Mister Exam

Other calculators

Solving integrals/ arctgsqrt2x-1dx

Integral of arctgsqrt2x-1dx dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                       
  /                       
 |                        
 |  /    /  _____\    \   
 |  \atan\\/ 2*x / - 1/ dx
 |                        
/                         
0
$$\int\limits_{0}^{1} \left(\operatorname{atan}{\left(\sqrt{2 x} \right)} - 1\right)\, dx$$ 
Integral(atan(sqrt(2*x)) - 1, (x, 0, 1))
The answer (Indefinite) [src] 
                                                            /          ___     /  ___   ___\\
  /                                                     ___ |  ___   \/ 2 *atan\\/ 2 *\/ x /|
 |                                                    \/ 2 *|\/ x  - -----------------------|
 | /    /  _____\    \                    /  _____\         \                   2           /
 | \atan\\/ 2*x / - 1/ dx = C - x + x*atan\\/ 2*x / - ---------------------------------------
 |                                                                       2                   
/
$$\int \left(\operatorname{atan}{\left(\sqrt{2 x} \right)} - 1\right)\, dx = C + x \operatorname{atan}{\left(\sqrt{2 x} \right)} - x - \frac{\sqrt{2} \left(\sqrt{x} - \frac{\sqrt{2} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} \right)}}{2}\right)}{2}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
       ___         /  ___\
     \/ 2    3*atan\\/ 2 /
-1 - ----- + -------------
       2           2
$$-1 - \frac{\sqrt{2}}{2} + \frac{3 \operatorname{atan}{\left(\sqrt{2} \right)}}{2}$$ 
=
= 
       ___         /  ___\
     \/ 2    3*atan\\/ 2 /
-1 - ----- + -------------
       2           2
$$-1 - \frac{\sqrt{2}}{2} + \frac{3 \operatorname{atan}{\left(\sqrt{2} \right)}}{2}$$ 
-1 - sqrt(2)/2 + 3*atan(sqrt(2))/2
Numerical answer [src] 
-0.274131853999784
-0.274131853999784

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

    © Mister Exam – Calculator