What is the integral of 2x^2cos(x) ?

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

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integral of 2x^2cos(x)

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

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

Add a constant to the solution

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

\frac{d}{d x} (4 arctan (2 x))

\frac{d y}{d x} = \frac{x - 2}{y + 1}

\int \frac{x}{5 ^{x^{2}}} d x

\int_{0}^{1} arctan (1) d x

\frac{d}{d x} (e^{s i n (x)} - 1)

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