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

The integral of (1+sqrt(x))/(1-sqrt(x)) is -4(-1+sqrt(x)+ln|1-sqrt(x)|)-x+C

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

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

- 4 (- 1 + x + ln 1 - x) - x + C

Solution steps

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

\frac{1 + x}{1 - x} = \frac{2}{1 - x} - 1

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

\int \frac{2}{1 - x} d x = - 4 (- 1 + x + ln 1 - x)

\int 1 d x = x

= - 4 (- 1 + x + ln 1 - x) - x

Add a constant to the solution

= - 4 (- 1 + x + ln 1 - x) - x + C

\int \frac{13 e ^{- 5 x} cos ( x )}{10} d x

x \cdot cos (2 x)

\int \frac{8 ln ( x + 9 )}{x ^{2}} d x

6 sin (2 t)

\frac{d}{d x} (a sin (2 x))

What is the integral of (1+sqrt(x))/(1-sqrt(x)) ?
The integral of (1+sqrt(x))/(1-sqrt(x)) is -4(-1+sqrt(x)+ln|1-sqrt(x)|)-x+C