What is the integral of e^x+x^2+x^3 ?

The integral of e^x+x^2+x^3 is e^x+(x^3)/3+(x^4)/4+C

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integral of e^x+x^2+x^3

\int e^{x} + x^{2} + x^{3} d x

e^{x} + \frac{x ^{3}}{3} + \frac{x ^{4}}{4} + C

Solution steps

\int e^{x} + x^{2} + x^{3} 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} d x + \int x^{3} d x

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

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

\int x^{3} d x = \frac{x ^{4}}{4}

= e^{x} + \frac{x ^{3}}{3} + \frac{x ^{4}}{4}

Add a constant to the solution

= e^{x} + \frac{x ^{3}}{3} + \frac{x ^{4}}{4} + C

What is the integral of e^x+x^2+x^3 ?
The integral of e^x+x^2+x^3 is e^x+(x^3)/3+(x^4)/4+C