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

The integral from 1 to 3 of 4^{3x} is (43680)/(ln(2))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

\frac{43680}{ln ( 2 )}

Decimal

63016.91938 \dots

Solution steps

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

Simplify

4^{3 x} : 6 4^{x}

= \int_{1}^{3} 6 4^{x} d x

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

= [\frac{6 4 ^{x}}{ln ( 64 )}]_{1}^{3}

\frac{6 4 ^{x}}{ln ( 64 )} = \frac{2 ^{6 x - 1}}{3 ln ( 2 )}

= [\frac{2 ^{6 x - 1}}{3 ln ( 2 )}]_{1}^{3}

Compute the boundaries:

\frac{43680}{ln ( 2 )}

= \frac{43680}{ln ( 2 )}

\int_{3}^{5} sin (I n x) d x

\int_{0}^{4} x + 1 d x

\int_{0}^{2} (6 x - 3) (4 x^{2} + 7) d x

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

\int_{- 1}^{1} 2 y^{2} - 2 d y

What is the integral from 1 to 3 of 4^{3x} ?
The integral from 1 to 3 of 4^{3x} is (43680)/(ln(2))