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

The integral of cos(x)sin(3x)-4sin(x) is 1/2 (-1/4 cos(4x)-1/2 cos(2x))+4cos(x)+C

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integral of cos(x)sin(3x)-4sin(x)

\int cos (x) sin (3 x) - 4 sin (x) d x

\frac{1}{2} (- \frac{1}{4} cos (4 x) - \frac{1}{2} cos (2 x)) + 4 cos (x) + C

Solution steps

\int cos (x) sin (3 x) - 4 sin (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 cos (x) sin (3 x) d x - \int 4 sin (x) d x

\int cos (x) sin (3 x) d x = \frac{1}{2} (- \frac{1}{4} cos (4 x) - \frac{1}{2} cos (2 x))

\int 4 sin (x) d x = - 4 cos (x)

= \frac{1}{2} (- \frac{1}{4} cos (4 x) - \frac{1}{2} cos (2 x)) - (- 4 cos (x))

Simplify

= \frac{1}{2} (- \frac{1}{4} cos (4 x) - \frac{1}{2} cos (2 x)) + 4 cos (x)

Add a constant to the solution

= \frac{1}{2} (- \frac{1}{4} cos (4 x) - \frac{1}{2} cos (2 x)) + 4 cos (x) + C

\frac{( x + 11 )}{( x - 11 )}

\int_{1}^{\infty} 41 \frac{e ^{- x}}{x} d x

2 x^{2} y + x^{3} \frac{d y}{d x} = 1

x \to 7 lim (e^{x - 7})

\frac{s}{s ^{2} - 14 s + 1}

What is the integral of cos(x)sin(3x)-4sin(x) ?
The integral of cos(x)sin(3x)-4sin(x) is 1/2 (-1/4 cos(4x)-1/2 cos(2x))+4cos(x)+C