What is the integral from 0 to 1 of x^9+9^x ?

The integral from 0 to 1 of x^9+9^x is 1/10+4/(ln(3))

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integral from 0 to 1 of x^9+9^x

\int_{0}^{1} x^{9} + 9^{x} d x

\frac{1}{10} + \frac{4}{ln ( 3 )}

Decimal

3.74095 \dots

Solution steps

\int_{0}^{1} x^{9} + 9^{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^{9} d x + \int_{0}^{1} 9^{x} d x

\int_{0}^{1} x^{9} d x = \frac{1}{10}

\int_{0}^{1} 9^{x} d x = \frac{4}{ln ( 3 )}

= \frac{1}{10} + \frac{4}{ln ( 3 )}

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What is the integral from 0 to 1 of x^9+9^x ?
The integral from 0 to 1 of x^9+9^x is 1/10+4/(ln(3))