What is the integral of x^2xe^{x^2} ?

The integral of x^2xe^{x^2} is 1/2 e^{x^2}x^2-1/2 e^{x^2}+C

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integral of x^2xe^{x^2}

\int x^{2} x e^{x^{2}} d x

\frac{1}{2} e^{x^{2}} x^{2} - \frac{1}{2} e^{x^{2}} + C

Solution steps

\int x^{2} x e^{x^{2}} d x

Apply Integration By Parts

: \frac{1}{2} e^{x^{2}} x^{2} - \int e^{x^{2}} x d x

= \frac{1}{2} e^{x^{2}} x^{2} - \int e^{x^{2}} x d x

\int e^{x^{2}} x d x = \frac{1}{2} e^{x^{2}}

= \frac{1}{2} e^{x^{2}} x^{2} - \frac{1}{2} e^{x^{2}}

Add a constant to the solution

= \frac{1}{2} e^{x^{2}} x^{2} - \frac{1}{2} e^{x^{2}} + C

y^{3} - (14 x + 2) + 3 x y^{2} y^{^{'}} = 0

\frac{d}{d x} (7 sin (2 x) + 3 tan (x - 1))

\int \frac{1}{( x ^{2} - 2 x + 5 ) ^{\frac{3}{2}}} d x

y^{^{'''}} - 5 y^{^{''}} - 22 y^{^{'}} + 56 y = 0

What is the integral of x^2xe^{x^2} ?
The integral of x^2xe^{x^2} is 1/2 e^{x^2}x^2-1/2 e^{x^2}+C