What is the integral of (-5sin(2x)-10cos(4x)) ?

The integral of (-5sin(2x)-10cos(4x)) is 5/2 cos(2x)-5/2 sin(4x)+C

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integral of (-5sin(2x)-10cos(4x))

\int (- 5 sin (2 x) - 10 cos (4 x)) d x

\frac{5}{2} cos (2 x) - \frac{5}{2} sin (4 x) + C

Solution steps

\int - 5 sin (2 x) - 10 cos (4 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 (2 x) d x - \int 10 cos (4 x) d x

\int 5 sin (2 x) d x = - \frac{5}{2} cos (2 x)

\int 10 cos (4 x) d x = \frac{5}{2} sin (4 x)

= - (- \frac{5}{2} cos (2 x)) - \frac{5}{2} sin (4 x)

Simplify

= \frac{5}{2} cos (2 x) - \frac{5}{2} sin (4 x)

Add a constant to the solution

= \frac{5}{2} cos (2 x) - \frac{5}{2} sin (4 x) + C

\int_{- π}^{π} cos (3 x) d x

\int \frac{x - 2}{x} d x

\frac{d}{d x} (csc (x^{3} + 2 x) - tan (x))

\frac{\partial}{\partial z} (- y^{2} sin (z))

x \to - 1 + lim ((x + 2 x^{3})^{4})

What is the integral of (-5sin(2x)-10cos(4x)) ?
The integral of (-5sin(2x)-10cos(4x)) is 5/2 cos(2x)-5/2 sin(4x)+C