What is the integral of (5-6x)*sin(4x) ?

The integral of (5-6x)*sin(4x) is -5/4 cos(4x)-6(-1/4 xcos(4x)+1/16 sin(4x))+C

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integral of (5-6x)*sin(4x)

\int (5 - 6 x) \cdot sin (4 x) d x

- \frac{5}{4} cos (4 x) - 6 (- \frac{1}{4} x cos (4 x) + \frac{1}{16} sin (4 x)) + C

Solution steps

\int (5 - 6 x) sin (4 x) d x

Expand

(5 - 6 x) sin (4 x) : 5 sin (4 x) - 6 x sin (4 x)

= \int 5 sin (4 x) - 6 x sin (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 (4 x) d x - \int 6 x sin (4 x) d x

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

\int 6 x sin (4 x) d x = 6 (- \frac{1}{4} x cos (4 x) + \frac{1}{16} sin (4 x))

= - \frac{5}{4} cos (4 x) - 6 (- \frac{1}{4} x cos (4 x) + \frac{1}{16} sin (4 x))

Add a constant to the solution

= - \frac{5}{4} cos (4 x) - 6 (- \frac{1}{4} x cos (4 x) + \frac{1}{16} sin (4 x)) + C

\int_{0}^{3} 2 x + 1 d x

\int_{1}^{4} - 10 x ln (x) d x

\int_{0}^{4} arctan (\frac{x}{4}) d x

\frac{3 y ^{2} - x ^{2}}{y ^{5}} \frac{d y}{d x} + \frac{x}{2 y ^{4}} = 0

x \to 210 lim (12 x - 350)

What is the integral of (5-6x)*sin(4x) ?
The integral of (5-6x)*sin(4x) is -5/4 cos(4x)-6(-1/4 xcos(4x)+1/16 sin(4x))+C