What is the integral from 1 to e^6 of (10ln(x))/x ?

The integral from 1 to e^6 of (10ln(x))/x is 180

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 1 to e^6 of (10ln(x))/x

\int_{1}^{e^{6}} \frac{10 ln ( x )}{x} d x

180

Solution steps

\int_{1}^{e^{6}} \frac{10 ln ( x )}{x} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 10 \cdot \int_{1}^{e^{6}} \frac{ln ( x )}{x} d x

Apply u-substitution

: \int_{0}^{6} u d u

= 10 \cdot \int_{0}^{6} u d u

Apply the Power Rule

: [\frac{u ^{2}}{2}]_{0}^{6}

= 10 [\frac{u ^{2}}{2}]_{0}^{6}

Compute the boundaries:

18

= 10 \cdot 18

Simplify

= 180

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

\int_{1}^{3} (3 x^{2} - 8 x + 1) d x

\int_{0}^{2 π} 16 cos^{2} (t) d t

What is the integral from 1 to e^6 of (10ln(x))/x ?
The integral from 1 to e^6 of (10ln(x))/x is 180