What is the integral of (2x)/(x^2-16) ?

The integral of (2x)/(x^2-16) is ln|x^2-16|+C

Popular >

integral of (2x)/(x^2-16)

\int \frac{2 x}{x ^{2} - 16} d x

ln x^{2} - 16 + C

Solution steps

\int \frac{2 x}{x ^{2} - 16} 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} - 16} 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} - 16

= 2 \cdot \frac{1}{2} ln x^{2} - 16

Simplify

2 \cdot \frac{1}{2} ln x^{2} - 16 : ln x^{2} - 16

= ln x^{2} - 16

Add a constant to the solution

= ln x^{2} - 16 + C

\frac{d y}{d x}, x^{2} + y^{2} = 0

R (t) = (t + e^{t}) (3 - t)

\frac{\partial}{\partial x} (\frac{x}{x ^{3} - y ^{5}})

n = 0 \sum \infty \frac{7}{n ( n + 3 )}

x = - y^{2} + 6, y = \frac{x}{2} - \frac{3}{2}

What is the integral of (2x)/(x^2-16) ?
The integral of (2x)/(x^2-16) is ln|x^2-16|+C