What is the integral of cos(2x)-sin(3x) ?

The integral of cos(2x)-sin(3x) is 1/2 sin(2x)+1/3 cos(3x)+C

Popular >

integral of cos(2x)-sin(3x)

\int cos (2 x) - sin (3 x) d x

\frac{1}{2} sin (2 x) + \frac{1}{3} cos (3 x) + C

Solution steps

\int cos (2 x) - sin (3 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 (2 x) d x - \int sin (3 x) d x

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

\int sin (3 x) d x = - \frac{1}{3} cos (3 x)

= \frac{1}{2} sin (2 x) - (- \frac{1}{3} cos (3 x))

Simplify

= \frac{1}{2} sin (2 x) + \frac{1}{3} cos (3 x)

Add a constant to the solution

= \frac{1}{2} sin (2 x) + \frac{1}{3} cos (3 x) + C

\int \frac{- 7 ( x - 9 )}{( x + 5 ) ( x - 2 )} d x

\int \frac{- 4}{( 1 - 2 x ^{2} )} d x

\int 11 tan^{5} (x) sec^{4} (x) d x

\int cos (x + 2 y) d x

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

What is the integral of cos(2x)-sin(3x) ?
The integral of cos(2x)-sin(3x) is 1/2 sin(2x)+1/3 cos(3x)+C