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

The integral of x^2e^{x^2} is 1/2 e^{x^2}x-(sqrt(pi))/4 \erfi(x)+C

Popular >

integral of x^2e^{x^2}

integral

x^{2} e^{x^{2}}

\frac{1}{2} e^{x^{2}} x - \frac{π}{4} erfi (x) + C

Solution steps

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

Simplify

x^{2} : xx

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

Apply Integration By Parts

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

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

\int \frac{1}{2} e^{x^{2}} d x = \frac{π}{4} erfi (x)

= \frac{1}{2} e^{x^{2}} x - \frac{π}{4} erfi (x)

Add a constant to the solution

= \frac{1}{2} e^{x^{2}} x - \frac{π}{4} erfi (x) + C

2 x sin (x^{2} + 1)

\frac{( x + 3 )}{( x ^{2} - x + 6 )}

h (x) = \frac{4 x ^{3} + 2 x + 5}{x}

\frac{t ^{2}}{2} + \frac{t ^{3}}{3} + \frac{t ^{4}}{4}

(\frac{sin ( x )}{x})^{2}

What is the integral of x^2e^{x^2} ?
The integral of x^2e^{x^2} is 1/2 e^{x^2}x-(sqrt(pi))/4 \erfi(x)+C