What is the integral of (6/x+5/(x^2)-3sqrt(x)) ?

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

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integral of (6/x+5/(x^2)-3sqrt(x))

\int (\frac{6}{x} + \frac{5}{x ^{2}} - 3 x) d x

6 ln ∣ x ∣ - \frac{5}{x} - 2 x^{\frac{3}{2}} + C

Solution steps

\int \frac{6}{x} + \frac{5}{x ^{2}} - 3 x 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{6}{x} d x + \int \frac{5}{x ^{2}} d x - \int 3 x d x

\int \frac{6}{x} d x = 6 ln ∣ x ∣

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

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

= 6 ln ∣ x ∣ - \frac{5}{x} - 2 x^{\frac{3}{2}}

Add a constant to the solution

= 6 ln ∣ x ∣ - \frac{5}{x} - 2 x^{\frac{3}{2}} + C

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