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

The integral of (5-4x)sin(6-5x) is cos(6-5x)-4(1/5 xcos(6-5x)+1/25 sin(6-5x))+C

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

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

cos (6 - 5 x) - 4 (\frac{1}{5} x cos (6 - 5 x) + \frac{1}{25} sin (6 - 5 x)) + C

Solution steps

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

Expand

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

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

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

\int 4 x sin (6 - 5 x) d x = 4 (\frac{1}{5} x cos (6 - 5 x) + \frac{1}{25} sin (6 - 5 x))

= cos (6 - 5 x) - 4 (\frac{1}{5} x cos (6 - 5 x) + \frac{1}{25} sin (6 - 5 x))

Add a constant to the solution

= cos (6 - 5 x) - 4 (\frac{1}{5} x cos (6 - 5 x) + \frac{1}{25} sin (6 - 5 x)) + C

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What is the integral of (5-4x)sin(6-5x) ?
The integral of (5-4x)sin(6-5x) is cos(6-5x)-4(1/5 xcos(6-5x)+1/25 sin(6-5x))+C