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

The integral from 1 to 3 of 3^{4x} is (132840)/(ln(3))

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

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

\frac{132840}{ln ( 3 )}

Decimal

120916.17886 \dots

Solution steps

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

Simplify

3^{4 x} : 8 1^{x}

= \int_{1}^{3} 8 1^{x} d x

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

= [\frac{8 1 ^{x}}{ln ( 81 )}]_{1}^{3}

Simplify

ln (81) : 4 ln (3)

= [\frac{8 1 ^{x}}{4 ln ( 3 )}]_{1}^{3}

Compute the boundaries:

\frac{132840}{ln ( 3 )}

= \frac{132840}{ln ( 3 )}

\int_{1}^{4} \frac{ln ( x )}{x} d x

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

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

\int_{0}^{\frac{π}{6}} sin^{3} (x) d x

\int_{- 2}^{1} x^{4} + x^{3} - 2 x^{2} + 4 d x

What is the integral from 1 to 3 of 3^{4x} ?
The integral from 1 to 3 of 3^{4x} is (132840)/(ln(3))