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

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

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

\int (\frac{5}{x} - \frac{4}{x ^{5}}) d x

5 ln ∣ x ∣ + \frac{1}{x ^{4}} + C

Solution steps

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

\int \frac{5}{x} d x = 5 ln ∣ x ∣

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

= 5 ln ∣ x ∣ - (- \frac{1}{x ^{4}})

Simplify

= 5 ln ∣ x ∣ + \frac{1}{x ^{4}}

Add a constant to the solution

= 5 ln ∣ x ∣ + \frac{1}{x ^{4}} + C

\frac{d y}{d t} = \frac{8}{7} y

\frac{\partial}{\partial x} ((2 x + 3) (y - 2))

y = x^{3} - 3 x + 1

\frac{d}{d x} (lo g_{3} (sin (x^{2})))

x \to - 2 + lim (2 - x)

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