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

The integral of (2^x+x^2) is (2^x}{ln(2)}+\frac{x^3)/3+C

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integral of (2^x+x^2)

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

\frac{2 ^{x}}{ln ( 2 )} + \frac{x ^{3}}{3} + C

Solution steps

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

\int 2^{x} d x = \frac{2 ^{x}}{ln ( 2 )}

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

= \frac{2 ^{x}}{ln ( 2 )} + \frac{x ^{3}}{3}

Add a constant to the solution

= \frac{2 ^{x}}{ln ( 2 )} + \frac{x ^{3}}{3} + C

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What is the integral of (2^x+x^2) ?
The integral of (2^x+x^2) is (2^x}{ln(2)}+\frac{x^3)/3+C