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

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

\frac{d}{d x} (\frac{8 x ^{3} - 6 x ^{2}}{x ^{2} + 3 x - 2})

3 cos (4 t)

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

\int 10 x + 3 x^{2} + 12 x^{3} + C d 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