Mister Exam

Other calculators

Solving integrals/ arctan(e^x)

Integral of arctan(e^x) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1            
  /            
 |             
 |      / x\   
 |  atan\E / dx
 |             
/              
0
$$\int\limits_{0}^{1} \operatorname{atan}{\left(e^{x} \right)}\, dx$$ 
Integral(atan(E^x), (x, 0, 1))
The answer (Indefinite) [src] 
                       /                        
  /                   |                         
 |                    |      x                  
 |     / x\           |   x*e               / x\
 | atan\E / dx = C -  | -------- dx + x*atan\E /
 |                    |      2*x                
/                     | 1 + e                   
                      |                         
                     /
$$\int \operatorname{atan}{\left(e^{x} \right)}\, dx = C + x \operatorname{atan}{\left(e^{x} \right)} - \int \frac{x e^{x}}{e^{2 x} + 1}\, dx$$
Simplify
The answer [src] 
  1            
  /            
 |             
 |      / x\   
 |  atan\e / dx
 |             
/              
0
$$\int\limits_{0}^{1} \operatorname{atan}{\left(e^{x} \right)}\, dx$$ 
=
= 
  1            
  /            
 |             
 |      / x\   
 |  atan\e / dx
 |             
/              
0
$$\int\limits_{0}^{1} \operatorname{atan}{\left(e^{x} \right)}\, dx$$ 
Integral(atan(exp(x)), (x, 0, 1))
Numerical answer [src] 
1.01743058303942
1.01743058303942

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

    © Mister Exam – Calculator