What is the integral of (7/x-6/(x^3)) ?

The integral of (7/x-6/(x^3)) is 7ln|x|+3/(x^2)+C

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integral of (7/x-6/(x^3))

\int (\frac{7}{x} - \frac{6}{x ^{3}}) d x

7 ln ∣ x ∣ + \frac{3}{x ^{2}} + C

Solution steps

\int \frac{7}{x} - \frac{6}{x ^{3}} 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{7}{x} d x - \int \frac{6}{x ^{3}} d x

\int \frac{7}{x} d x = 7 ln ∣ x ∣

\int \frac{6}{x ^{3}} d x = - \frac{3}{x ^{2}}

= 7 ln ∣ x ∣ - (- \frac{3}{x ^{2}})

Simplify

= 7 ln ∣ x ∣ + \frac{3}{x ^{2}}

Add a constant to the solution

= 7 ln ∣ x ∣ + \frac{3}{x ^{2}} + C

(x, y) \to (1, - 1) lim ((e^{- x y}) (cos (x + y)))

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

\int x 1 + 2 x d x

\int_{0}^{3} \frac{1}{5 x + 1} d x

\int_{0}^{5} (5 x - 1) d x

What is the integral of (7/x-6/(x^3)) ?
The integral of (7/x-6/(x^3)) is 7ln|x|+3/(x^2)+C