1. Integration puzzle.

[I don't think Schaum's will be of much use (chapter 34)]

Can you find the simplest method to solving this integral:

$\int4sinx\cdot cosxdx/(cos^2x - sin^2x)$

2. $\dfrac{4\sin x\cos x}{{{\cos }^{2}}x-{{\sin }^{2}}x}=\dfrac{2\sin 2x}{\cos 2x}.$

rather than an integral problem, it's actually a trig. identity problem.

3. Krizalid

Originally Posted by Krizalid
$\dfrac{4\sin x\cos x}{{{\cos }^{2}}x-{{\sin }^{2}}x}=\dfrac{2\sin 2x}{\cos 2x}.$

rather than an integral problem, it's actually a trig. identity problem.
You hit the nail on the head with this puzzle that was in the puzzle section. Even with the integral sign, it was really a trig problem that's easy to transform by working with both the numerator and denominator, changing it into another problem which is easy to integrate (with one more slight transformation into tan2x).

Moderator edit: Yes, it was in the Puzzles section. And it was explained very clearly to the OP why the Puzzles subforum was not appropriate. In fact, this issue has been explained several times now.