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Identical expressions
(one)/(x*sqrt(x- eleven))
(1) divide by (x multiply by square root of (x minus 11))
(one) divide by (x multiply by square root of (x minus eleven))
(1)/(x*√(x-11))
(1)/(xsqrt(x-11))
1/xsqrtx-11
(1) divide by (x*sqrt(x-11))
(1)/(x*sqrt(x-11))dx
Similar expressions
(1)/(x*sqrt(x+11))

Integral of (1)/(x*sqrt(x-11)) dx

The solution

You have entered [src]

  1                
  /                
 |                 
 |       1         
 |  ------------ dx
 |      ________   
 |  x*\/ x - 11    
 |                 
/                  
0

\int\limits_{0}^{1} \frac{1}{x \sqrt{x - 11}}\, dx

Integral(1/(x*sqrt(x - 11)), (x, 0, 1))

The answer (Indefinite) [src]

                         //                /  ____\             \
                         ||      ____      |\/ 11 |             |
                         ||2*I*\/ 11 *acosh|------|             |
                         ||                |  ___ |             |
  /                      ||                \\/ x  /       11    |
 |                       ||------------------------  for --- > 1|
 |      1                ||           11                 |x|    |
 | ------------ dx = C + |<                                     |
 |     ________          ||               /  ____\              |
 | x*\/ x - 11           ||      ____     |\/ 11 |              |
 |                       || -2*\/ 11 *asin|------|              |
/                        ||               |  ___ |              |
                         ||               \\/ x  /              |
                         || ----------------------    otherwise |
                         \\           11                        /

\int \frac{1}{x \sqrt{x - 11}}\, dx = C + \begin{cases} \frac{2 \sqrt{11} i \operatorname{acosh}{\left(\frac{\sqrt{11}}{\sqrt{x}} \right)}}{11} & \text{for}\: \frac{11}{\left|{x}\right|} > 1 \\- \frac{2 \sqrt{11} \operatorname{asin}{\left(\frac{\sqrt{11}}{\sqrt{x}} \right)}}{11} & \text{otherwise} \end{cases}

Simplify

The graph

Plot the graph f(x)

The answer [src]

              ____      /  ____\
        2*I*\/ 11 *acosh\\/ 11 /
-oo*I + ------------------------
                   11

- \infty i + \frac{2 \sqrt{11} i \operatorname{acosh}{\left(\sqrt{11} \right)}}{11}

              ____      /  ____\
        2*I*\/ 11 *acosh\\/ 11 /
-oo*I + ------------------------
                   11

- \infty i + \frac{2 \sqrt{11} i \operatorname{acosh}{\left(\sqrt{11} \right)}}{11}

-oo*i + 2*i*sqrt(11)*acosh(sqrt(11))/11

Numerical answer [src]

(0.0 - 13.3079670796836j)

(0.0 - 13.3079670796836j)

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

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Integral of (1)/(x*sqrt(x-11)) dx

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Piecewise:

The solution