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

Popular >

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

\int 6 x^{2} (3 - 2 x^{3})^{3} d x

\int \frac{x ^{2} - 6 x + 9}{x ^{2} - 6 x + 58} d x

\int (2 x^{2} - \frac{3}{4} x) d x

\int \frac{x}{( x ^{2} - 2 ) x ^{4} - 4 x ^{2} + 5} d x

\int (\frac{x ^{3}}{3} - \frac{x ^{4}}{2} + \frac{x ^{5}}{5}) d x

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