What is the integral of (2x^2+1)sin(x) ?

The integral of (2x^2+1)sin(x) is -2x^2cos(x)+4xsin(x)+3cos(x)+C

Popular >

integral of (2x^2+1)sin(x)

\int (2 x^{2} + 1) sin (x) d x

- 2 x^{2} cos (x) + 4 x sin (x) + 3 cos (x) + C

Solution steps

\int (2 x^{2} + 1) sin (x) d x

Apply Integration By Parts

: - cos (x) (2 x^{2} + 1) - \int - 4 x cos (x) d x

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

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

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

Simplify

- cos (x) (2 x^{2} + 1) - (- 4 (x sin (x) + cos (x))) : - 2 x^{2} cos (x) + 4 x sin (x) + 3 cos (x)

= - 2 x^{2} cos (x) + 4 x sin (x) + 3 cos (x)

Add a constant to the solution

= - 2 x^{2} cos (x) + 4 x sin (x) + 3 cos (x) + C

\int (5 t^{3} + 2 t^{2} + t) d t

\int csc^{3} (θ) d θ

\int sin (0.01 x) + x^{3} d x

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

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

What is the integral of (2x^2+1)sin(x) ?
The integral of (2x^2+1)sin(x) is -2x^2cos(x)+4xsin(x)+3cos(x)+C