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

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

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

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

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

Solution steps

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

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

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

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

Add a constant to the solution

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

\int - 3 e^{- t} d t

3 t cos (2 t)

\int e^{- 0.5 x} d x

\int (x^{2} + 4)^{7} d x

f (x) = x^{2} arctan (3 x)

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