What is the integral from 1 to 9 of (2ln(x))/x ?

The integral from 1 to 9 of (2ln(x))/x is 4ln^2(3)

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integral from 1 to 9 of (2ln(x))/x

\int_{1}^{9} \frac{2 ln ( x )}{x} d x

4 ln^{2} (3)

Decimal

4.82779 \dots

Solution steps

\int_{1}^{9} \frac{2 ln ( x )}{x} d x

Take the constant out:

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

= 2 \cdot \int_{1}^{9} \frac{ln ( x )}{x} d x

Apply u-substitution

= 2 \cdot \int_{0}^{2 l n (3)} u d u

Apply the Power Rule

= 2 [\frac{u ^{2}}{2}]_{0}^{2 l n (3)}

Compute the boundaries:

2 ln^{2} (3)

= 2 \cdot 2 ln^{2} (3)

Simplify

= 4 ln^{2} (3)

What is the integral from 1 to 9 of (2ln(x))/x ?
The integral from 1 to 9 of (2ln(x))/x is 4ln^2(3)