What is the integral of 1/(sqrt(x^2-144)) ?

The integral of 1/(sqrt(x^2-144)) is ln(1/12 |sqrt(x^2-144)+x|)+C

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integral of 1/(sqrt(x^2-144))

\int \frac{1}{x ^{2} - 144} d x

ln (\frac{1}{12} x^{2} - 144 + x) + C

Solution steps

\int \frac{1}{x ^{2} - 144} 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}{12} x)

= ln tan (arcsec (\frac{1}{12} x)) + sec (arcsec (\frac{1}{12} x))

Simplify

ln tan (arcsec (\frac{1}{12} x)) + sec (arcsec (\frac{1}{12} x)) : ln (\frac{1}{12} x^{2} - 144 + x)

= ln (\frac{1}{12} x^{2} - 144 + x)

Add a constant to the solution

= ln (\frac{1}{12} x^{2} - 144 + x) + C

\frac{\partial}{\partial x} (2 y^{3} - 6 y + x^{2})

\int_{0}^{\frac{π}{2}} x sin (x) d x

x \to 1 lim (+ f (x))

\int_{0}^{1} 4 - y - 2 y - 1 d y

\int (3 x^{2} + 2) (2 x^{3} + 4 x + 1)^{\frac{1}{2}} d x

What is the integral of 1/(sqrt(x^2-144)) ?
The integral of 1/(sqrt(x^2-144)) is ln(1/12 |sqrt(x^2-144)+x|)+C