What is the integral of (x-2)^2sin(x) ?

The integral of (x-2)^2sin(x) is -x^2cos(x)+4xcos(x)+2xsin(x)-2cos(x)-4sin(x)+C

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integral of (x-2)^2sin(x)

\int (x - 2)^{2} sin (x) d x

- x^{2} cos (x) + 4 x cos (x) + 2 x sin (x) - 2 cos (x) - 4 sin (x) + C

Solution steps

\int (x - 2)^{2} sin (x) d x

Apply Integration By Parts

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

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

\int - 2 cos (x) (x - 2) d x = - 2 (sin (x) (x - 2) + cos (x))

= - cos (x) (x - 2)^{2} - (- 2 (sin (x) (x - 2) + cos (x)))

Simplify

- cos (x) (x - 2)^{2} - (- 2 (sin (x) (x - 2) + cos (x))) : - x^{2} cos (x) + 4 x cos (x) + 2 x sin (x) - 2 cos (x) - 4 sin (x)

= - x^{2} cos (x) + 4 x cos (x) + 2 x sin (x) - 2 cos (x) - 4 sin (x)

Add a constant to the solution

= - x^{2} cos (x) + 4 x cos (x) + 2 x sin (x) - 2 cos (x) - 4 sin (x) + C

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

y^{^{''}} + 6 y^{^{'}} + 9 y = 0, y (0) = 2, y^{^{'}} (0) = - 7

\int sin (x) + sec^{2} (x) + sec (x) tan (x) d x

\int \frac{3}{x} + x^{3} d x

\frac{\partial}{\partial x} (4 y cos (x))

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