What is the integral from 0 to 9 of 1/(sqrt(81+x^2)) ?

The integral from 0 to 9 of 1/(sqrt(81+x^2)) is ln(1+sqrt(2))

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integral from 0 to 9 of 1/(sqrt(81+x^2))

\int_{0}^{9} \frac{1}{81 + x ^{2}} d x

ln (1 + 2)

Decimal

0.88137 \dots

Solution steps

\int_{0}^{9} \frac{1}{81 + 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)

\int sec^{5} (t) d t

\frac{\partial ^{2}}{\partial x ^{2}} (x^{2} - e^{y^{2}})

ln ∣ sec (θ) + tan (θ) ∣

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

\frac{s - 1}{s + 1}

What is the integral from 0 to 9 of 1/(sqrt(81+x^2)) ?
The integral from 0 to 9 of 1/(sqrt(81+x^2)) is ln(1+sqrt(2))