What is the integral of (x^2-4)sin(x) ?

The integral of (x^2-4)sin(x) is -x^2cos(x)+2xsin(x)+6cos(x)+C

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integral of (x^2-4)sin(x)

\int (x^{2} - 4) sin (x) d x

- x^{2} cos (x) + 2 x sin (x) + 6 cos (x) + C

Solution steps

\int (x^{2} - 4) sin (x) d x

Expand

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

= \int x^{2} sin (x) - 4 sin (x) d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int x^{2} sin (x) d x - \int 4 sin (x) d x

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

\int 4 sin (x) d x = - 4 cos (x)

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

Simplify

- x^{2} cos (x) + 2 (x sin (x) + cos (x)) - (- 4 cos (x)) : - x^{2} cos (x) + 2 x sin (x) + 6 cos (x)

= - x^{2} cos (x) + 2 x sin (x) + 6 cos (x)

Add a constant to the solution

= - x^{2} cos (x) + 2 x sin (x) + 6 cos (x) + C

\int \frac{2 x + 11}{( x + 4 ) ^{2}} d x

\int \frac{2 x + 7}{x ^{2} + 3 x + 1} d x

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

\int \frac{32 x ^{3}}{2 x ^{4} + 5} d x

What is the integral of (x^2-4)sin(x) ?
The integral of (x^2-4)sin(x) is -x^2cos(x)+2xsin(x)+6cos(x)+C