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

The integral from 1 to 3 of 5^{3x} is (651000)/(ln(5))

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integral from 1 to 3 of 5^{3x}

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

\frac{651000}{ln ( 5 )}

Decimal Notation

404489.04239 \dots

Solution steps

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

Simplify

5^{3 x} : 12 5^{x}

= \int_{1}^{3} 12 5^{x} d x

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

= [\frac{12 5 ^{x}}{ln ( 125 )}]_{1}^{3}

Simplify

ln (125) : 3 ln (5)

= [\frac{12 5 ^{x}}{3 ln ( 5 )}]_{1}^{3}

Compute the boundaries:

\frac{651000}{ln ( 5 )}

= \frac{651000}{ln ( 5 )}

\int_{0}^{\frac{π}{4}} 3 sec^{2} (t) d t

\int_{0}^{3} 3 8 x + 1 d x

\int_{4}^{6} x^{2} d x

\int_{0}^{4} x ln (5 - x) d x

\int_{0}^{5} x e^{5 x} d x

What is the integral from 1 to 3 of 5^{3x} ?
The integral from 1 to 3 of 5^{3x} is (651000)/(ln(5))