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

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

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

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

ln x^{3} + 2 x + C

Solution steps

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

Apply u-substitution

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

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= ln ∣ u ∣

Substitute back

u = x^{3} + 2 x

= ln x^{3} + 2 x

Add a constant to the solution

= ln x^{3} + 2 x + C

\frac{d y}{d x} - 3 y = \frac{y}{x}

\frac{d}{d x} ((x - y)^{10})

\int (x^{2} + 5) e^{2 x} d x

x \to 8 - lim (x^{2} + 5)

\frac{d}{d x} (x^{2} e^{y z})

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