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

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

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integral of x^2xsin(x^2)

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

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

Solution steps

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

Apply Integration By Parts

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

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

\int - x cos (x^{2}) d x = - \frac{1}{2} sin (x^{2})

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

Simplify

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

Add a constant to the solution

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

arctan (x^{2})

\frac{d}{d z} (2 z)

f (x) = sin (x^{2}) + \frac{1 - x}{1 + x}

\int_{6}^{7} x x - 6 d x

\frac{d}{d x} (3 x^{2} - 12)

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