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Solving integrals/ (sqrt(x-1))/sqrt(1+x)

Integral of (sqrt(x-1))/sqrt(1+x) dx

Limits of integration:

from to
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The graph:

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Piecewise:

The solution

You have entered [src] 
  1             
  /             
 |              
 |    _______   
 |  \/ x - 1    
 |  --------- dx
 |    _______   
 |  \/ 1 + x    
 |              
/               
0
$$\int\limits_{0}^{1} \frac{\sqrt{x - 1}}{\sqrt{x + 1}}\, dx$$ 
Integral(sqrt(x - 1)/sqrt(1 + x), (x, 0, 1))
The answer (Indefinite) [src] 
                      //          /  ___   _______\          3/2       _______                   \
  /                   ||          |\/ 2 *\/ 1 + x |   (1 + x)      2*\/ 1 + x         |1 + x|    |
 |                    || - 2*acosh|---------------| + ---------- - -----------    for ------- > 1|
 |   _______          ||          \       2       /     ________      ________           2       |
 | \/ x - 1           ||                              \/ -1 + x     \/ -1 + x                    |
 | --------- dx = C + |<                                                                         |
 |   _______          ||        /  ___   _______\            3/2         _______                 |
 | \/ 1 + x           ||        |\/ 2 *\/ 1 + x |   I*(1 + x)      2*I*\/ 1 + x                  |
 |                    ||2*I*asin|---------------| - ------------ + -------------     otherwise   |
/                     ||        \       2       /      _______         _______                   |
                      \\                             \/ 1 - x        \/ 1 - x                    /
$$\int \frac{\sqrt{x - 1}}{\sqrt{x + 1}}\, dx = C + \begin{cases} - 2 \operatorname{acosh}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)} + \frac{\left(x + 1\right)^{\frac{3}{2}}}{\sqrt{x - 1}} - \frac{2 \sqrt{x + 1}}{\sqrt{x - 1}} & \text{for}\: \frac{\left|{x + 1}\right|}{2} > 1 \\2 i \operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{x + 1}}{2} \right)} - \frac{i \left(x + 1\right)^{\frac{3}{2}}}{\sqrt{1 - x}} + \frac{2 i \sqrt{x + 1}}{\sqrt{1 - x}} & \text{otherwise} \end{cases}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
     pi*I
-I + ----
      2
$$- i + \frac{i \pi}{2}$$ 
=
= 
     pi*I
-I + ----
      2
$$- i + \frac{i \pi}{2}$$ 
-i + pi*i/2
Numerical answer [src] 
(0.0 + 0.570796326794897j)
(0.0 + 0.570796326794897j)

    Use the examples entering the upper and lower limits of integration.

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