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

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

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integral of (x^2+x^{-2})/(x^3-3x^{-1)}

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

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

Solution steps

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

Apply u-substitution

: \int \frac{1}{3 u} d u

= \int \frac{1}{3 u} d u

Take the constant out:

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

= \frac{1}{3} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{3} ln ∣ u ∣

Substitute back

u = x^{3} - 3 x^{- 1}

= \frac{1}{3} ln x^{3} - 3 x^{- 1}

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

= \frac{1}{3} ln x^{3} - \frac{3}{x}

Add a constant to the solution

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

y^{^{'}} + 7 (tan (7 x)) y = 5 cos (7 x)

\frac{x ^{5}}{x ^{3}}

\int \frac{5}{x ^{2} x ^{2} - 9} d x

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

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

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