What is the integral of 1/(sqrt(x^2-324)) ?

The integral of 1/(sqrt(x^2-324)) is ln(1/18 |sqrt(x^2-324)+x|)+C

Popular >

integral of 1/(sqrt(x^2-324))

\int \frac{1}{x ^{2} - 324} d x

ln (\frac{1}{18} x^{2} - 324 + x) + C

Solution steps

\int \frac{1}{x ^{2} - 324} 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}{18} x)

= ln tan (arcsec (\frac{1}{18} x)) + sec (arcsec (\frac{1}{18} x))

Simplify

ln tan (arcsec (\frac{1}{18} x)) + sec (arcsec (\frac{1}{18} x)) : ln (\frac{1}{18} x^{2} - 324 + x)

= ln (\frac{1}{18} x^{2} - 324 + x)

Add a constant to the solution

= ln (\frac{1}{18} x^{2} - 324 + x) + C

\frac{d}{d x} ((x^{2} - 6) e^{8 x})

\int 0 x d x

y = x^{2} (5 x - 1)^{3}

f (x) = (3 x + 1) (5 x + 4)

x \to 0 lim (cos (x^{2} + x))

What is the integral of 1/(sqrt(x^2-324)) ?
The integral of 1/(sqrt(x^2-324)) is ln(1/18 |sqrt(x^2-324)+x|)+C