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**[SOLVED]Is this integral evaluation valid?**

Hi, so I started with \(\displaystyle \int \frac{\sin(x)\cos^2(x)}{5+\cos^2(x)}dx\)I made u=cos(x) dx=sin(x) leaving \(\displaystyle \int \frac{u^2}{5+u^2}dx\)At this point I was thinking that it looked like an inverse tan, but I was lazy, so instead I tried \(\displaystyle \int\frac{u^2}{5}dx+\int\frac{u^2dx}{u^2}\)In the name of brevity, I concluded with \(\displaystyle \frac{\cos^3(x)}{15}+ \cos(x) + C\)was this a valid way to perform the integration, or should I have went with partial fractions instead? Or just stuck with the inverse tan?Thanks.

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