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Identical expressions
(three x^ two +x+ three)/(((x- one)^3)*(x^ two + one))
(3x squared plus x plus 3) divide by (((x minus 1) cubed ) multiply by (x squared plus 1))
(three x to the power of two plus x plus three) divide by (((x minus one) cubed ) multiply by (x to the power of two plus one))
(3x2+x+3)/(((x-1)3)*(x2+1))
3x2+x+3/x-13*x2+1
(3x²+x+3)/(((x-1)³)*(x²+1))
(3x to the power of 2+x+3)/(((x-1) to the power of 3)*(x to the power of 2+1))
(3x^2+x+3)/(((x-1)^3)(x^2+1))
(3x2+x+3)/(((x-1)3)(x2+1))
3x2+x+3/x-13x2+1
3x^2+x+3/x-1^3x^2+1
(3x^2+x+3) divide by (((x-1)^3)*(x^2+1))
(3x^2+x+3)/(((x-1)^3)*(x^2+1))dx
Similar expressions
(3x^2+x+3)/(((x-1)^3)*(x^2-1))
(3x^2+x-3)/(((x-1)^3)*(x^2+1))
(3x^2-x+3)/(((x-1)^3)*(x^2+1))
(3x^2+x+3)/(((x+1)^3)*(x^2+1))

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

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

The solution

You have entered [src]

  1                     
  /                     
 |                      
 |        2             
 |     3*x  + x + 3     
 |  ----------------- dx
 |         3 / 2    \   
 |  (x - 1) *\x  + 1/   
 |                      
/                       
0

$$\int\limits_{0}^{1} \frac{\left(3 x^{2} + x\right) + 3}{\left(x - 1\right)^{3} \left(x^{2} + 1\right)}\, dx$$

Integral((3*x^2 + x + 3)/(((x - 1)^3*(x^2 + 1))), (x, 0, 1))

The answer (Indefinite) [src]

  /                                                                            
 |                                                                             
 |       2                                                             /     2\
 |    3*x  + x + 3                 7        log(-1 + x)   atan(x)   log\1 + x /
 | ----------------- dx = C - ----------- - ----------- + ------- + -----------
 |        3 / 2    \                    2        4           4           8     
 | (x - 1) *\x  + 1/          4*(-1 + x)                                       
 |                                                                             
/

$$\int \frac{\left(3 x^{2} + x\right) + 3}{\left(x - 1\right)^{3} \left(x^{2} + 1\right)}\, dx = C - \frac{\log{\left(x - 1 \right)}}{4} + \frac{\log{\left(x^{2} + 1 \right)}}{8} + \frac{\operatorname{atan}{\left(x \right)}}{4} - \frac{7}{4 \left(x - 1\right)^{2}}$$

Simplify

The answer [src]

      pi*I
-oo + ----
       4

$$-\infty + \frac{i \pi}{4}$$

      pi*I
-oo + ----
       4

$$-\infty + \frac{i \pi}{4}$$

-oo + pi*i/4

Numerical answer [src]

-3.2079963638096e+38

-3.2079963638096e+38

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

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

Limits of integration:

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Piecewise:

The solution