What is the integral from 0 to 1 of (x^{13}+13^x) ?

The integral from 0 to 1 of (x^{13}+13^x) is 1/14+(12)/(ln(13))

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integral from 0 to 1 of (x^{13}+13^x)

\int_{0}^{1} (x^{13} + 1 3^{x}) d x

\frac{1}{14} + \frac{12}{ln ( 13 )}

Decimal

4.74988 \dots

Solution steps

\int_{0}^{1} x^{13} + 1 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_{0}^{1} x^{13} d x + \int_{0}^{1} 1 3^{x} d x

\int_{0}^{1} x^{13} d x = \frac{1}{14}

\int_{0}^{1} 1 3^{x} d x = \frac{12}{ln ( 13 )}

= \frac{1}{14} + \frac{12}{ln ( 13 )}

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\int_{0}^{5} - x^{2} + 5 x d x

What is the integral from 0 to 1 of (x^{13}+13^x) ?
The integral from 0 to 1 of (x^{13}+13^x) is 1/14+(12)/(ln(13))