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

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

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integral of (cos(2θ)+sin^2(θ))/(2cos(θ))

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

\frac{1}{2} sin (θ) + C

Solution steps

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \int \frac{cos ( 2 θ ) + sin ^{2} ( θ )}{cos ( θ )} d θ

Rewrite using trig identities

= \frac{1}{2} \cdot \int cos (θ) d θ

Use the common integral:

\int cos (θ) d θ = sin (θ)

= \frac{1}{2} sin (θ)

Add a constant to the solution

= \frac{1}{2} sin (θ) + C

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