What is the integral from 0 to 1 of x^{14}+14^x ?

The integral from 0 to 1 of x^{14}+14^x is 1/15+(13)/(ln(14))

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integral from 0 to 1 of x^{14}+14^x

\int_{0}^{1} x^{14} + 1 4^{x} d x

\frac{1}{15} + \frac{13}{ln ( 14 )}

Decimal

4.99266 \dots

Solution steps

\int_{0}^{1} x^{14} + 1 4^{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^{14} d x + \int_{0}^{1} 1 4^{x} d x

\int_{0}^{1} x^{14} d x = \frac{1}{15}

\int_{0}^{1} 1 4^{x} d x = \frac{13}{ln ( 14 )}

= \frac{1}{15} + \frac{13}{ln ( 14 )}

What is the integral from 0 to 1 of x^{14}+14^x ?
The integral from 0 to 1 of x^{14}+14^x is 1/15+(13)/(ln(14))