What is the integral from 1 to 4 of 5^{4x} ?

The integral from 1 to 4 of 5^{4x} is (625^4-625)/(4ln(5))

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integral from 1 to 4 of 5^{4x}

\int_{1}^{4} 5^{4 x} d x

\frac{62 5 ^{4} - 625}{4 ln ( 5 )}

Decimal

23702046661.934814

Solution steps

\int_{1}^{4} 5^{4 x} d x

Simplify

5^{4 x} : 62 5^{x}

= \int_{1}^{4} 62 5^{x} d x

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

= [\frac{62 5 ^{x}}{ln ( 625 )}]_{1}^{4}

Simplify

ln (625) : 4 ln (5)

= [\frac{62 5 ^{x}}{4 ln ( 5 )}]_{1}^{4}

Compute the boundaries:

\frac{62 5 ^{4} - 625}{4 ln ( 5 )}

= \frac{62 5 ^{4} - 625}{4 ln ( 5 )}

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What is the integral from 1 to 4 of 5^{4x} ?
The integral from 1 to 4 of 5^{4x} is (625^4-625)/(4ln(5))