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  • Identical expressions

  • atan(x)/x^(one / three)
  • arc tangent of gent of (x) divide by x to the power of (1 divide by 3)
  • arc tangent of gent of (x) divide by x to the power of (one divide by three)
  • atan(x)/x(1/3)
  • atanx/x1/3
  • atanx/x^1/3
  • atan(x) divide by x^(1 divide by 3)
  • atan(x)/x^(1/3)dx

  • Similar expressions

  • arctan(x)/x^(1/3)
  • arctanx/x^(1/3)
Solving integrals/ atan(x)/x^(1/3)

Integral of atan(x)/x^(1/3) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 -100          
   /           
  |            
  |  atan(x)   
  |  ------- dx
  |   3 ___    
  |   \/ x     
  |            
 /             
 0
$$\int\limits_{0}^{-100} \frac{\operatorname{atan}{\left(x \right)}}{\sqrt[3]{x}}\, dx$$ 
Integral(atan(x)/x^(1/3), (x, 0, -100))
The answer (Indefinite) [src] 
  /                                                                                                                                                                                         
 |                        /3 ___\         /  ___     3 ___\         /    ___     3 ___\       ___    /       2/3       ___ 3 ___\      2/3               ___    /       2/3       ___ 3 ___\
 | atan(x)          3*atan\\/ x /   3*atan\\/ 3  + 2*\/ x /   3*atan\- \/ 3  + 2*\/ x /   3*\/ 3 *log\4 + 4*x    - 4*\/ 3 *\/ x /   3*x   *atan(x)   3*\/ 3 *log\4 + 4*x    + 4*\/ 3 *\/ x /
 | ------- dx = C - ------------- - ----------------------- - ------------------------- - --------------------------------------- + -------------- + ---------------------------------------
 |  3 ___                 2                    4                          4                                  8                            2                             8                   
 |  \/ x                                                                                                                                                                                    
 |                                                                                                                                                                                          
/
$$\int \frac{\operatorname{atan}{\left(x \right)}}{\sqrt[3]{x}}\, dx = C + \frac{3 x^{\frac{2}{3}} \operatorname{atan}{\left(x \right)}}{2} - \frac{3 \sqrt{3} \log{\left(4 x^{\frac{2}{3}} - 4 \sqrt{3} \sqrt[3]{x} + 4 \right)}}{8} + \frac{3 \sqrt{3} \log{\left(4 x^{\frac{2}{3}} + 4 \sqrt{3} \sqrt[3]{x} + 4 \right)}}{8} - \frac{3 \operatorname{atan}{\left(\sqrt[3]{x} \right)}}{2} - \frac{3 \operatorname{atan}{\left(2 \sqrt[3]{x} - \sqrt{3} \right)}}{4} - \frac{3 \operatorname{atan}{\left(2 \sqrt[3]{x} + \sqrt{3} \right)}}{4}$$
Simplify
Numerical answer [src] 
(23.3483049051421 - 40.4404503663158j)
(23.3483049051421 - 40.4404503663158j)

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

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