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

The integral of ((e^x)/3+2x) is 1/3 e^x+x^2+C

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integral of ((e^x)/3+2x)

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

\frac{1}{3} e^{x} + x^{2} + C

Solution steps

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

\int \frac{e ^{x}}{3} d x = \frac{1}{3} e^{x}

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

= \frac{1}{3} e^{x} + x^{2}

Add a constant to the solution

= \frac{1}{3} e^{x} + x^{2} + C

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What is the integral of ((e^x)/3+2x) ?
The integral of ((e^x)/3+2x) is 1/3 e^x+x^2+C