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

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

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

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

\frac{1}{2} sin (x) + C

Solution steps

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

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 x ) + sin ^{2} ( x )}{cos ( x )} d x

Rewrite using trig identities

= \frac{1}{2} \cdot \int cos (x) d x

Use the common integral:

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

= \frac{1}{2} sin (x)

Add a constant to the solution

= \frac{1}{2} sin (x) + C

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