What is the integral of (7/x-3/(x^2)) ?

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

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integral of (7/x-3/(x^2))

\int (\frac{7}{x} - \frac{3}{x ^{2}}) d x

7 ln ∣ x ∣ + \frac{3}{x} + C

Solution steps

\int \frac{7}{x} - \frac{3}{x ^{2}} 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{3}{x ^{2}} d x

\int \frac{7}{x} d x = 7 ln ∣ x ∣

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

= 7 ln ∣ x ∣ - (- \frac{3}{x})

Simplify

= 7 ln ∣ x ∣ + \frac{3}{x}

Add a constant to the solution

= 7 ln ∣ x ∣ + \frac{3}{x} + C

\int (3 x^{5} - 8)^{9} 6 x^{4} d x

y^{^{'}} = \frac{x y ^{3}}{( 1 + x ^{2} ) ^{\frac{1}{2}}}

\frac{d}{d x} (arctan (\frac{a}{x}))

\int \frac{1}{1 + sin ( x ) + cos ( x )} d x

f (x) = \frac{1}{3 x + 2}

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