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

The integral from 2 to 4 of 2/(sqrt(x^2-4)) is 2ln(2+sqrt(3))

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integral from 2 to 4 of 2/(sqrt(x^2-4))

\int_{2}^{4} \frac{2}{x ^{2} - 4} d x

2 ln (2 + 3)

Decimal Notation

2.63391 \dots

Solution steps

\int_{2}^{4} \frac{2}{x ^{2} - 4} d x

Take the constant out:

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

= 2 \cdot \int_{2}^{4} \frac{1}{x ^{2} - 4} d x

Apply Trigonometric Substitution

: \int_{0}^{\frac{π}{3}} sec (u) d u

= 2 \cdot \int_{0}^{\frac{π}{3}} sec (u) d u

Use the common integral:

\int sec (u) d u = ln ∣ tan (u) + sec (u) ∣

= 2 [ln ∣ tan (u) + sec (u) ∣]_{0}^{\frac{π}{3}}

Compute the boundaries:

ln (2 + 3)

= 2 ln (2 + 3)

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What is the integral from 2 to 4 of 2/(sqrt(x^2-4)) ?
The integral from 2 to 4 of 2/(sqrt(x^2-4)) is 2ln(2+sqrt(3))