(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

My book has given me this example, with a step by step, but one of the steps have left me dumbfounded, they seem to have left a huge gap in steps..

2. Relevant equations

3. The attempt at a solution

[itex]\int sin^{5}xdx[/itex]

[itex]\int sin^{4}x sinx dx[/itex]

[itex]\int (1-cos^{2}x)^{2} sinx dx[/itex]

[itex]\int (1 - 2cos^{2} x + cos^{4} x) sinx dx[/itex]

Cool story bro. Here's the next step, what happened?

[itex]= - cos x + \frac{2}{3}cos^{3}x - \frac{1}{5}cos^{5} x + C[/itex]

Did they bring a negative out of the integral and do some kind of U substitution?

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# Learning Trigonometric Substitution

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