What is the integral of (15)/(|x|sqrt(x^2-1)) ?

The integral of (15)/(|x|sqrt(x^2-1)) is 15arcsec(x)+C

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integral of (15)/(|x|sqrt(x^2-1))

\int \frac{15}{∣ x ∣ x ^{2} - 1} d x

15 arcsec (x) + C

Solution steps

\int \frac{15}{∣ x ∣ x ^{2} - 1} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 15 \cdot \int \frac{1}{∣ x ∣ x ^{2} - 1} d x

Use the common integral:

\int \frac{1}{∣ x ∣ x ^{2} - 1} d x = arcsec (x)

= 15 arcsec (x)

Add a constant to the solution

= 15 arcsec (x) + C

What is the integral of (15)/(|x|sqrt(x^2-1)) ?
The integral of (15)/(|x|sqrt(x^2-1)) is 15arcsec(x)+C