What is the integral of 4/(xsqrt(x^2-1)) ?

The integral of 4/(xsqrt(x^2-1)) is 4arctan(sqrt(x^2-1))+C

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integral of 4/(xsqrt(x^2-1))

\int \frac{4}{x x ^{2} - 1} d x

4 arctan (x^{2} - 1) + C

Solution steps

\int \frac{4}{x x ^{2} - 1} d x

Take the constant out:

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

= 4 \cdot \int \frac{1}{x x ^{2} - 1} d x

Apply u-substitution

= 4 \cdot \int \frac{1}{u ^{2} + 1} d u

Use the common integral:

\int \frac{1}{u ^{2} + 1} d u = arctan (u)

= 4 arctan (u)

Substitute back

u = x^{2} - 1

= 4 arctan (x^{2} - 1)

Add a constant to the solution

= 4 arctan (x^{2} - 1) + C

\int 4 y^{2} d y

\frac{d}{d x} (\frac{x ^{2}}{x ^{2} - 36})

\int \frac{1}{x ^{2} - 5} d x

\int - 12 x d x

\int 2 t^{3} (t^{4} - 3)^{5} d t

What is the integral of 4/(xsqrt(x^2-1)) ?
The integral of 4/(xsqrt(x^2-1)) is 4arctan(sqrt(x^2-1))+C