What is the integral of (csc(x))/(sin(x)) ?

The integral of (csc(x))/(sin(x)) is -cot(x)+C

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integral of (csc(x))/(sin(x))

\int \frac{csc ( x )}{sin ( x )} d x

- cot (x) + C

Solution steps

\int \frac{csc ( x )}{sin ( x )} d x

Rewrite using trig identities

= \int csc^{2} (x) d x

Use the common integral:

\int csc^{2} (x) d x = - cot (x)

= - cot (x)

Add a constant to the solution

= - cot (x) + C

\int \frac{- 10}{9 + 4 x ^{2}} d x

\int \frac{( x + 2 )}{4 - x ^{2}} d x

\int sec^{2} (\frac{x}{6}) d x

\int sin^{4} (\frac{x}{9}) cos (\frac{x}{9}) d x

\frac{1}{( x ^{2} + 1 )}

What is the integral of (csc(x))/(sin(x)) ?
The integral of (csc(x))/(sin(x)) is -cot(x)+C