What is the integral of x^22sin(x) ?

The integral of x^22sin(x) is 2(-x^2cos(x)+2(xsin(x)+cos(x)))+C

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integral of x^22sin(x)

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

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

Solution steps

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

Take the constant out:

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

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

Apply Integration By Parts

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

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

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

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

Simplify

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

Add a constant to the solution

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

\frac{x ^{2}}{x + 6}

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

x \to 6 lim (x π + x - 3)

\int 3 x^{2} (x^{3} + 4)^{10} d x

\frac{d}{d x} (\frac{5 x}{1 - x})

What is the integral of x^22sin(x) ?
The integral of x^22sin(x) is 2(-x^2cos(x)+2(xsin(x)+cos(x)))+C