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

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

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integral from 2 to 4 of 4/(x(ln(x))^2)

\int_{2}^{4} \frac{4}{x ( ln ( x ) ) ^{2}} d x

\frac{2}{ln ( 2 )}

Decimal

2.88539 \dots

Solution steps

\int_{2}^{4} \frac{4}{x ( ln ( x ) ) ^{2}} d x

Take the constant out:

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

= 4 \cdot \int_{2}^{4} \frac{1}{x ( ln ( x ) ) ^{2}} d x

Apply u-substitution

: \int_{l n (2)}^{2 l n (2)} \frac{1}{u ^{2}} d u

= 4 \cdot \int_{l n (2)}^{2 l n (2)} \frac{1}{u ^{2}} d u

Apply the Power Rule

: [- \frac{1}{u}]_{l n (2)}^{2 l n (2)}

= 4 [- \frac{1}{u}]_{l n (2)}^{2 l n (2)}

Compute the boundaries:

\frac{1}{2 ln ( 2 )}

= 4 \cdot \frac{1}{2 ln ( 2 )}

Simplify

= \frac{2}{ln ( 2 )}

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