What is the integral from 1 to 4 of 3^{3x} ?

The integral from 1 to 4 of 3^{3x} is (177138)/(ln(3))

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integral from 1 to 4 of 3^{3x}

\int_{1}^{4} 3^{3 x} d x

\frac{177138}{ln ( 3 )}

Decimal

161237.95612 \dots

Solution steps

\int_{1}^{4} 3^{3 x} d x

Simplify

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

= \int_{1}^{4} 2 7^{x} d x

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

= [\frac{2 7 ^{x}}{ln ( 27 )}]_{1}^{4}

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

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

Compute the boundaries:

\frac{177138}{ln ( 3 )}

= \frac{177138}{ln ( 3 )}

\int_{0}^{1} (1 - x^{3})^{2} x^{2} d x

\int_{4}^{x} x^{2} + 9 d x

\int_{\frac{π}{4}}^{\frac{π}{2}} csc^{2} (θ) d θ

\int_{0}^{\frac{π}{2}} (x sin (x)) d x

\int_{0}^{\frac{1}{4}} \frac{3}{1 + 16 x ^{2}} d x

What is the integral from 1 to 4 of 3^{3x} ?
The integral from 1 to 4 of 3^{3x} is (177138)/(ln(3))