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

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

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integral of (x^2+1)/(x^3)

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

ln ∣ x ∣ - \frac{1}{2 x ^{2}} + C

Solution steps

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

Expand

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

= \int \frac{1}{x} + \frac{1}{x ^{3}} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int \frac{1}{x} d x + \int \frac{1}{x ^{3}} d x

\int \frac{1}{x} d x = ln ∣ x ∣

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

= ln ∣ x ∣ - \frac{1}{2 x ^{2}}

Add a constant to the solution

= ln ∣ x ∣ - \frac{1}{2 x ^{2}} + C

x \to 0 lim (4 - x)

\frac{\partial}{\partial x} (ln (x y) + ln (yz) + 5 ln (x z))

\frac{d}{d y} (\frac{1}{x ^{2} + y ^{2}})

x^{2} - 4, x + 2

x \to 0 lim (- x ln (x))

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