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

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

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

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

- \frac{1}{x} + ln ∣ x ∣ + C

Solution steps

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

Expand

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

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

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

\int \frac{1}{x} d x = ln ∣ x ∣

= - \frac{1}{x} + ln ∣ x ∣

Add a constant to the solution

= - \frac{1}{x} + ln ∣ x ∣ + C

\int_{- 1}^{3} (x + 1)^{3} d x

(x^{4} + 2 y) d x - x d y = 0

0.2 x^{3} \cdot 3^{x}

x \to \infty lim (- 1^{2 x})

\int e^{a}

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