What is the integral of 3sin(4x)+4sin(3x) ?

The integral of 3sin(4x)+4sin(3x) is -3/4 cos(4x)-4/3 cos(3x)+C

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integral of 3sin(4x)+4sin(3x)

\int 3 sin (4 x) + 4 sin (3 x) d x

- \frac{3}{4} cos (4 x) - \frac{4}{3} cos (3 x) + C

Solution steps

\int 3 sin (4 x) + 4 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 3 sin (4 x) d x + \int 4 sin (3 x) d x

\int 3 sin (4 x) d x = - \frac{3}{4} cos (4 x)

\int 4 sin (3 x) d x = - \frac{4}{3} cos (3 x)

= - \frac{3}{4} cos (4 x) - \frac{4}{3} cos (3 x)

Add a constant to the solution

= - \frac{3}{4} cos (4 x) - \frac{4}{3} cos (3 x) + C

What is the integral of 3sin(4x)+4sin(3x) ?
The integral of 3sin(4x)+4sin(3x) is -3/4 cos(4x)-4/3 cos(3x)+C