What is the integral of 3/x-4/(x^5) ?

The integral of 3/x-4/(x^5) is 3ln|x|+1/(x^4)+C

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integral of 3/x-4/(x^5)

\int \frac{3}{x} - \frac{4}{x ^{5}} d x

3 ln ∣ x ∣ + \frac{1}{x ^{4}} + C

Solution steps

\int \frac{3}{x} - \frac{4}{x ^{5}} 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{3}{x} d x - \int \frac{4}{x ^{5}} d x

\int \frac{3}{x} d x = 3 ln ∣ x ∣

\int \frac{4}{x ^{5}} d x = - \frac{1}{x ^{4}}

= 3 ln ∣ x ∣ - (- \frac{1}{x ^{4}})

Simplify

= 3 ln ∣ x ∣ + \frac{1}{x ^{4}}

Add a constant to the solution

= 3 ln ∣ x ∣ + \frac{1}{x ^{4}} + C

\frac{9 s}{5 ( s ^{2} + 5 s + 11 )}

\frac{x}{x - 1}

\frac{\partial}{\partial y} (y - x - z)

f (x) = 5 - 3 (1 + x^{2})^{- 1}

x \to 1 lim (\frac{2 x ^{3} - 14 x ^{2} + 12 x}{x ^{3} - 10 x ^{2} + 27 x - 18})

What is the integral of 3/x-4/(x^5) ?
The integral of 3/x-4/(x^5) is 3ln|x|+1/(x^4)+C