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

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

Popular >

integral of (2x)/(x^2+2)

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

ln x^{2} + 2 + C

Solution steps

\int \frac{2 x}{x ^{2} + 2} 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} + 2} 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} + 2

= 2 \cdot \frac{1}{2} ln x^{2} + 2

Simplify

2 \cdot \frac{1}{2} ln x^{2} + 2 : ln x^{2} + 2

= ln x^{2} + 2

Add a constant to the solution

= ln x^{2} + 2 + C

f (x) = \frac{3}{4} x^{8}

\frac{3}{sin ( 2 x )}

2 y^{^{''}} + 5 y^{^{'}} - 3 y = 0, y (0) = 3, y^{^{'}} (0) = 19

f (x) = \frac{7}{8 t ^{4}}

f (x) = 2 x^{3} - x^{2} + 2, at x = 1

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