What is the integral of-6cos(3x)+5sin(7x) ?

The integral of-6cos(3x)+5sin(7x) is -2sin(3x)-5/7 cos(7x)+C

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integral of-6cos(3x)+5sin(7x)

\int - 6 cos (3 x) + 5 sin (7 x) d x

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

Solution steps

\int - 6 cos (3 x) + 5 sin (7 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 6 cos (3 x) d x + \int 5 sin (7 x) d x

\int 6 cos (3 x) d x = 2 sin (3 x)

\int 5 sin (7 x) d x = - \frac{5}{7} cos (7 x)

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

Add a constant to the solution

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

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What is the integral of-6cos(3x)+5sin(7x) ?
The integral of-6cos(3x)+5sin(7x) is -2sin(3x)-5/7 cos(7x)+C