What is the integral from 2 to 3 of 5^{3x} ?

The integral from 2 to 3 of 5^{3x} is (1937500)/(3ln(5))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral from 2 to 3 of 5^{3x}

\int_{2}^{3} 5^{3 x} d x

\frac{1937500}{3 ln ( 5 )}

Decimal

401278.81190 \dots

Solution steps

\int_{2}^{3} 5^{3 x} d x

Simplify

5^{3 x} : 12 5^{x}

= \int_{2}^{3} 12 5^{x} d x

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

= [\frac{12 5 ^{x}}{ln ( 125 )}]_{2}^{3}

Simplify

ln (125) : 3 ln (5)

= [\frac{12 5 ^{x}}{3 ln ( 5 )}]_{2}^{3}

Compute the boundaries:

\frac{1937500}{3 ln ( 5 )}

= \frac{1937500}{3 ln ( 5 )}

What is the integral from 2 to 3 of 5^{3x} ?
The integral from 2 to 3 of 5^{3x} is (1937500)/(3ln(5))