- #1
Telemachus
- 835
- 30
Homework Statement
Hi there. I'm dealing with undefined integrals now. And I found this one that I don't know how to solve.
The problem statement says: Solve the next integrals using the substitution method.
[tex]\displaystyle\int_{}^{}\displaystyle\frac{\cos(x)}{\sin^3(x)}[/tex]
The Attempt at a Solution
I've tried this way, but I don't know how to continue, and maybe there is a simpler way for solving it.
I thought of this substitution:
[tex]u=\sin^3(x)[/tex]
[tex]du=3\sin^2(x)\cos(x)dx[/tex]
[tex]du=3\cos(x)[1-cos^2(x)]dx[/tex]
[tex]du=3\cos(x)dx-3\cos^3(x)dx[/tex]
But then I don't know how to use it in my integral: [tex]\displaystyle\int_{}^{}\displaystyle\frac{\cos(x)}{\sin^3(x)}[/tex]
Any suggestion?
Bye.
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