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

The integral of (2/x-3/(x^4)) is 2ln|x|+1/(x^3)+C

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

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

2 ln ∣ x ∣ + \frac{1}{x ^{3}} + C

Solution steps

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

\int \frac{2}{x} d x = 2 ln ∣ x ∣

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

= 2 ln ∣ x ∣ - (- \frac{1}{x ^{3}})

Simplify

= 2 ln ∣ x ∣ + \frac{1}{x ^{3}}

Add a constant to the solution

= 2 ln ∣ x ∣ + \frac{1}{x ^{3}} + C

y = \frac{2}{x}

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

\int 1 0^{2 x} d x

x \to 0 lim (x + 3)

\int 2 x + 6 x^{- 2} d x

What is the integral of (2/x-3/(x^4)) ?
The integral of (2/x-3/(x^4)) is 2ln|x|+1/(x^3)+C