What is the integral from 1 to infinity of 1/(3^x) ?

The integral from 1 to infinity of 1/(3^x) is 1/(3ln(3))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 1 to infinity of 1/(3^x)

\int_{1}^{\infty} \frac{1}{3 ^{x}} d x

\frac{1}{3 ln ( 3 )}

Decimal Notation

0.30341 \dots

Solution steps

\int_{1}^{\infty} \frac{1}{3 ^{x}} d x

Compute the indefinite integral:

\int \frac{1}{3 ^{x}} d x = - \frac{1}{ln ( 3 ) \cdot 3 ^{x}} + C

Compute the boundaries:

\int_{1}^{\infty} \frac{1}{3 ^{x}} d x = 0 - (- \frac{1}{3 ln ( 3 )})

= 0 - (- \frac{1}{3 ln ( 3 )})

Simplify

= \frac{1}{3 ln ( 3 )}

\int_{1}^{\infty} 3 x^{- 3} d x

\int_{1}^{b} \frac{1}{x} d x

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

\int_{- 7}^{7} (4 x - 3) d x

\int_{0}^{100} x^{2} d x

What is the integral from 1 to infinity of 1/(3^x) ?
The integral from 1 to infinity of 1/(3^x) is 1/(3ln(3))