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

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

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

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

- \frac{2}{x ^{2}} + 2 ln ∣ x ∣ + C

Solution steps

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

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

\int \frac{2}{x} d x = 2 ln ∣ x ∣

= - \frac{2}{x ^{2}} + 2 ln ∣ x ∣

Add a constant to the solution

= - \frac{2}{x ^{2}} + 2 ln ∣ x ∣ + C

\int \frac{2 x ^{2}}{x ^{3} + 8} d x

\int 2 x (x^{2} + 11)^{4} d x

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

\int \frac{( x + 1 )}{( x ^{2} + 2 )} d x

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