What is the integral of (7-5x)cos(3-2x) ?

The integral of (7-5x)cos(3-2x) is -1/2 sin(3-2x)(7-5x)-5/4 cos(3-2x)+C

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integral of (7-5x)cos(3-2x)

\int (7 - 5 x) cos (3 - 2 x) d x

- \frac{1}{2} sin (3 - 2 x) (7 - 5 x) - \frac{5}{4} cos (3 - 2 x) + C

Solution steps

\int (7 - 5 x) cos (3 - 2 x) d x

Apply Integration By Parts

: - \frac{1}{2} sin (3 - 2 x) (7 - 5 x) - \int \frac{5}{2} sin (3 - 2 x) d x

= - \frac{1}{2} sin (3 - 2 x) (7 - 5 x) - \int \frac{5}{2} sin (3 - 2 x) d x

\int \frac{5}{2} sin (3 - 2 x) d x = \frac{5}{4} cos (3 - 2 x)

= - \frac{1}{2} sin (3 - 2 x) (7 - 5 x) - \frac{5}{4} cos (3 - 2 x)

Add a constant to the solution

= - \frac{1}{2} sin (3 - 2 x) (7 - 5 x) - \frac{5}{4} cos (3 - 2 x) + C

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What is the integral of (7-5x)cos(3-2x) ?
The integral of (7-5x)cos(3-2x) is -1/2 sin(3-2x)(7-5x)-5/4 cos(3-2x)+C