What is the integral from 1 to e^8 of (10ln(x))/x ?

The integral from 1 to e^8 of (10ln(x))/x is 320

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^8 of (10ln(x))/x

\int_{1}^{e^{8}} \frac{10 ln ( x )}{x} d x

320

Solution steps

\int_{1}^{e^{8}} \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^{8}} \frac{ln ( x )}{x} d x

Apply u-substitution

: \int_{0}^{8} u d u

= 10 \cdot \int_{0}^{8} u d u

Apply the Power Rule

: [\frac{u ^{2}}{2}]_{0}^{8}

= 10 [\frac{u ^{2}}{2}]_{0}^{8}

Compute the boundaries:

32

= 10 \cdot 32

Simplify

= 320

\int_{- \frac{π}{2}}^{\frac{π}{2}} cos (n x) d x

\int_{1}^{x} tan (x) d x

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

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

\int_{0}^{\frac{π}{2}} x^{2} \cdot sin (x) d x

What is the integral from 1 to e^8 of (10ln(x))/x ?
The integral from 1 to e^8 of (10ln(x))/x is 320