What is the integral of 2xsin(-4x+3) ?

The integral of 2xsin(-4x+3) is 2(1/4 xcos(-4x+3)+1/16 sin(-4x+3))+C

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integral of 2xsin(-4x+3)

\int 2 x sin (- 4 x + 3) d x

2 (\frac{1}{4} x cos (- 4 x + 3) + \frac{1}{16} sin (- 4 x + 3)) + C

Solution steps

\int 2 x sin (- 4 x + 3) d x

Take the constant out:

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

= 2 \cdot \int x sin (- 4 x + 3) d x

Apply Integration By Parts

: \frac{1}{4} x cos (- 4 x + 3) - \int \frac{1}{4} cos (- 4 x + 3) d x

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

\int \frac{1}{4} cos (- 4 x + 3) d x = - \frac{1}{16} sin (- 4 x + 3)

= 2 (\frac{1}{4} x cos (- 4 x + 3) - (- \frac{1}{16} sin (- 4 x + 3)))

Simplify

= 2 (\frac{1}{4} x cos (- 4 x + 3) + \frac{1}{16} sin (- 4 x + 3))

Add a constant to the solution

= 2 (\frac{1}{4} x cos (- 4 x + 3) + \frac{1}{16} sin (- 4 x + 3)) + C

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What is the integral of 2xsin(-4x+3) ?
The integral of 2xsin(-4x+3) is 2(1/4 xcos(-4x+3)+1/16 sin(-4x+3))+C