What is the integral of 1/(-x^{-2)+2x} ?

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

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integral of 1/(-x^{-2)+2x}

\int \frac{1}{- x ^{- 2} + 2 x} d x

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

Solution steps

\int \frac{1}{- x ^{- 2} + 2 x} d x

Simplify

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

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

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

Add a constant to the solution

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

y^{^{'}} + \frac{y}{9.33} = 6.429

y^{^{''}} = x^{4}

\frac{s}{s + 3}

\frac{d x}{d t} = \frac{x ^{2} + t 9 t ^{2} + x ^{2}}{t x}

\frac{( 1 + x )}{1 - x}

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