What is the integral of (x^2+3^x) ?

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

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integral of (x^2+3^x)

\int (x^{2} + 3^{x}) d x

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

Solution steps

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

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

\int 3^{x} d x = \frac{3 ^{x}}{ln ( 3 )}

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

Add a constant to the solution

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

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