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

The integral from 2 to 5 of 3^{5x} is (243^5-59049)/(5ln(3))

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

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

\frac{24 3 ^{5} - 59049}{5 ln ( 3 )}

Decimal

154247054968.08173

Solution steps

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

Simplify

3^{5 x} : 24 3^{x}

= \int_{2}^{5} 24 3^{x} d x

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

= [\frac{24 3 ^{x}}{ln ( 243 )}]_{2}^{5}

Simplify

ln (243) : 5 ln (3)

= [\frac{24 3 ^{x}}{5 ln ( 3 )}]_{2}^{5}

Compute the boundaries:

\frac{24 3 ^{5} - 59049}{5 ln ( 3 )}

= \frac{24 3 ^{5} - 59049}{5 ln ( 3 )}

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

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

\int_{0}^{1} - x^{2} + x d x

\int_{0}^{1} (x^{2} + y^{2}) d x

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

What is the integral from 2 to 5 of 3^{5x} ?
The integral from 2 to 5 of 3^{5x} is (243^5-59049)/(5ln(3))