What is the integral of (5sin(2x)-7cos(3x)) ?

The integral of (5sin(2x)-7cos(3x)) is -5/2 cos(2x)-7/3 sin(3x)+C

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integral of (5sin(2x)-7cos(3x))

\int (5 sin (2 x) - 7 cos (3 x)) d x

- \frac{5}{2} cos (2 x) - \frac{7}{3} sin (3 x) + C

Solution steps

\int 5 sin (2 x) - 7 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 5 sin (2 x) d x - \int 7 cos (3 x) d x

\int 5 sin (2 x) d x = - \frac{5}{2} cos (2 x)

\int 7 cos (3 x) d x = \frac{7}{3} sin (3 x)

= - \frac{5}{2} cos (2 x) - \frac{7}{3} sin (3 x)

Add a constant to the solution

= - \frac{5}{2} cos (2 x) - \frac{7}{3} sin (3 x) + C

What is the integral of (5sin(2x)-7cos(3x)) ?
The integral of (5sin(2x)-7cos(3x)) is -5/2 cos(2x)-7/3 sin(3x)+C