What is the integral of (sin^2(x)+cos^2(x))/(csc(x)) ?

The integral of (sin^2(x)+cos^2(x))/(csc(x)) is -cos(x)+C

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integral of (sin^2(x)+cos^2(x))/(csc(x))

\int \frac{sin ^{2} ( x ) + cos ^{2} ( x )}{csc ( x )} d x

- cos (x) + C

Solution steps

\int \frac{sin ^{2} ( x ) + cos ^{2} ( x )}{csc ( x )} d x

Rewrite using trig identities

= \int sin (x) d x

Use the common integral:

\int sin (x) d x = - cos (x)

= - cos (x)

Add a constant to the solution

= - cos (x) + C

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What is the integral of (sin^2(x)+cos^2(x))/(csc(x)) ?
The integral of (sin^2(x)+cos^2(x))/(csc(x)) is -cos(x)+C