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Solving integrals/ 1/(xsqrt(x-16))

Integral of 1/(xsqrt(x-16)) dx

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src] 
  1                
  /                
 |                 
 |       1         
 |  ------------ dx
 |      ________   
 |  x*\/ x - 16    
 |                 
/                  
0
∫011xx−16 dx\int\limits_{0}^{1} \frac{1}{x \sqrt{x - 16}}\, dx 
Integral(1/(x*sqrt(x - 16)), (x, 0, 1))
The answer (Indefinite) [src] 
                         //       /  4  \             \
                         ||I*acosh|-----|             |
                         ||       |  ___|             |
  /                      ||       \\/ x /       16    |
 |                       ||--------------  for --- > 1|
 |      1                ||      2             |x|    |
 | ------------ dx = C + |<                           |
 |     ________          ||     /  4  \               |
 | x*\/ x - 16           ||-asin|-----|               |
 |                       ||     |  ___|               |
/                        ||     \\/ x /               |
                         ||-------------    otherwise |
                         \\      2                    /
∫1xx−16 dx=C+{iacosh⁡(4x)2for 16∣x∣>1−asin⁡(4x)2otherwise\int \frac{1}{x \sqrt{x - 16}}\, dx = C + \begin{cases} \frac{i \operatorname{acosh}{\left(\frac{4}{\sqrt{x}} \right)}}{2} & \text{for}\: \frac{16}{\left|{x}\right|} > 1 \\- \frac{\operatorname{asin}{\left(\frac{4}{\sqrt{x}} \right)}}{2} & \text{otherwise} \end{cases}
Simplify
The graph
-0.010-0.008-0.006-0.004-0.0020.0100.0000.0020.0040.0060.0080.00
Plot the graph f(x)
The answer [src] 
        I*acosh(4)
-oo*I + ----------
            2
−∞i+iacosh⁡(4)2- \infty i + \frac{i \operatorname{acosh}{\left(4 \right)}}{2} 
=
= 
        I*acosh(4)
-oo*I + ----------
            2
−∞i+iacosh⁡(4)2- \infty i + \frac{i \operatorname{acosh}{\left(4 \right)}}{2} 
-oo*i + i*acosh(4)/2
Numerical answer [src] 
(0.0 - 11.0306137698904j)
(0.0 - 11.0306137698904j)

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

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