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2/((2x+2)^2+3)

Integral of 2/((2x+2)^2+3) dx

Limits of integration:

from to
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The graph:

from to

Piecewise:

The solution

You have entered [src]
  1                  
  /                  
 |                   
 |        2          
 |  -------------- dx
 |           2       
 |  (2*x + 2)  + 3   
 |                   
/                    
0                    
$$\int\limits_{0}^{1} \frac{2}{\left(2 x + 2\right)^{2} + 3}\, dx$$
Integral(2/((2*x + 2)^2 + 3), (x, 0, 1))
The answer (Indefinite) [src]
                                     /    ___        \
  /                          ___     |2*\/ 3 *(1 + x)|
 |                         \/ 3 *atan|---------------|
 |       2                           \       3       /
 | -------------- dx = C + ---------------------------
 |          2                           3             
 | (2*x + 2)  + 3                                     
 |                                                    
/                                                     
$${{\arctan \left({{8\,x+8}\over{4\,\sqrt{3}}}\right)}\over{\sqrt{3} }}$$
The graph
The answer [src]
            /    ___\             /    ___\
    ___     |2*\/ 3 |     ___     |4*\/ 3 |
  \/ 3 *atan|-------|   \/ 3 *atan|-------|
            \   3   /             \   3   /
- ------------------- + -------------------
           3                     3         
$$2\,\left({{\arctan \left({{4}\over{\sqrt{3}}}\right)}\over{2\, \sqrt{3}}}-{{\arctan \left({{2}\over{\sqrt{3}}}\right)}\over{2\, \sqrt{3}}}\right)$$
=
=
            /    ___\             /    ___\
    ___     |2*\/ 3 |     ___     |4*\/ 3 |
  \/ 3 *atan|-------|   \/ 3 *atan|-------|
            \   3   /             \   3   /
- ------------------- + -------------------
           3                     3         
$$- \frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3}}{3} \right)}}{3} + \frac{\sqrt{3} \operatorname{atan}{\left(\frac{4 \sqrt{3}}{3} \right)}}{3}$$
Numerical answer [src]
0.176141786669293
0.176141786669293
The graph
Integral of 2/((2x+2)^2+3) dx

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