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## Homework Statement

First make a substitution and then use integration by parts to evaluate the integral.

∫x[itex]^{7}[/itex]cos(x[itex]^{4}[/itex])dx

## Homework Equations

Equation for Substitution: ∫f(g(x))g'(x)dx = ∫f(u)du

Equation for Integration by Parts: ∫udv = uv - ∫vdu

## 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 :)