What is the integral from 1 to 4 of 2^{3x} ?

The integral from 1 to 4 of 2^{3x} is (4088)/(3ln(2))

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integral from 1 to 4 of 2^{3x}

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

\frac{4088}{3 ln ( 2 )}

Decimal

1965.91244 \dots

Solution steps

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

Simplify

2^{3 x} : 8^{x}

= \int_{1}^{4} 8^{x} d x

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

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

Simplify

ln (8) : 3 ln (2)

= [\frac{8 ^{x}}{3 ln ( 2 )}]_{1}^{4}

Compute the boundaries:

\frac{4088}{3 ln ( 2 )}

= \frac{4088}{3 ln ( 2 )}

\int_{- 7}^{7} \frac{t ^{3}}{11 + 8 t ^{2}} d t

\int_{- 7}^{7} 7^{2} - x^{2} d x

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

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

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

What is the integral from 1 to 4 of 2^{3x} ?
The integral from 1 to 4 of 2^{3x} is (4088)/(3ln(2))