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(2*x)/(x^2+2*x+2)^(1/2)

  • How to use it?

  • Integral of d{x}:
  • Integral of x^3/(x-1) Integral of x^3/(x-1)
  • Integral of x*2^x Integral of x*2^x
  • Integral of sin^5 Integral of sin^5
  • Integral of x^2*a^x

  • Identical expressions

  • (two *x)/(x^ two + two *x+ two)^(one / two)
  • (2 multiply by x) divide by (x squared plus 2 multiply by x plus 2) to the power of (1 divide by 2)
  • (two multiply by x) divide by (x to the power of two plus two multiply by x plus two) to the power of (one divide by two)
  • (2*x)/(x2+2*x+2)(1/2)
  • 2*x/x2+2*x+21/2
  • (2*x)/(x²+2*x+2)^(1/2)
  • (2*x)/(x to the power of 2+2*x+2) to the power of (1/2)
  • (2x)/(x^2+2x+2)^(1/2)
  • (2x)/(x2+2x+2)(1/2)
  • 2x/x2+2x+21/2
  • 2x/x^2+2x+2^1/2
  • (2*x) divide by (x^2+2*x+2)^(1 divide by 2)
  • (2*x)/(x^2+2*x+2)^(1/2)dx

  • Similar expressions

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

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

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                     
  /                     
 |                      
 |         2*x          
 |  ----------------- dx
 |     ______________   
 |    /  2              
 |  \/  x  + 2*x + 2    
 |                      
/                       
0
$$\int\limits_{0}^{1} \frac{2 x}{\sqrt{x^{2} + 2 x + 2}}\, dx$$ 
Integral(2*x/(sqrt(x^2 + 2*x + 2)), (x, 0, 1))
The answer (Indefinite) [src] 
  /                                                               
 |                                                  ______________
 |        2*x                                      /      2       
 | ----------------- dx = C - 2*asinh(1 + x) + 2*\/  2 + x  + 2*x 
 |    ______________                                              
 |   /  2                                                         
 | \/  x  + 2*x + 2                                               
 |                                                                
/
$$2\,\left(\sqrt{x^2+2\,x+2}-{\rm asinh}\; \left({{2\,x+2}\over{2}} \right)\right)$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
      ___                    ___        /      ___\
- 2*\/ 2  - 2*asinh(2) + 2*\/ 5  + 2*log\1 + \/ 2 /
$$2\,\left(-{\rm asinh}\; 2+{\rm asinh}\; 1+\sqrt{5}-\sqrt{2}\right)$$ 
=
= 
      ___                    ___        /      ___\
- 2*\/ 2  - 2*asinh(2) + 2*\/ 5  + 2*log\1 + \/ 2 /
$$- 2 \operatorname{asinh}{\left(2 \right)} - 2 \sqrt{2} + 2 \log{\left(1 + \sqrt{2} \right)} + 2 \sqrt{5}$$
Упростить
Numerical answer [src] 
0.519185053934855
0.519185053934855
The graph
Integral of (2*x)/(x^2+2*x+2)^(1/2) dx

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

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