What is the integral of 3x^2e^{x^{3-1}} ?

The integral of 3x^2e^{x^{3-1}} is 3(1/2 e^{x^2}x-(sqrt(pi))/4 \erfi(x))+C

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integral of 3x^2e^{x^{3-1}}

\int 3 x^{2} e^{x^{3 - 1}} d x

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

Solution steps

\int 3 x^{2} e^{x^{3 - 1}} d x

Take the constant out:

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

= 3 \cdot \int x^{2} e^{x^{3 - 1}} d x

Simplify

= 3 \cdot \int e^{x^{2}} x^{2} d x

Simplify

x^{2} : xx

= 3 \cdot \int e^{x^{2}} xx d x

Apply Integration By Parts

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

= 3 (\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)

= 3 (\frac{1}{2} e^{x^{2}} x - \frac{π}{4} erfi (x))

Add a constant to the solution

= 3 (\frac{1}{2} e^{x^{2}} x - \frac{π}{4} erfi (x)) + C

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What is the integral of 3x^2e^{x^{3-1}} ?
The integral of 3x^2e^{x^{3-1}} is 3(1/2 e^{x^2}x-(sqrt(pi))/4 \erfi(x))+C