What is the integral of (7-2x)/(x^{1/2)} ?

The integral of (7-2x)/(x^{1/2)} is 14x^{1/2}-4/3 x^{3/2}+C

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integral of (7-2x)/(x^{1/2)}

\int \frac{7 - 2 x}{x ^{\frac{1}{2}}} d x

14 x^{\frac{1}{2}} - \frac{4}{3} x^{\frac{3}{2}} + C

Solution steps

\int \frac{7 - 2 x}{x ^{\frac{1}{2}}} d x

Expand

\frac{7 - 2 x}{x ^{\frac{1}{2}}} : \frac{7}{x ^{\frac{1}{2}}} - 2 x^{\frac{1}{2}}

= \int \frac{7}{x ^{\frac{1}{2}}} - 2 x^{\frac{1}{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 ^{\frac{1}{2}}} d x - \int 2 x^{\frac{1}{2}} d x

\int \frac{7}{x ^{\frac{1}{2}}} d x = 14 x^{\frac{1}{2}}

\int 2 x^{\frac{1}{2}} d x = \frac{4}{3} x^{\frac{3}{2}}

= 14 x^{\frac{1}{2}} - \frac{4}{3} x^{\frac{3}{2}}

Add a constant to the solution

= 14 x^{\frac{1}{2}} - \frac{4}{3} x^{\frac{3}{2}} + C

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\frac{d}{d x} (1000 x e^{- 0.5 x})

What is the integral of (7-2x)/(x^{1/2)} ?
The integral of (7-2x)/(x^{1/2)} is 14x^{1/2}-4/3 x^{3/2}+C