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

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

Popular >

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

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

sin (x) + cos (x) + C

Solution steps

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

Rewrite using trig identities

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

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

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

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

= sin (x) - (- cos (x))

Simplify

= sin (x) + cos (x)

Add a constant to the solution

= sin (x) + cos (x) + C

\int \frac{1}{x} + \frac{1}{x ^{2} + 1} d x

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

\int \frac{2}{- x ^{2} - 2 x} d x

\int \frac{e ^{2 x} - 1}{e ^{x} - 1} d x

\int \frac{1}{- x ^{2} - 4 x + 5} d x

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