What is the integral from 0 to 1 of 2^x+x ?

The integral from 0 to 1 of 2^x+x is 1/(ln(2))+1/2

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integral from 0 to 1 of 2^x+x

\int_{0}^{1} 2^{x} + x d x

\frac{1}{ln ( 2 )} + \frac{1}{2}

Solution steps

\int_{0}^{1} 2^{x} + 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_{0}^{1} 2^{x} d x + \int_{0}^{1} x d x

\int_{0}^{1} 2^{x} d x = \frac{1}{ln ( 2 )}

\int_{0}^{1} x d x = \frac{1}{2}

= \frac{1}{ln ( 2 )} + \frac{1}{2}

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What is the integral from 0 to 1 of 2^x+x ?
The integral from 0 to 1 of 2^x+x is 1/(ln(2))+1/2