What is the integral from 0 to 1 of 2^x*3^x ?

The integral from 0 to 1 of 2^x*3^x is 5/(ln(6))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral from 0 to 1 of 2^x*3^x

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

\frac{5}{ln ( 6 )}

Decimal

2.79055 \dots

Solution steps

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

Simplify

2^{x} \cdot 3^{x} : 6^{x}

= \int_{0}^{1} 6^{x} d x

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

= [\frac{6 ^{x}}{ln ( 6 )}]_{0}^{1}

Compute the boundaries:

\frac{5}{ln ( 6 )}

= \frac{5}{ln ( 6 )}

What is the integral from 0 to 1 of 2^x*3^x ?
The integral from 0 to 1 of 2^x*3^x is 5/(ln(6))