What is the integral of 3/(xsqrt(x^2-1)) ?

The integral of 3/(xsqrt(x^2-1)) is 3arctan(sqrt(x^2-1))+C

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integral of 3/(xsqrt(x^2-1))

\int \frac{3}{x x ^{2} - 1} d x

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

Solution steps

\int \frac{3}{x x ^{2} - 1} d x

Take the constant out:

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

= 3 \cdot \int \frac{1}{x x ^{2} - 1} d x

Apply u-substitution

: \int \frac{1}{u ^{2} + 1} d u

= 3 \cdot \int \frac{1}{u ^{2} + 1} d u

Use the common integral:

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

= 3 arctan (u)

Substitute back

u = x^{2} - 1

= 3 arctan (x^{2} - 1)

Add a constant to the solution

= 3 arctan (x^{2} - 1) + C

\frac{d}{d x} f (x) = 4 x - 9 x^{2}

\int_{2}^{4} x (\frac{( 2 x - 3 )}{6}) d x

\int \frac{5 x + 14}{( x + 1 ) ( x ^{2} - 4 )} d x

x \to \frac{π}{2} lim (e^{s e c (x)})

\frac{3}{( s + 2 ) ^{2}}

What is the integral of 3/(xsqrt(x^2-1)) ?
The integral of 3/(xsqrt(x^2-1)) is 3arctan(sqrt(x^2-1))+C