What is the integral of e^{x^2-4}+5x+6 ?

The integral of e^{x^2-4}+5x+6 is (sqrt(pi)}{2e^4}\erfi(x)+\frac{5x^2)/2+6x+C

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integral of e^{x^2-4}+5x+6

\int e^{x^{2} - 4} + 5 x + 6 d x

\frac{π}{2 e ^{4}} erfi (x) + \frac{5 x ^{2}}{2} + 6 x + C

Solution steps

\int e^{x^{2} - 4} + 5 x + 6 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 e^{x^{2} - 4} d x + \int 5 x d x + \int 6 d x

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

\int 5 x d x = \frac{5 x ^{2}}{2}

\int 6 d x = 6 x

= \frac{π}{2 e ^{4}} erfi (x) + \frac{5 x ^{2}}{2} + 6 x

Add a constant to the solution

= \frac{π}{2 e ^{4}} erfi (x) + \frac{5 x ^{2}}{2} + 6 x + C

y = \frac{x}{2 + x}

x \to - 2 - lim (- x - 2 + 4)

t \to 2 lim ([e^{- 3 t} i])

\int_{- 5}^{- 7} (- 5)^{- 3} d x

\frac{d}{d x} (\frac{2}{5} x^{5} - 3 x^{2} + 8 x - 5)

What is the integral of e^{x^2-4}+5x+6 ?
The integral of e^{x^2-4}+5x+6 is (sqrt(pi)}{2e^4}\erfi(x)+\frac{5x^2)/2+6x+C