What is the integral from 0 to 1 of (5^x-3^x) ?

The integral from 0 to 1 of (5^x-3^x) is 4/(ln(5))-2/(ln(3))

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integral from 0 to 1 of (5^x-3^x)

\int_{0}^{1} (5^{x} - 3^{x}) d x

\frac{4}{ln ( 5 )} - \frac{2}{ln ( 3 )}

Decimal

0.66486 \dots

Solution steps

\int_{0}^{1} 5^{x} - 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} 5^{x} d x - \int_{0}^{1} 3^{x} d x

\int_{0}^{1} 5^{x} d x = \frac{4}{ln ( 5 )}

\int_{0}^{1} 3^{x} d x = \frac{2}{ln ( 3 )}

= \frac{4}{ln ( 5 )} - \frac{2}{ln ( 3 )}

What is the integral from 0 to 1 of (5^x-3^x) ?
The integral from 0 to 1 of (5^x-3^x) is 4/(ln(5))-2/(ln(3))