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

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

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

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

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

Solution steps

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

Simplify

\frac{x x + x}{x} : \frac{x + 1}{x}

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

Expand

\frac{x + 1}{x} : x + \frac{1}{x}

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

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

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

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

Add a constant to the solution

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

\int_{1}^{\infty} x^{- 8} d x

e^{x}, 2 x - 1, x = 1, x = 2

x \to 1 - lim (\frac{x + 1}{x ^{2} - 1})

f (x) = (x^{2} - 10)^{4}

\int_{0}^{π} (1 - cos^{2} (x)) d x

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