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Solving integrals/ (7x-1)/((x-3)^2+4)

Integral of (7x-1)/((x-3)^2+4) dx

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src] 
  1                
  /                
 |                 
 |    7*x - 1      
 |  ------------ dx
 |         2       
 |  (x - 3)  + 4   
 |                 
/                  
0
∫017x−1(x−3)2+4 dx\int\limits_{0}^{1} \frac{7 x - 1}{\left(x - 3\right)^{2} + 4}\, dx 
Integral((7*x - 1)/((x - 3)^2 + 4), (x, 0, 1))
The answer (Indefinite) [src] 
  /                                                             
 |                                               /      2      \
 |   7*x - 1                    /  3   x\   7*log\13 + x  - 6*x/
 | ------------ dx = C + 10*atan|- - + -| + --------------------
 |        2                     \  2   2/            2          
 | (x - 3)  + 4                                                 
 |                                                              
/
∫7x−1(x−3)2+4 dx=C+7log⁡(x2−6x+13)2+10atan⁡(x2−32)\int \frac{7 x - 1}{\left(x - 3\right)^{2} + 4}\, dx = C + \frac{7 \log{\left(x^{2} - 6 x + 13 \right)}}{2} + 10 \operatorname{atan}{\left(\frac{x}{2} - \frac{3}{2} \right)}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.902-2
Plot the graph f(x)
The answer [src] 
               7*log(13)   5*pi   7*log(8)
10*atan(3/2) - --------- - ---- + --------
                   2        2        2
−7log⁡(13)2−5π2+7log⁡(8)2+10atan⁡(32)- \frac{7 \log{\left(13 \right)}}{2} - \frac{5 \pi}{2} + \frac{7 \log{\left(8 \right)}}{2} + 10 \operatorname{atan}{\left(\frac{3}{2} \right)} 
=
= 
               7*log(13)   5*pi   7*log(8)
10*atan(3/2) - --------- - ---- + --------
                   2        2        2
−7log⁡(13)2−5π2+7log⁡(8)2+10atan⁡(32)- \frac{7 \log{\left(13 \right)}}{2} - \frac{5 \pi}{2} + \frac{7 \log{\left(8 \right)}}{2} + 10 \operatorname{atan}{\left(\frac{3}{2} \right)} 
10*atan(3/2) - 7*log(13)/2 - 5*pi/2 + 7*log(8)/2
Numerical answer [src] 
0.274678243262855
0.274678243262855

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

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