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

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

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integral of x*1/(x^2)

\int x \cdot \frac{1}{x ^{2}} d x

ln ∣ x ∣ + C

Solution steps

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

Simplify

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

= \int \frac{1}{x} d x

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= ln ∣ x ∣

Add a constant to the solution

= ln ∣ x ∣ + C

x \to - 3 lim (- 2 x^{3})

f (x) = x + 2, at x = - 1

x \to 1 + lim (x^{2} - 3)

\frac{d}{d x} (- 6 e^{5 x})

\int (ln (4 x)) d x