What is the integral of e^x-(x^2-1) ?

The integral of e^x-(x^2-1) is e^x-(x^3)/3+x+C

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integral of e^x-(x^2-1)

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

e^{x} - \frac{x ^{3}}{3} + x + C

Solution steps

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

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

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

= e^{x} - (\frac{x ^{3}}{3} - x)

Simplify

= e^{x} - \frac{x ^{3}}{3} + x

Add a constant to the solution

= e^{x} - \frac{x ^{3}}{3} + x + C

What is the integral of e^x-(x^2-1) ?
The integral of e^x-(x^2-1) is e^x-(x^3)/3+x+C