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 (x^{2} + 1) sin (3 x) d x

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

\int x^{2} (x^{3} + 7)^{10} d x

\int 8 x^{2} e^{x^{3}} d 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