How do I integrate the function $f (x) = \frac{cos (x)}{{sin}^{2} (x)} + sin (x)$ $f(x)=cos(x)/(sin^2(x))+sin(x)$ ?

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Answer 1 · 2015-03-19T21:30:17

Try this:
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Answer 2 · 2015-03-19T22:31:09

Rewrite $\frac{cos x}{{sin}^{2} x}$ $cosx/sin^2x$ and then integrate term by term.

$\frac{cos x}{{sin}^{2} x} = \frac{1}{sin x} \frac{cos x}{sin x} = csc x cot x$ $cosx/sin^2x=1/sinx cosx/sinx=cscxcotx$ So,

$\int (\frac{cos x}{{sin}^{2} x} + sin x) d x = \int csc x cot x d x + \int sin x d x$ $int (cosx/sin^2x+sinx)dx=intcscxcotx dx+int sinx dx$

$= - csc x - cos x + C$ $=-cscx-cosx+C$ .

How do I integrate the function f(x)=cos(x)/(sin^2(x))+sin(x)f(x)=cos(x)sin2(x)+sin(x)f(x)=cos(x)/(sin^2(x))+sin(x)?