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

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

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

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

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

Solution steps

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

Expand

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

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

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

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

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

Add a constant to the solution

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

\frac{1}{( x - 2 )}

\frac{d ^{2} y}{d t ^{2}} + 3 \frac{d y}{d t} - 40 y = 1 - 4 t

\int_{2}^{\infty} x e^{- 8 x} d x

e^{x}, x e^{x}, 0, 1

y = \frac{x ^{4}}{4} + \frac{1}{8 x ^{2}}

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