What is the integral from 2 to 4 of 3^{3x} ?

The integral from 2 to 4 of 3^{3x} is (176904)/(ln(3))

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integral from 2 to 4 of 3^{3x}

\int_{2}^{4} 3^{3 x} d x

\frac{176904}{ln ( 3 )}

Decimal

161024.96014 \dots

Solution steps

\int_{2}^{4} 3^{3 x} d x

Simplify

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

= \int_{2}^{4} 2 7^{x} d x

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

= [\frac{2 7 ^{x}}{ln ( 27 )}]_{2}^{4}

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

= [\frac{3 ^{3 x - 1}}{ln ( 3 )}]_{2}^{4}

Compute the boundaries:

\frac{176904}{ln ( 3 )}

= \frac{176904}{ln ( 3 )}

\int_{- 1}^{1} \frac{x ^{2} - 1}{x ^{2} - 4} d x

\int_{0}^{1} \frac{x ^{2}}{4} d x

\int_{1}^{5} \frac{2}{x ^{2}} + x d x

\int_{1}^{3} \frac{x}{( x ^{2} + 9 ) ^{3}} d x

\int_{0}^{3} x^{2} + 3 d x

What is the integral from 2 to 4 of 3^{3x} ?
The integral from 2 to 4 of 3^{3x} is (176904)/(ln(3))