What is the integral of (2x)/(x^2-36) ?

The integral of (2x)/(x^2-36) is ln|x^2-36|+C

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integral of (2x)/(x^2-36)

\int \frac{2 x}{x ^{2} - 36} d x

ln x^{2} - 36 + C

Solution steps

\int \frac{2 x}{x ^{2} - 36} d x

Take the constant out:

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

= 2 \cdot \int \frac{x}{x ^{2} - 36} d x

Apply u-substitution

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

= 2 \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

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 2 \cdot \frac{1}{2} ln ∣ u ∣

Substitute back

u = x^{2} - 36

= 2 \cdot \frac{1}{2} ln x^{2} - 36

Simplify

2 \cdot \frac{1}{2} ln x^{2} - 36 : ln x^{2} - 36

= ln x^{2} - 36

Add a constant to the solution

= ln x^{2} - 36 + C

\int \frac{4}{3} d x

\frac{\partial}{\partial x} (y \cdot sin (x + y))

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

g (x) = 4 - x

\frac{A}{y ^{13}} + B e^{y}

What is the integral of (2x)/(x^2-36) ?
The integral of (2x)/(x^2-36) is ln|x^2-36|+C