What is the integral of 1/(sqrt(x^2-289)) ?

The integral of 1/(sqrt(x^2-289)) is ln(1/17 |sqrt(x^2-289)+x|)+C

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integral of 1/(sqrt(x^2-289))

\int \frac{1}{x ^{2} - 289} d x

ln (\frac{1}{17} x^{2} - 289 + x) + C

Solution steps

\int \frac{1}{x ^{2} - 289} d x

Apply Trigonometric Substitution

: \int sec (u) d u

= \int sec (u) d u

Use the common integral:

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

= ln ∣ tan (u) + sec (u) ∣

Substitute back

u = arcsec (\frac{1}{17} x)

= ln tan (arcsec (\frac{1}{17} x)) + sec (arcsec (\frac{1}{17} x))

Simplify

ln tan (arcsec (\frac{1}{17} x)) + sec (arcsec (\frac{1}{17} x)) : ln (\frac{1}{17} x^{2} - 289 + x)

= ln (\frac{1}{17} x^{2} - 289 + x)

Add a constant to the solution

= ln (\frac{1}{17} x^{2} - 289 + x) + C

\int_{0}^{1} \frac{5}{x ^{2} + 1} d x

\int (\frac{3}{x} + 2 e^{x}) d x

8 x^{2} y^{^{'}} = y^{^{'}} + 9 x e^{- y}

x^{2}, 12 - x, [- 3, 4]

x \to - 0 lim (e^{\frac{1}{x}})

What is the integral of 1/(sqrt(x^2-289)) ?
The integral of 1/(sqrt(x^2-289)) is ln(1/17 |sqrt(x^2-289)+x|)+C