What is the integral from 2 to 5 of 2^{4x} ?

The integral from 2 to 5 of 2^{4x} is (262080)/(ln(2))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 2 to 5 of 2^{4x}

\int_{2}^{5} 2^{4 x} d x

\frac{262080}{ln ( 2 )}

Decimal

378101.51631 \dots

Solution steps

\int_{2}^{5} 2^{4 x} d x

Simplify

2^{4 x} : 1 6^{x}

= \int_{2}^{5} 1 6^{x} d x

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

= [\frac{1 6 ^{x}}{ln ( 16 )}]_{2}^{5}

\frac{1 6 ^{x}}{ln ( 16 )} = \frac{2 ^{4 x - 2}}{ln ( 2 )}

= [\frac{2 ^{4 x - 2}}{ln ( 2 )}]_{2}^{5}

Compute the boundaries:

\frac{262080}{ln ( 2 )}

= \frac{262080}{ln ( 2 )}

\int_{- 1}^{8} \frac{1}{x ^{3}} d x

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

\int_{0}^{2} (2 x - 9) (8 x^{2} + 6) d x

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

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

What is the integral from 2 to 5 of 2^{4x} ?
The integral from 2 to 5 of 2^{4x} is (262080)/(ln(2))