What is the integral of 2/x-4/(x^3) ?

The integral of 2/x-4/(x^3) is 2ln|x|+2/(x^2)+C

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integral of 2/x-4/(x^3)

\int \frac{2}{x} - \frac{4}{x ^{3}} d x

2 ln ∣ x ∣ + \frac{2}{x ^{2}} + C

Solution steps

\int \frac{2}{x} - \frac{4}{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{2}{x} d x - \int \frac{4}{x ^{3}} d x

\int \frac{2}{x} d x = 2 ln ∣ x ∣

\int \frac{4}{x ^{3}} d x = - \frac{2}{x ^{2}}

= 2 ln ∣ x ∣ - (- \frac{2}{x ^{2}})

Simplify

= 2 ln ∣ x ∣ + \frac{2}{x ^{2}}

Add a constant to the solution

= 2 ln ∣ x ∣ + \frac{2}{x ^{2}} + C

3 sin^{2} (t)

\int \frac{4 e ^{x}}{e ^{2 x} + 8 e ^{x} + 16} d x

\frac{\partial}{\partial x} (- x e^{\frac{x}{y}})

x \to 2 lim (13 - 2 x)

x \to 0 lim (8 x + 4 h - 3)

What is the integral of 2/x-4/(x^3) ?
The integral of 2/x-4/(x^3) is 2ln|x|+2/(x^2)+C