What is the integral of (xsqrt(x)+sqrt(x))/(x^2) ?

The integral of (xsqrt(x)+sqrt(x))/(x^2) is 2sqrt(x)-2/(sqrt(x))+C

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integral of (xsqrt(x)+sqrt(x))/(x^2)

\int \frac{x x + x}{x ^{2}} d x

2 x - \frac{2}{x} + C

Solution steps

\int \frac{x x + x}{x ^{2}} d x

\frac{x x + x}{x ^{2}} = (\frac{x x}{x ^{2}} + \frac{x}{x ^{2}})

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

Simplify

\frac{x x}{x ^{2}} + \frac{x}{x ^{2}} : \frac{1}{x} + \frac{1}{x ^{\frac{3}{2}}}

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

\int \frac{1}{x} d x = 2 x

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

= 2 x - \frac{2}{x}

Add a constant to the solution

= 2 x - \frac{2}{x} + C

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\int \frac{( x ^{7} + 3 x ^{5} - 2 x ^{3} - 4 )}{x ^{3}} d x

\frac{\partial}{\partial y} (1000 - 4 x y + x y^{2})

\frac{\partial}{\partial x} (e^{- 3 t} cos (π x))

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