What is the integral of 10x^2sin(x) ?

The integral of 10x^2sin(x) is 10(-x^2cos(x)+2(xsin(x)+cos(x)))+C

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integral of 10x^2sin(x)

\int 10 x^{2} sin (x) d x

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

Solution steps

\int 10 x^{2} sin (x) d x

Take the constant out:

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

= 10 \cdot \int x^{2} sin (x) d x

Apply Integration By Parts

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

= 10 (- x^{2} cos (x) - \int - 2 x cos (x) d x)

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

= 10 (- x^{2} cos (x) - (- 2 (x sin (x) + cos (x))))

Simplify

= 10 (- x^{2} cos (x) + 2 (x sin (x) + cos (x)))

Add a constant to the solution

= 10 (- x^{2} cos (x) + 2 (x sin (x) + cos (x))) + C

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What is the integral of 10x^2sin(x) ?
The integral of 10x^2sin(x) is 10(-x^2cos(x)+2(xsin(x)+cos(x)))+C