What is the integral of (2x^2+1)e^{x^2} ?

The integral of (2x^2+1)e^{x^2} is e^{x^2}x+C

Popular >

integral of (2x^2+1)e^{x^2}

\int (2 x^{2} + 1) e^{x^{2}} d x

e^{x^{2}} x + C

Solution steps

\int (2 x^{2} + 1) e^{x^{2}} d x

Expand

(2 x^{2} + 1) e^{x^{2}} : 2 e^{x^{2}} x^{2} + e^{x^{2}}

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

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

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

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

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

Add similar elements:

- \frac{π}{2} erfi (x) + \frac{π}{2} erfi (x) = 0

= e^{x^{2}} x

Add a constant to the solution

= e^{x^{2}} x + C

\int e^{6 t} cos (2 t) d t

\int_{0}^{2 π} 3 sin (2 t) d t

\frac{d}{d x} (ln (\frac{8 x}{x + 5}))

x \to 5 lim (\frac{1}{( x - 5 ) ^{3}})

\frac{\partial}{\partial x} (\frac{e ^{x}}{y + x ^{8}})

What is the integral of (2x^2+1)e^{x^2} ?
The integral of (2x^2+1)e^{x^2} is e^{x^2}x+C