What is the integral from e^3 to e^6 of ln(x) ?

The integral from e^3 to e^6 of ln(x) is 5e^6-2e^3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from e^3 to e^6 of ln(x)

\int_{e^{3}}^{e^{6}} ln (x) d x

5 e^{6} - 2 e^{3}

Decimal Notation

1976.97289 \dots

Solution steps

\int_{e^{3}}^{e^{6}} ln (x) d x

Apply Integration By Parts

: [x ln (x) - \int 1 d x]_{e^{3}}^{e^{6}}

= [x ln (x) - \int 1 d x]_{e^{3}}^{e^{6}}

\int 1 d x = x

= [x ln (x) - x]_{e^{3}}^{e^{6}}

Compute the boundaries:

5 e^{6} - 2 e^{3}

= 5 e^{6} - 2 e^{3}

\int_{1}^{4} x + \frac{1}{x} d x

\int_{- \infty}^{0} x e^{a x} d x

\int_{0}^{π} x^{3} cos (2 x) d x

\int_{2}^{\infty} x^{- \frac{1}{3}} d x

\int_{- 1}^{2} (- x^{4} - x^{2} + 6 x + 8) d x

What is the integral from e^3 to e^6 of ln(x) ?
The integral from e^3 to e^6 of ln(x) is 5e^6-2e^3