What is the integral from 0 to 1 of 5^{3x} ?

The integral from 0 to 1 of 5^{3x} is (124)/(3ln(5))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 0 to 1 of 5^{3x}

\int_{0}^{1} 5^{3 x} d x

\frac{124}{3 ln ( 5 )}

Decimal Notation

25.68184 \dots

Solution steps

\int_{0}^{1} 5^{3 x} d x

Simplify

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

= \int_{0}^{1} 12 5^{x} d x

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

= [\frac{12 5 ^{x}}{ln ( 125 )}]_{0}^{1}

Simplify

ln (125) : 3 ln (5)

= [\frac{12 5 ^{x}}{3 ln ( 5 )}]_{0}^{1}

Compute the boundaries:

\frac{124}{3 ln ( 5 )}

= \frac{124}{3 ln ( 5 )}

\int_{- 4}^{4} x^{2} + x - 6 d x

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

\int_{\frac{π}{6}}^{\frac{π}{2}} cot^{2} (x) d x

\int_{0}^{π} π - x d x

\int_{0}^{8} x^{2} - 6 x + 5 d x

What is the integral from 0 to 1 of 5^{3x} ?
The integral from 0 to 1 of 5^{3x} is (124)/(3ln(5))