1. Reduction formulae......again.

Just when I think I have mastered reduction formulae, the "miscellaneous exercise" happens!

The question is:

My working goes like this:

I'm clearly on the right track, I just can't see what's going wrong.

Thanks to anyone who posts!

2. Hello,

Yup, you're on the right track

$I_n=\frac{e^\pi}4- \left[\frac n4 e^{2x} \sin^{n-1}(x) \cos(x)\right]_0^{\tfrac \pi 2} {\color{red}+} \frac{(n-1)n}{4} \dots$

Because it's -*-

I haven't looked further, correct it and then see if it corresponds

3. thanks!

I can't believe I didn't spot that mistake!

I made another mistake as well later on but it's all sorted now:

That question really was a train wreck in mathematical form.