We are learning summation currently, but since he is not finished with the lesson he assigned us a few more substitution problems. I am finding them very difficult, actually.

$\displaystyle \int \sec{2\theta} \tan{2\theta} d\theta$

I let u=$\displaystyle \sec{2\theta}$ to get du=$\displaystyle (\sec{2\theta} \tan{2\theta}) 2 d\theta$

All that's missing in the original problem is "2". I have never encountered a problem where taking the derivative of u would substitute theentireproblem, with the exception of 2, of course. The only thing I'd get out of it is $\displaystyle \frac{1}{2} + C$, and that doesn't seem right.

Next problem is also causing me some difficulty...

$\displaystyle \int \frac{cos(\pi/x)}{x^2} dx$

I let u= $\displaystyle \frac{\pi}{x}$ to get du= $\displaystyle \frac{-\pi}{x^2} dx$

Final answer $\displaystyle \frac{-1}{\pi} \sin{(pi/x)} + C$

I have a huge hunch I did that one wrong.

Any assistance is greatly appreciated, as always.