What is the integral from 1 to e^2 of (10ln(x))/x ?

The integral from 1 to e^2 of (10ln(x))/x is 20

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integral from 1 to e^2 of (10ln(x))/x

\int_{1}^{e^{2}} \frac{10 ln ( x )}{x} d x

20

Solution steps

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

Apply u-substitution

: \int_{0}^{2} u d u

= 10 \cdot \int_{0}^{2} u d u

Apply the Power Rule

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

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

Compute the boundaries:

2

= 10 \cdot 2

Simplify

= 20

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What is the integral from 1 to e^2 of (10ln(x))/x ?
The integral from 1 to e^2 of (10ln(x))/x is 20