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

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

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

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

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

Solution steps

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

Expand

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

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

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^{t^{2} + 1} t d t + \int e^{t^{2} + 1} d t

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

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

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

Add a constant to the solution

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

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