What is the integral from 0 to 3 of 3^{3x} ?

The integral from 0 to 3 of 3^{3x} is (19682)/(3ln(3))

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integral from 0 to 3 of 3^{3x}

\int_{0}^{3} 3^{3 x} d x

\frac{19682}{3 ln ( 3 )}

Decimal

5971.77615 \dots

Solution steps

\int_{0}^{3} 3^{3 x} d x

Simplify

3^{3 x} : 2 7^{x}

= \int_{0}^{3} 2 7^{x} d x

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

= [\frac{2 7 ^{x}}{ln ( 27 )}]_{0}^{3}

\frac{2 7 ^{x}}{ln ( 27 )} = \frac{3 ^{3 x - 1}}{ln ( 3 )}

= [\frac{3 ^{3 x - 1}}{ln ( 3 )}]_{0}^{3}

Compute the boundaries:

\frac{19682}{3 ln ( 3 )}

= \frac{19682}{3 ln ( 3 )}

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What is the integral from 0 to 3 of 3^{3x} ?
The integral from 0 to 3 of 3^{3x} is (19682)/(3ln(3))