What is the integral of (3/x-5/(x^6)) ?

The integral of (3/x-5/(x^6)) is 3ln|x|+1/(x^5)+C

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integral of (3/x-5/(x^6))

\int (\frac{3}{x} - \frac{5}{x ^{6}}) d x

3 ln ∣ x ∣ + \frac{1}{x ^{5}} + C

Solution steps

\int \frac{3}{x} - \frac{5}{x ^{6}} 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{5}{x ^{6}} d x

\int \frac{3}{x} d x = 3 ln ∣ x ∣

\int \frac{5}{x ^{6}} d x = - \frac{1}{x ^{5}}

= 3 ln ∣ x ∣ - (- \frac{1}{x ^{5}})

Simplify

= 3 ln ∣ x ∣ + \frac{1}{x ^{5}}

Add a constant to the solution

= 3 ln ∣ x ∣ + \frac{1}{x ^{5}} + C

\frac{d y}{d x} = \frac{x ^{3} - x ^{2} + x}{x}

y = tan (x) + \frac{1}{3} tan^{3} (x)

x \to - 3 lim (x^{3} + 4 x^{2} - 7)

y^{^{''}} + 4 y = e^{- x} (7 - 4 x + 5 x^{2})

\frac{d y}{d x} = (y + 1) (y - 2), y (0) = 0

What is the integral of (3/x-5/(x^6)) ?
The integral of (3/x-5/(x^6)) is 3ln|x|+1/(x^5)+C