Question

Can someone please help me simplify this integral for a Calc3 class. Im supposed to simplify then look it up on table of integrals.
Integral Cosx/Sin^2x=Sinx dx

Answer 1

\[
\int \frac{\cos x }{\sin^2 x}dx = \int \cot(x)\csc(x)\;dx=\int -d[\csc x]
\]

Answer 2

Since \(d[\csc x]=-\cot x \csc x\;dx\)

Answer 3

Oh wait, something tells me that isn't supposed to be an equals sign... please right the integrand properly.

Answer 4

sorry I typed that wrong it was supposed to be
\[\int\limits \cos x/ \sin^2 x + \sin x\]

Answer 5

So this equals
\[\int\limits \cot x / (sinx)+1\]

Answer 6

correct?

Answer 7

Then that becomes
\[\int\limits \cot x \csc (x+1) dx\]
?