What is the integral from 0 to 2 of 5^{2x-1}-2^{3x} ?

The integral from 0 to 2 of 5^{2x-1}-2^{3x} is (312)/(5ln(5))-(21)/(ln(2))

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integral from 0 to 2 of 5^{2x-1}-2^{3x}

\int_{0}^{2} 5^{2 x - 1} - 2^{3 x} d x

\frac{312}{5 ln ( 5 )} - \frac{21}{ln ( 2 )}

Decimal

8.47470 \dots

Solution steps

\int_{0}^{2} 5^{2 x - 1} - 2^{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}^{2} 5^{2 x - 1} d x - \int_{0}^{2} 2^{3 x} d x

\int_{0}^{2} 5^{2 x - 1} d x = \frac{312}{5 ln ( 5 )}

\int_{0}^{2} 2^{3 x} d x = \frac{21}{ln ( 2 )}

= \frac{312}{5 ln ( 5 )} - \frac{21}{ln ( 2 )}

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What is the integral from 0 to 2 of 5^{2x-1}-2^{3x} ?
The integral from 0 to 2 of 5^{2x-1}-2^{3x} is (312)/(5ln(5))-(21)/(ln(2))