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

\frac{d y}{d t} = 2 y - t

\frac{d}{d x} ((1 + x^{2})^{5})

\frac{d}{d x} (sin (2 x) \cdot 2)

\frac{d}{d x} (a e^{v} + \frac{b}{v} + \frac{c}{v ^{2}})

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