What is the integral from 0 to 2 of 1/(sqrt(4+x^2)) ?

The integral from 0 to 2 of 1/(sqrt(4+x^2)) is ln(1+sqrt(2))

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integral from 0 to 2 of 1/(sqrt(4+x^2))

\int_{0}^{2} \frac{1}{4 + x ^{2}} d x

ln (1 + 2)

Decimal Notation

0.88137 \dots

Solution steps

\int_{0}^{2} \frac{1}{4 + x ^{2}} d x

Apply Trigonometric Substitution

: \int_{0}^{\frac{π}{4}} sec (u) d u

= \int_{0}^{\frac{π}{4}} sec (u) d u

Use the common integral:

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

= [ln ∣ tan (u) + sec (u) ∣]_{0}^{\frac{π}{4}}

Compute the boundaries:

ln (1 + 2)

= ln (1 + 2)

f (x) = \frac{2}{x + 1}, at x = 1

x \to 1 lim (x^{2} - x)

\frac{s ^{2} - 8 s + 15}{s ^{2} + 3 s + 2}

\frac{d}{d x} (\frac{x ^{2}}{4} + y^{2} - 1)

x y^{^{'}} - 2 y = 11 x^{2}

What is the integral from 0 to 2 of 1/(sqrt(4+x^2)) ?
The integral from 0 to 2 of 1/(sqrt(4+x^2)) is ln(1+sqrt(2))