What is the integral from 0 to log_{9 of (4)}9^x ?

The integral from 0 to log_{9 of (4)}9^x is 3/(2ln(3))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 0 to log_{9 of (4)}9^x

\int_{0}^{l o g_{9} (4)} 9^{x} d x

\frac{3}{2 ln ( 3 )}

Decimal Notation

1.36535 \dots

Solution steps

\int_{0}^{l o g_{9} (4)} 9^{x} d x

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

= [\frac{9 ^{x}}{ln ( 9 )}]_{0}^{l o g_{9} (4)}

Simplify

[\frac{9 ^{x}}{ln ( 9 )}]_{0}^{l o g_{9} (4)} : [\frac{9 ^{x}}{2 ln ( 3 )}]_{0}^{2 l o g_{9} (2)}

= [\frac{9 ^{x}}{2 ln ( 3 )}]_{0}^{2 l o g_{9} (2)}

Compute the boundaries:

\frac{3}{2 ln ( 3 )}

= \frac{3}{2 ln ( 3 )}

\int_{0}^{\frac{π}{3}} 2 sin (x) d x

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

\int_{0}^{4} - 6 x^{2} + 24 x d x

\int_{1}^{4} \frac{2 ln ( x )}{x} d x

\int_{0}^{2} \frac{y ^{3}}{y ^{4} + 1} d y

What is the integral from 0 to log_{9 of (4)}9^x ?
The integral from 0 to log_{9 of (4)}9^x is 3/(2ln(3))