What is the integral from 0 to e^9 of ln(8x) ?

The integral from 0 to e^9 of ln(8x) is 3e^9ln(2)+8e^9

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 0 to e^9 of ln(8x)

\int_{0}^{e^{9}} ln (8 x) d x

3 e^{9} ln (2) + 8 e^{9}

Decimal

81674.56075 \dots

Solution steps

\int_{0}^{e^{9}} ln (8 x) d x

Apply Integration By Parts

: [x ln (8 x) - \int 1 d x]_{0}^{e^{9}}

= [x ln (8 x) - \int 1 d x]_{0}^{e^{9}}

\int 1 d x = x

= [x ln (8 x) - x]_{0}^{e^{9}}

Compute the boundaries:

3 e^{9} ln (2) + 8 e^{9}

= 3 e^{9} ln (2) + 8 e^{9}

\int_{0}^{\frac{1}{3}} \frac{1}{144 x ^{2} + 16} d x

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

\int_{1}^{5} x^{- 4} d x

\int_{0}^{0.28} ln (1 + x^{2}) d x

\int_{4}^{2} x^{2} d x

What is the integral from 0 to e^9 of ln(8x) ?
The integral from 0 to e^9 of ln(8x) is 3e^9ln(2)+8e^9