What is the integral of 9x^2sin(8x) ?

The integral of 9x^2sin(8x) is 9(-1/8 x^2cos(8x)+1/256 (8xsin(8x)+cos(8x)))+C

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integral of 9x^2sin(8x)

\int 9 x^{2} sin (8 x) d x

9 (- \frac{1}{8} x^{2} cos (8 x) + \frac{1}{256} (8 x sin (8 x) + cos (8 x))) + C

Solution steps

\int 9 x^{2} sin (8 x) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 9 \cdot \int x^{2} sin (8 x) d x

Apply Integration By Parts

= 9 (- \frac{1}{8} x^{2} cos (8 x) - \int - \frac{1}{4} x cos (8 x) d x)

\int - \frac{1}{4} x cos (8 x) d x = - \frac{1}{256} (8 x sin (8 x) + cos (8 x))

= 9 (- \frac{1}{8} x^{2} cos (8 x) - (- \frac{1}{256} (8 x sin (8 x) + cos (8 x))))

Simplify

= 9 (- \frac{1}{8} x^{2} cos (8 x) + \frac{1}{256} (8 x sin (8 x) + cos (8 x)))

Add a constant to the solution

= 9 (- \frac{1}{8} x^{2} cos (8 x) + \frac{1}{256} (8 x sin (8 x) + cos (8 x))) + C

What is the integral of 9x^2sin(8x) ?
The integral of 9x^2sin(8x) is 9(-1/8 x^2cos(8x)+1/256 (8xsin(8x)+cos(8x)))+C