What is the integral of (3/x-(10)/(x^6)) ?

The integral of (3/x-(10)/(x^6)) is 3ln|x|+2/(x^5)+C

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integral of (3/x-(10)/(x^6))

\int (\frac{3}{x} - \frac{10}{x ^{6}}) d x

3 ln ∣ x ∣ + \frac{2}{x ^{5}} + C

Solution steps

\int \frac{3}{x} - \frac{10}{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{10}{x ^{6}} d x

\int \frac{3}{x} d x = 3 ln ∣ x ∣

\int \frac{10}{x ^{6}} d x = - \frac{2}{x ^{5}}

= 3 ln ∣ x ∣ - (- \frac{2}{x ^{5}})

Simplify

= 3 ln ∣ x ∣ + \frac{2}{x ^{5}}

Add a constant to the solution

= 3 ln ∣ x ∣ + \frac{2}{x ^{5}} + C

\frac{d}{d x} (\frac{1}{( 2 x + 1 ) ^{3}})

\int 1 + t d t

\frac{d}{d x} (\frac{( x + 30 ) x ^{2} + 100}{x})

f (x) = 9 + 4 x

\int x^{5} + 8 x^{3} - 9 x^{2} + 7 x - 5 d x

What is the integral of (3/x-(10)/(x^6)) ?
The integral of (3/x-(10)/(x^6)) is 3ln|x|+2/(x^5)+C