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

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

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

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

- \frac{6}{x} + \frac{5}{x} + C

Solution steps

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

Expand

\frac{3 x - 5}{x ^{2}} : \frac{3}{x ^{\frac{3}{2}}} - \frac{5}{x ^{2}}

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

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

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

= - \frac{6}{x} - (- \frac{5}{x})

Simplify

= - \frac{6}{x} + \frac{5}{x}

Add a constant to the solution

= - \frac{6}{x} + \frac{5}{x} + C

\int \frac{x ^{3} + 23}{x ^{2} + 7 x + 12} d x

\frac{d}{d x} ((2 x + 1)^{4})

y = csc (x) (x + cot (x))

f (x) = \frac{2 x}{7 x ^{2} + 1}

\int 7^{x} cot^{2} (7^{x}) d x

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