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

The integral of (3x)/(x^2-1) is 3/2 ln|x^2-1|+C

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

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

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

Apply u-substitution

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

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

Take the constant out:

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

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 3 \cdot \frac{1}{2} ln ∣ u ∣

Substitute back

u = x^{2} - 1

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

Simplify

3 \cdot \frac{1}{2} ln x^{2} - 1 : \frac{3}{2} ln x^{2} - 1

= \frac{3}{2} ln x^{2} - 1

Add a constant to the solution

= \frac{3}{2} ln x^{2} - 1 + C

\int 2 x x + 2 d x

y^{^{''}} - 22 y^{^{'}} + 121 y = 0

n \to \infty lim (i = 1 \sum n \frac{1}{2 n + i})

\frac{\partial}{\partial x} (5 x^{2} y^{3} + 2 x^{2} + 7 y)

f (x) = e^{- x}, 5

What is the integral of (3x)/(x^2-1) ?
The integral of (3x)/(x^2-1) is 3/2 ln|x^2-1|+C