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Solving integrals/ arctg(4*x)*(x+2)

Integral of arctg(4*x)*(x+2) dx

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src] 
  1                     
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 |  atan(4*x)*(x + 2) dx
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0
$$\int\limits_{0}^{1} \left(x + 2\right) \operatorname{atan}{\left(4 x \right)}\, dx$$ 
Integral(atan(4*x)*(x + 2), (x, 0, 1))
The answer (Indefinite) [src] 
  /                              /        2\                    2                          
 |                            log\1 + 16*x /   x   atan(4*x)   x *atan(4*x)                
 | atan(4*x)*(x + 2) dx = C - -------------- - - + --------- + ------------ + 2*x*atan(4*x)
 |                                  4          8       32           2                      
/
$$\int \left(x + 2\right) \operatorname{atan}{\left(4 x \right)}\, dx = C + \frac{x^{2} \operatorname{atan}{\left(4 x \right)}}{2} + 2 x \operatorname{atan}{\left(4 x \right)} - \frac{x}{8} - \frac{\log{\left(16 x^{2} + 1 \right)}}{4} + \frac{\operatorname{atan}{\left(4 x \right)}}{32}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
  1   log(17)   81*atan(4)
- - - ------- + ----------
  8      4          32
$$- \frac{\log{\left(17 \right)}}{4} - \frac{1}{8} + \frac{81 \operatorname{atan}{\left(4 \right)}}{32}$$ 
=
= 
  1   log(17)   81*atan(4)
- - - ------- + ----------
  8      4          32
$$- \frac{\log{\left(17 \right)}}{4} - \frac{1}{8} + \frac{81 \operatorname{atan}{\left(4 \right)}}{32}$$ 
-1/8 - log(17)/4 + 81*atan(4)/32
Numerical answer [src] 
2.52267262514565
2.52267262514565

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

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