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**1. Homework Statement**

Hey folks, I think I know how to solve this by parts but I need a substitution to get there. I've been staring at examples for a while but I still don't understand how to apply the substitution rule. Anyway, here's the integral:

[tex]\int x^9cos(x^5)[/tex]

**2. Homework Equations**

integration by parts: [tex]\int f(x)g\prime (x)dx=f(x)g(x)-\int g(x)f\prime (x)dx[/tex]

substitution rule: [tex]\int f(g(x))g\prime (x)dx=\int f(u)du[/tex]

**3. The Attempt at a Solution**

By applying integration by parts:

[tex]f(x)=x^9[/tex]

[tex]f\prime (x)=9x^{8}[/tex]

[tex]g\prime (x)=cos(x^5)[/tex]

Now I need to apply the substitution rule to find [tex]g(x)[/tex] by integrating [tex]cos(x^5)[/tex]:

[tex]u=x^5[/tex]

[tex]du=5x^4dx[/tex]

Then maybe [tex]sin(u)du[/tex]? I'm not sure how to proceed. Thanks!

I've got another post that's still unanswered just in case you've got some more time to kill

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