Mister Exam

Lang:

Other calculators

How to use it?
Integral of d{x}:
Integral of sinx
Integral of 1/(x^2*dx)
Integral of x^2/(x^2+4)^1/2
Integral of sin(x)*lnx
Identical expressions
(t^ two - eleven)^(- one / two)
(t squared minus 11) to the power of ( minus 1 divide by 2)
(t to the power of two minus eleven) to the power of ( minus one divide by two)
(t2-11)(-1/2)
t2-11-1/2
(t²-11)^(-1/2)
(t to the power of 2-11) to the power of (-1/2)
t^2-11^-1/2
(t^2-11)^(-1 divide by 2)
Similar expressions
(t^2+11)^(-1/2)
(t^2-11)^(1/2)

Solving integrals/ (t^2-11)^(-1/2)

Integral of (t^2-11)^(-1/2) dx

The solution

You have entered [src]

  1                
  /                
 |                 
 |       1         
 |  ------------ dt
 |     _________   
 |    /  2         
 |  \/  t  - 11    
 |                 
/                  
0

$$\int\limits_{0}^{1} \frac{1}{\sqrt{t^{2} - 11}}\, dt$$

Integral(1/sqrt(t^2 - 1*11), (t, 0, 1))

Detail solution

ReciprocalSqrtQuadraticRule(a=-11, b=0, c=1, context=1/sqrt(t**2 - 1*11), symbol=t)

Add the constant of integration:

$\log{\left(2 t + 2 \sqrt{t^{2} - 11} \right)}+ \mathrm{constant}$

The answer is:

$\log{\left(2 t + 2 \sqrt{t^{2} - 11} \right)}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                                
 |                          /           __________\
 |      1                   |          /        2 |
 | ------------ dt = C + log\2*t + 2*\/  -11 + t  /
 |    _________                                    
 |   /  2                                          
 | \/  t  - 11                                     
 |                                                 
/

$$\log \left(2\,\sqrt{t^2-11}+2\,t\right)$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

     /  ____\   pi*I      /        ____\
- log\\/ 11 / - ---- + log\1 + I*\/ 10 /
                 2

$${\it \%a}$$

     /  ____\   pi*I      /        ____\
- log\\/ 11 / - ---- + log\1 + I*\/ 10 /
                 2

$$- \log{\left(\sqrt{11} \right)} - \frac{i \pi}{2} + \log{\left(1 + \sqrt{10} i \right)}$$

Упростить

Numerical answer [src]

(0.0 - 0.306277369169669j)

(0.0 - 0.306277369169669j)

The graph

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

Other calculators

How to use it?

Identical expressions

Similar expressions

Integral of (t^2-11)^(-1/2) dx

Limits of integration:

The graph:

Piecewise:

The solution