts

1. Feb 20, 2014

### sashab

1. The problem statement, all variables and given/known data
First make a substitution and then use integration by parts to evaluate the integral.

∫x$^{7}$cos(x$^{4}$)dx

2. Relevant equations

Equation for Substitution: ∫f(g(x))g'(x)dx = ∫f(u)du
Equation for Integration by Parts: ∫udv = uv - ∫vdu

3. The attempt at a solution

So here's my attempted solution

I made a substitution and tried using integration by parts twice but I got stuck on the last line since it turns out to be zero... I know I went wrong somewhere but I can't seem to find my mistake. Any help would be really appreciated! Thanks :)

2. Feb 20, 2014

### CAF123

The second line is incorrect - when you made the u substitution you did not use your expression for dx in terms of du.

3. Feb 20, 2014

### HallsofIvy

Staff Emeritus
Start by writing the integral as $\int x^4cos(x^4)(x^3dx)$ and it is clearer.

4. Feb 20, 2014

### sashab

I see my mistake now! Thanks for the help :)