What is the integral from 2 to 5 of 5^{5x} ?

The integral from 2 to 5 of 5^{5x} is (5^{24}-1953125)/(ln(5))

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integral from 2 to 5 of 5^{5x}

\int_{2}^{5} 5^{5 x} d x

\frac{5 ^{24} - 1953125}{ln ( 5 )}

Solution steps

\int_{2}^{5} 5^{5 x} d x

Simplify

5^{5 x} : 312 5^{x}

= \int_{2}^{5} 312 5^{x} d x

\int a^{x} d x = \frac{a ^{x}}{ln a}

= [\frac{312 5 ^{x}}{ln ( 3125 )}]_{2}^{5}

\frac{312 5 ^{x}}{ln ( 3125 )} = \frac{5 ^{5 x - 1}}{ln ( 5 )}

= [\frac{5 ^{5 x - 1}}{ln ( 5 )}]_{2}^{5}

Compute the boundaries:

\frac{5 ^{24} - 1953125}{ln ( 5 )}

= \frac{5 ^{24} - 1953125}{ln ( 5 )}

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

\int_{- 1}^{1} \frac{1}{x ^{2} + 2 x + 5} d x

\int_{0}^{\frac{1}{2}} \frac{1}{36 x ^{2} + 9} d x

\int_{2}^{\infty} \frac{3}{4 + x ^{2}} d x

What is the integral from 2 to 5 of 5^{5x} ?
The integral from 2 to 5 of 5^{5x} is (5^{24}-1953125)/(ln(5))