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

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

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integral of 5xsin(3-2x)

\int 5 x sin (3 - 2 x) d x

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

Solution steps

\int 5 x sin (3 - 2 x) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 5 \cdot \int x sin (3 - 2 x) d x

Apply Integration By Parts

: \frac{1}{2} x cos (3 - 2 x) - \int \frac{1}{2} cos (3 - 2 x) d x

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

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

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

Simplify

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

Add a constant to the solution

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

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