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Solving integrals/ ((x^4-1)arctgx)/4

Integral of ((x^4-1)arctgx)/4 dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                    
  /                    
 |                     
 |  / 4    \           
 |  \x  - 1/*acot(x)   
 |  ---------------- dx
 |         4           
 |                     
/                      
0
$$\int\limits_{0}^{1} \frac{\left(x^{4} - 1\right) \operatorname{acot}{\left(x \right)}}{4}\, dx$$ 
Integral(((x^4 - 1)*acot(x))/4, (x, 0, 1))
Detail solution

  1. The integral of a constant times a function is the constant times the integral of the function:

    1. Rewrite the integrand:

    2. Integrate term-by-term:

      1. Don't know the steps in finding this integral.

        But the integral is

      1. The integral of a constant times a function is the constant times the integral of the function:

        1. Don't know the steps in finding this integral.

          But the integral is

        So, the result is:

      The result is:

    So, the result is:

  2. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                                                        
 |                                                                         
 | / 4    \                     /     2\    2    4                5        
 | \x  - 1/*acot(x)          log\1 + x /   x    x    x*acot(x)   x *acot(x)
 | ---------------- dx = C - ----------- - -- + -- - --------- + ----------
 |        4                       10       40   80       4           20    
 |                                                                         
/
$$\int \frac{\left(x^{4} - 1\right) \operatorname{acot}{\left(x \right)}}{4}\, dx = C + \frac{x^{5} \operatorname{acot}{\left(x \right)}}{20} + \frac{x^{4}}{80} - \frac{x^{2}}{40} - \frac{x \operatorname{acot}{\left(x \right)}}{4} - \frac{\log{\left(x^{2} + 1 \right)}}{10}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
  1    log(2)   pi
- -- - ------ - --
  80     10     20
$$- \frac{\pi}{20} - \frac{\log{\left(2 \right)}}{10} - \frac{1}{80}$$ 
=
= 
  1    log(2)   pi
- -- - ------ - --
  80     10     20
$$- \frac{\pi}{20} - \frac{\log{\left(2 \right)}}{10} - \frac{1}{80}$$ 
-1/80 - log(2)/10 - pi/20
Numerical answer [src] 
-0.238894350735484
-0.238894350735484

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

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