What is the integral of (5/x+(15)/(x^6)) ?

The integral of (5/x+(15)/(x^6)) is 5ln|x|-3/(x^5)+C

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integral of (5/x+(15)/(x^6))

\int (\frac{5}{x} + \frac{15}{x ^{6}}) d x

5 ln ∣ x ∣ - \frac{3}{x ^{5}} + C

Solution steps

\int \frac{5}{x} + \frac{15}{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{5}{x} d x + \int \frac{15}{x ^{6}} d x

\int \frac{5}{x} d x = 5 ln ∣ x ∣

\int \frac{15}{x ^{6}} d x = - \frac{3}{x ^{5}}

= 5 ln ∣ x ∣ - \frac{3}{x ^{5}}

Add a constant to the solution

= 5 ln ∣ x ∣ - \frac{3}{x ^{5}} + C

t - 4

(x + y) \cdot y^{^{'}} = 2 \cdot x + 2 \cdot y - 3

\int \frac{e ^{x - 1}}{x} d x

35 x - x x

x \to 0 lim (sin (4 x))

What is the integral of (5/x+(15)/(x^6)) ?
The integral of (5/x+(15)/(x^6)) is 5ln|x|-3/(x^5)+C