What is the integral of (4sin(5x)+5cos(3x)) ?

The integral of (4sin(5x)+5cos(3x)) is -4/5 cos(5x)+5/3 sin(3x)+C

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integral of (4sin(5x)+5cos(3x))

\int (4 sin (5 x) + 5 cos (3 x)) d x

- \frac{4}{5} cos (5 x) + \frac{5}{3} sin (3 x) + C

Solution steps

\int 4 sin (5 x) + 5 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 4 sin (5 x) d x + \int 5 cos (3 x) d x

\int 4 sin (5 x) d x = - \frac{4}{5} cos (5 x)

\int 5 cos (3 x) d x = \frac{5}{3} sin (3 x)

= - \frac{4}{5} cos (5 x) + \frac{5}{3} sin (3 x)

Add a constant to the solution

= - \frac{4}{5} cos (5 x) + \frac{5}{3} sin (3 x) + C

- cos (x^{2}) sin (x) + e^{- x - 2}

\frac{\partial}{\partial x} (e^{2 x + 5 y})

\frac{d}{d x} (cos (x - \frac{π}{4}))

y = 4 x^{2} - 2 x + (- 9)

\frac{d}{d u} (uv)

What is the integral of (4sin(5x)+5cos(3x)) ?
The integral of (4sin(5x)+5cos(3x)) is -4/5 cos(5x)+5/3 sin(3x)+C