What is the integral of (x^2+3)sin(x) ?

The integral of (x^2+3)sin(x) is -x^2cos(x)+2xsin(x)-cos(x)+C

integral of (x^2+3)sin(x)

\int (x^{2} + 3) sin (x) d x

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

Solution steps

\int (x^{2} + 3) sin (x) d x

Apply Integration By Parts

= - cos (x) (x^{2} + 3) - \int - 2 x cos (x) d x

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

= - cos (x) (x^{2} + 3) - (- 2 (x sin (x) + cos (x)))

Simplify

- cos (x) (x^{2} + 3) - (- 2 (x sin (x) + cos (x))) : - x^{2} cos (x) + 2 x sin (x) - cos (x)

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

Add a constant to the solution

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

\int \frac{cos ( x )}{sin ^{4} ( x ) - 16} d x

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

d er i v a t i v e y = x (x - 14)

\int x (2 + x x)^{5} d x

\frac{d}{d x} (- e^{- x} x^{2} + e^{- x} x)

What is the integral of (x^2+3)sin(x) ?
The integral of (x^2+3)sin(x) is -x^2cos(x)+2xsin(x)-cos(x)+C