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Solving integrals/ atan(x+3/2)+1

Integral of atan(x+3/2)+1 dx

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src] 
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 |  (atan(x + 3/2) + 1) dx
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∫01(atan⁡(x+32)+1) dx\int\limits_{0}^{1} \left(\operatorname{atan}{\left(x + \frac{3}{2} \right)} + 1\right)\, dx 
Integral(atan(x + 3/2) + 1, (x, 0, 1))
The answer (Indefinite) [src] 
  /                                    /             2\                          
 |                                  log\1 + (x + 3/2) /                          
 | (atan(x + 3/2) + 1) dx = C + x - ------------------- + (x + 3/2)*atan(x + 3/2)
 |                                           2                                   
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∫(atan⁡(x+32)+1) dx=C+x+(x+32)atan⁡(x+32)−log⁡((x+32)2+1)2\int \left(\operatorname{atan}{\left(x + \frac{3}{2} \right)} + 1\right)\, dx = C + x + \left(x + \frac{3}{2}\right) \operatorname{atan}{\left(x + \frac{3}{2} \right)} - \frac{\log{\left(\left(x + \frac{3}{2}\right)^{2} + 1 \right)}}{2}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.900.02.5
Plot the graph f(x)
The answer [src] 
    log(13)   3*atan(3/2)   log(29)   5*atan(5/2)
1 + ------- - ----------- - ------- + -----------
       2           2           2           2
−log⁡(29)2−3atan⁡(32)2+1+log⁡(13)2+5atan⁡(52)2- \frac{\log{\left(29 \right)}}{2} - \frac{3 \operatorname{atan}{\left(\frac{3}{2} \right)}}{2} + 1 + \frac{\log{\left(13 \right)}}{2} + \frac{5 \operatorname{atan}{\left(\frac{5}{2} \right)}}{2} 
=
= 
    log(13)   3*atan(3/2)   log(29)   5*atan(5/2)
1 + ------- - ----------- - ------- + -----------
       2           2           2           2
−log⁡(29)2−3atan⁡(32)2+1+log⁡(13)2+5atan⁡(52)2- \frac{\log{\left(29 \right)}}{2} - \frac{3 \operatorname{atan}{\left(\frac{3}{2} \right)}}{2} + 1 + \frac{\log{\left(13 \right)}}{2} + \frac{5 \operatorname{atan}{\left(\frac{5}{2} \right)}}{2} 
1 + log(13)/2 - 3*atan(3/2)/2 - log(29)/2 + 5*atan(5/2)/2
Numerical answer [src] 
2.10036105307287
2.10036105307287

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

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