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}}

Add a constant to the solution

= 2 ln ∣ x ∣ - \frac{2}{x ^{2}} + C

\int \frac{1}{( a + x )} d x

\int + 0.0025 x - 0.075 d x

\int \frac{x ^{3} - 4 x - 1}{x ^{2}} d x

\int - x^{2} + 2 x + 2 d x

\int \frac{2 x ^{5}}{x ^{6} + 5} d x

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