What is the integral of 8xsin(5-4x) ?

The integral of 8xsin(5-4x) is 8(1/4 xcos(5-4x)+1/16 sin(5-4x))+C

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integral of 8xsin(5-4x)

\int 8 x sin (5 - 4 x) d x

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

Solution steps

\int 8 x sin (5 - 4 x) d x

Take the constant out:

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

= 8 \cdot \int x sin (5 - 4 x) d x

Apply Integration By Parts

: \frac{1}{4} x cos (5 - 4 x) - \int \frac{1}{4} cos (5 - 4 x) d x

= 8 (\frac{1}{4} x cos (5 - 4 x) - \int \frac{1}{4} cos (5 - 4 x) d x)

\int \frac{1}{4} cos (5 - 4 x) d x = - \frac{1}{16} sin (5 - 4 x)

= 8 (\frac{1}{4} x cos (5 - 4 x) - (- \frac{1}{16} sin (5 - 4 x)))

Simplify

= 8 (\frac{1}{4} x cos (5 - 4 x) + \frac{1}{16} sin (5 - 4 x))

Add a constant to the solution

= 8 (\frac{1}{4} x cos (5 - 4 x) + \frac{1}{16} sin (5 - 4 x)) + C

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What is the integral of 8xsin(5-4x) ?
The integral of 8xsin(5-4x) is 8(1/4 xcos(5-4x)+1/16 sin(5-4x))+C