What is the integral of (x+7)/(sqrt(x)) ?

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

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integral of (x+7)/(sqrt(x))

\int \frac{x + 7}{x} d x

\frac{2}{3} x^{\frac{3}{2}} + 14 x + C

Solution steps

\int \frac{x + 7}{x} d x

Expand

\frac{x + 7}{x} : x + \frac{7}{x}

= \int x + \frac{7}{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 x d x + \int \frac{7}{x} d x

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

\int \frac{7}{x} d x = 14 x

= \frac{2}{3} x^{\frac{3}{2}} + 14 x

Add a constant to the solution

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

y = x - 1, 1, 2

\frac{d}{d x} (π x^{7} - 2 x^{5} - 5 x^{- 2})

\int (x x + 5) d x

\frac{x ^{2} - 4}{x}

8 sin (x)

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