What is the integral of xsin(1-2x) ?

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

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integral of xsin(1-2x)

\int x sin (1 - 2 x) d x

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

Solution steps

\int x sin (1 - 2 x) d x

Apply Integration By Parts

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

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

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

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

Simplify

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

Add a constant to the solution

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

\int \frac{2 - x}{x ^{2} - 2 x + 1} d x

x^{3}, x

7 x^{3} e^{x}

f (x) = - \frac{1}{( x - 5 ) ^{2}}, at x = - 4

\int \frac{x ^{3} + 3 x - 1}{x ^{4} - 4 x ^{2}} d x

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