Question

evaluate integral of (2-cosx + sinx)/(sin^2x) dx

Answer 1

\[\int\limits \frac{2-\cos(x)+\sin(x)}{\sin^2(x)}dx=2\int\limits \csc^2(x)dx-\int\limits \cot(x)\csc(x)dx+\int\limits \csc(x)dx\]
\[-2\cot(x)+\csc(x)-\ln|\csc(x)+\cot(x)|+C\]

Answer 2

where did the 2integral csc^2 (x) dx come from? Its correct by the way...

Answer 3

Because you have:
\[2 \int\limits \frac{dx}{\sin^2(x)}\]
And we know:
\[\frac{1}{\sin(x)}=\csc(x)\]

Answer 4

you saved me

Answer 5

Haha, you're welcome :P

Answer 6

quick question, where did you get \[\int\limits_{}^{}\cot(x)\csc(x)dx\] from?

Answer 7

\[\cot(x)=\frac{\cos(x)}{\sin(x)}\]