Recent content by Nihilist Comedian

Thanks. It's really quite simple. I can't believe I missed that!

Sorry, forgot to put in the "n" and "m" in the original function. Any help now?

\int{\sin^{n}(x)\cos^{m}(x)dx} =\frac{\sin^{n+1}(x)\cos^{m-1}(x)}{n+1}+\frac{m-1}{n+1}\int{\sin^{n+2}(x)\cos^{m-2}(x)dx} That was quite easy, but it's the simplification process following this that throws me. My answer is perfectly correct, but it is simplified in the answers (in my maths book)...

\begin{equation*}\begin{split}\int \tan(x) \tan(2x) \tan(3x) \, dx\\ &=\int \frac{\sin(x)}{\cos(x)} \frac{\sin(2x)}{\cos(2x)} \frac{\sin(3x)}{\cos(3x)} \, dx\\ &= \int \frac{f '(x)}{f (x)}\dx\end{split}\end{equation*}

This may help: \int \frac{f'(x)}{f(x)}dx=ln|f(x)|+c