What is the integral of 1/x-2/(x^2)+5/(x^3) ?

The integral of 1/x-2/(x^2)+5/(x^3) is ln|x|+2/x-5/(2x^2)+C

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integral of 1/x-2/(x^2)+5/(x^3)

\int \frac{1}{x} - \frac{2}{x ^{2}} + \frac{5}{x ^{3}} d x

ln ∣ x ∣ + \frac{2}{x} - \frac{5}{2 x ^{2}} + C

Solution steps

\int \frac{1}{x} - \frac{2}{x ^{2}} + \frac{5}{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{2}{x ^{2}} d x + \int \frac{5}{x ^{3}} d x

\int \frac{1}{x} d x = ln ∣ x ∣

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

\int \frac{5}{x ^{3}} d x = - \frac{5}{2 x ^{2}}

= ln ∣ x ∣ - (- \frac{2}{x}) - \frac{5}{2 x ^{2}}

Simplify

= ln ∣ x ∣ + \frac{2}{x} - \frac{5}{2 x ^{2}}

Add a constant to the solution

= ln ∣ x ∣ + \frac{2}{x} - \frac{5}{2 x ^{2}} + C

\frac{d}{d t} (z (t))

f (x) = x^{2} e^{x} - 2 x e^{x} + 4 e^{x}

\int - 2 x cos (x) d x

y^{^{''}} = \frac{6}{x ^{4}}

\frac{d}{d x} (x + 15)

What is the integral of 1/x-2/(x^2)+5/(x^3) ?
The integral of 1/x-2/(x^2)+5/(x^3) is ln|x|+2/x-5/(2x^2)+C