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

The integral of x/(3x^2+2) is 1/6 ln|3x^2+2|+C

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integral of x/(3x^2+2)

\int \frac{x}{3 x ^{2} + 2} d x

\frac{1}{6} ln 3 x^{2} + 2 + C

Solution steps

\int \frac{x}{3 x ^{2} + 2} d x

Apply u-substitution

: \int \frac{1}{6 u} d u

= \int \frac{1}{6 u} d u

Take the constant out:

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

= \frac{1}{6} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{6} ln ∣ u ∣

Substitute back

u = 3 x^{2} + 2

= \frac{1}{6} ln 3 x^{2} + 2

Add a constant to the solution

= \frac{1}{6} ln 3 x^{2} + 2 + C

6 e^{6 e^{x} + x}

(x^{3} + 7) e^{x}

f (x) = - 1 x^{- \frac{3}{5}}

\frac{d}{d x} (cos (\frac{x}{y}))

\frac{d}{d a} (2 sin (2 a) + 2 cos^{2} (a))

What is the integral of x/(3x^2+2) ?
The integral of x/(3x^2+2) is 1/6 ln|3x^2+2|+C