Mister Exam

Other calculators

Solving integrals/ sqrt(x-2)/(x+2)

Integral of sqrt(x-2)/(x+2) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1             
  /             
 |              
 |    _______   
 |  \/ x - 2    
 |  --------- dx
 |    x + 2     
 |              
/               
0
$$\int\limits_{0}^{1} \frac{\sqrt{x - 2}}{x + 2}\, dx$$ 
Integral(sqrt(x - 2)/(x + 2), (x, 0, 1))
The answer (Indefinite) [src] 
  /                                                    
 |                                                     
 |   _______                /  ________\               
 | \/ x - 2                 |\/ -2 + x |       ________
 | --------- dx = C - 4*atan|----------| + 2*\/ -2 + x 
 |   x + 2                  \    2     /               
 |                                                     
/
$$\int \frac{\sqrt{x - 2}}{x + 2}\, dx = C + 2 \sqrt{x - 2} - 4 \operatorname{atan}{\left(\frac{\sqrt{x - 2}}{2} \right)}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
               /    ___\                               
               |2*\/ 3 |         ___            /  ___\
2*I - 4*I*acosh|-------| - 2*I*\/ 2  + 4*I*acosh\\/ 2 /
               \   3   /
$$- 2 \sqrt{2} i - 4 i \operatorname{acosh}{\left(\frac{2 \sqrt{3}}{3} \right)} + 2 i + 4 i \operatorname{acosh}{\left(\sqrt{2} \right)}$$ 
=
= 
               /    ___\                               
               |2*\/ 3 |         ___            /  ___\
2*I - 4*I*acosh|-------| - 2*I*\/ 2  + 4*I*acosh\\/ 2 /
               \   3   /
$$- 2 \sqrt{2} i - 4 i \operatorname{acosh}{\left(\frac{2 \sqrt{3}}{3} \right)} + 2 i + 4 i \operatorname{acosh}{\left(\sqrt{2} \right)}$$ 
2*i - 4*i*acosh(2*sqrt(3)/3) - 2*i*sqrt(2) + 4*i*acosh(sqrt(2))
Numerical answer [src] 
(0.0 + 0.499842645995763j)
(0.0 + 0.499842645995763j)

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

    © Mister Exam – Calculator