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

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

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integral of x^2sin(8x)

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

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

Solution steps

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

Apply Integration By Parts

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

= - \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))

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

Simplify

= - \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

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

arcsin (3 x) + arccos (3 x)

\frac{d}{d x} (- \frac{2 x ( - x ^{2} + 27 )}{( x ^{2} + 9 ) ^{3}})

x \to 0 + lim (x^{10 x})

\frac{\partial}{\partial x} (x^{5} + y^{5} - 5 x^{3} y^{3})

x \to 1 lim (\frac{x ^{2} - 1}{x + 2})

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