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

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

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

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

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

Solution steps

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

Apply Integration By Parts

: - sin (6 - 5 x) + \frac{4}{5} x sin (6 - 5 x) - \int \frac{4}{5} sin (6 - 5 x) d x

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

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

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

Add a constant to the solution

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

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