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

The integral from 1 to 3 of (5^{2x}-2^{5x}) is (7800)/(ln(5))-(32736)/(5ln(2))

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

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

\frac{7800}{ln ( 5 )} - \frac{32736}{5 ln ( 2 )}

Decimal Notation

- 4599.20048 \dots

Solution steps

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

Simplify

5^{2 x} - 2^{5 x} : 2 5^{x} - 3 2^{x}

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

\int_{1}^{3} 2 5^{x} d x = \frac{7800}{ln ( 5 )}

\int_{1}^{3} 3 2^{x} d x = \frac{32736}{5 ln ( 2 )}

= \frac{7800}{ln ( 5 )} - \frac{32736}{5 ln ( 2 )}

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What is the integral from 1 to 3 of (5^{2x}-2^{5x}) ?
The integral from 1 to 3 of (5^{2x}-2^{5x}) is (7800)/(ln(5))-(32736)/(5ln(2))