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

The integral from 1 to 2 of 5^{3x} is (15500)/(3ln(5))

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

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

\frac{15500}{3 ln ( 5 )}

Decimal Notation

3210.23049 \dots

Solution steps

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

Simplify

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

= \int_{1}^{2} 12 5^{x} d x

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

= [\frac{12 5 ^{x}}{ln ( 125 )}]_{1}^{2}

Simplify

ln (125) : 3 ln (5)

= [\frac{12 5 ^{x}}{3 ln ( 5 )}]_{1}^{2}

Compute the boundaries:

\frac{15500}{3 ln ( 5 )}

= \frac{15500}{3 ln ( 5 )}

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What is the integral from 1 to 2 of 5^{3x} ?
The integral from 1 to 2 of 5^{3x} is (15500)/(3ln(5))