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

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

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integral of (2+x+2x^2+e^x)

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

2 x + \frac{x ^{2}}{2} + \frac{2 x ^{3}}{3} + e^{x} + C

Solution steps

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

\int 2 d x = 2 x

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

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

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

= 2 x + \frac{x ^{2}}{2} + \frac{2 x ^{3}}{3} + e^{x}

Add a constant to the solution

= 2 x + \frac{x ^{2}}{2} + \frac{2 x ^{3}}{3} + e^{x} + C

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