What is the integral of (8+x+7x^2+e^x) ?

The integral of (8+x+7x^2+e^x) is 8x+(x^2)/2+(7x^3)/3+e^x+C

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integral of (8+x+7x^2+e^x)

\int (8 + x + 7 x^{2} + e^{x}) d x

8 x + \frac{x ^{2}}{2} + \frac{7 x ^{3}}{3} + e^{x} + C

Solution steps

\int 8 + x + 7 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 8 d x + \int x d x + \int 7 x^{2} d x + \int e^{x} d x

\int 8 d x = 8 x

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

\int 7 x^{2} d x = \frac{7 x ^{3}}{3}

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

= 8 x + \frac{x ^{2}}{2} + \frac{7 x ^{3}}{3} + e^{x}

Add a constant to the solution

= 8 x + \frac{x ^{2}}{2} + \frac{7 x ^{3}}{3} + e^{x} + C

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What is the integral of (8+x+7x^2+e^x) ?
The integral of (8+x+7x^2+e^x) is 8x+(x^2)/2+(7x^3)/3+e^x+C