Mister Exam

Other calculators

Solving integrals/ (2x+5)/((x-3)(x+1)^2)

Integral of (2x+5)/((x-3)(x+1)^2) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                    
  /                    
 |                     
 |      2*x + 5        
 |  ---------------- dx
 |                 2   
 |  (x - 3)*(x + 1)    
 |                     
/                      
0
$$\int\limits_{0}^{1} \frac{2 x + 5}{\left(x - 3\right) \left(x + 1\right)^{2}}\, dx$$ 
Integral((2*x + 5)/(((x - 3)*(x + 1)^2)), (x, 0, 1))
The answer (Indefinite) [src] 
  /                                                                    
 |                                                                     
 |     2*x + 5               11*log(1 + x)       3       11*log(-3 + x)
 | ---------------- dx = C - ------------- + --------- + --------------
 |                2                16        4*(1 + x)         16      
 | (x - 3)*(x + 1)                                                     
 |                                                                     
/
$$\int \frac{2 x + 5}{\left(x - 3\right) \left(x + 1\right)^{2}}\, dx = C + \frac{11 \log{\left(x - 3 \right)}}{16} - \frac{11 \log{\left(x + 1 \right)}}{16} + \frac{3}{4 \left(x + 1\right)}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
  3   11*log(3)
- - - ---------
  8       16
$$- \frac{11 \log{\left(3 \right)}}{16} - \frac{3}{8}$$ 
=
= 
  3   11*log(3)
- - - ---------
  8       16
$$- \frac{11 \log{\left(3 \right)}}{16} - \frac{3}{8}$$ 
-3/8 - 11*log(3)/16
Numerical answer [src] 
-1.13029594845933
-1.13029594845933

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

    © Mister Exam – Calculator