What is the integral of 1/(cos(2x)+sin^2(x)) ?

The integral of 1/(cos(2x)+sin^2(x)) is tan(x)+C

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integral of 1/(cos(2x)+sin^2(x))

\int \frac{1}{cos ( 2 x ) + sin ^{2} ( x )} d x

tan (x) + C

Solution steps

\int \frac{1}{cos ( 2 x ) + sin ^{2} ( x )} d x

Simplify

\frac{1}{cos ( 2 x ) + sin ^{2} ( x )} : sec^{2} (x)

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

Use the common integral:

\int sec^{2} (x) d x = tan (x)

= tan (x)

Add a constant to the solution

= tan (x) + C

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What is the integral of 1/(cos(2x)+sin^2(x)) ?
The integral of 1/(cos(2x)+sin^2(x)) is tan(x)+C