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 )}

y = 2 x^{3}, (1, 2)

f (x) = 6 x + 3

\int \frac{ln ( 11 x )}{x ^{9}} d x

\int \frac{( 7 x ^{2} + 5 x - 6 )}{( x ^{2} - 4 ) ( x + 2 )} d x

4 cos (- x)

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))