What is the integral of 5sin(6x)+6sin(5x) ?

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

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integral of 5sin(6x)+6sin(5x)

\int 5 sin (6 x) + 6 sin (5 x) d x

- \frac{5}{6} cos (6 x) - \frac{6}{5} cos (5 x) + C

Solution steps

\int 5 sin (6 x) + 6 sin (5 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 (6 x) d x + \int 6 sin (5 x) d x

\int 5 sin (6 x) d x = - \frac{5}{6} cos (6 x)

\int 6 sin (5 x) d x = - \frac{6}{5} cos (5 x)

= - \frac{5}{6} cos (6 x) - \frac{6}{5} cos (5 x)

Add a constant to the solution

= - \frac{5}{6} cos (6 x) - \frac{6}{5} cos (5 x) + C

\frac{d}{d x} ((x - 2)^{3} (x - 1))

\frac{x - 1}{x + 1}

y = (2 x + 1)^{3} + 6 x (2 x + 1)^{2}

\frac{\partial}{\partial y} (e^{- 3 x} cos (6 y))

\frac{d y}{d x} = y tan (x)

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