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

The integral of (3x^2+2)/((x^3+2x)^2) is -1/(x^3+2x)+C

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

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

- \frac{1}{x ^{3} + 2 x} + C

Solution steps

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

Apply u-substitution

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

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

Apply the Power Rule

: - \frac{1}{u}

= - \frac{1}{u}

Substitute back

u = x^{3} + 2 x

= - \frac{1}{x ^{3} + 2 x}

Add a constant to the solution

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

y = \frac{2 x}{x + 1}, (1, 1)

\frac{d}{d x} (\frac{5 x}{x + 1})

x \to + (- 1) lim (\frac{sin ( x )}{x})

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

f (x) = \frac{x}{9 - x}

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