What is the integral of sqrt((x+1)/x) ?

The integral of sqrt((x+1)/x) is sqrt((x+1)/x)x+ln|sqrt(x+1)+sqrt(x)|+C

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integral of sqrt((x+1)/x)

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

\frac{x + 1}{x} x + ln x + 1 + x + C

Solution steps

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

Apply Integration By Parts

: \frac{x + 1}{x} x - \int - \frac{1}{2 x ^{\frac{1}{2}} x + 1} d x

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

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

= \frac{x + 1}{x} x - (- ln x + 1 + x)

Simplify

= \frac{x + 1}{x} x + ln x + 1 + x

Add a constant to the solution

= \frac{x + 1}{x} x + ln x + 1 + x + C

\frac{\partial}{\partial x} (\frac{x - y}{x})

\frac{d}{d x} (ln (\frac{x}{4}) (x - 4))

\int \frac{sin ( x )}{cot ( x )} d x

\frac{s}{s ^{2} - 16}

y^{^{'}} = x^{2} - y - 2, y (0) = 1

What is the integral of sqrt((x+1)/x) ?
The integral of sqrt((x+1)/x) is sqrt((x+1)/x)x+ln|sqrt(x+1)+sqrt(x)|+C