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(3*x-1)/((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

  • (three *x- one)/((x^ two + two *x+ two)^ one / two)
  • (3 multiply by x minus 1) divide by ((x squared plus 2 multiply by x plus 2) to the power of 1 divide by 2)
  • (three multiply by x minus one) divide by ((x to the power of two plus two multiply by x plus two) to the power of one divide by two)
  • (3*x-1)/((x2+2*x+2)1/2)
  • 3*x-1/x2+2*x+21/2
  • (3*x-1)/((x²+2*x+2)^1/2)
  • (3*x-1)/((x to the power of 2+2*x+2) to the power of 1/2)
  • (3x-1)/((x^2+2x+2)^1/2)
  • (3x-1)/((x2+2x+2)1/2)
  • 3x-1/x2+2x+21/2
  • 3x-1/x^2+2x+2^1/2
  • (3*x-1) divide by ((x^2+2*x+2)^1 divide by 2)
  • (3*x-1)/((x^2+2*x+2)^1/2)dx

  • Similar expressions

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

Integral of (3*x-1)/((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                     
  /                     
 |                      
 |       3*x - 1        
 |  ----------------- dx
 |     ______________   
 |    /  2              
 |  \/  x  + 2*x + 2    
 |                      
/                       
0
$$\int\limits_{0}^{1} \frac{3 x - 1}{\sqrt{x^{2} + 2 x + 2}}\, dx$$ 
Integral((3*x - 1*1)/(sqrt(x^2 + 2*x + 2)), (x, 0, 1))
The answer (Indefinite) [src] 
  /                                                               
 |                                                  ______________
 |      3*x - 1                                    /      2       
 | ----------------- dx = C - 4*asinh(1 + x) + 3*\/  2 + x  + 2*x 
 |    ______________                                              
 |   /  2                                                         
 | \/  x  + 2*x + 2                                               
 |                                                                
/
$$3\,\sqrt{x^2+2\,x+2}-4\,{\rm asinh}\; \left({{2\,x+2}\over{2}} \right)$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
                  ___       ___        /      ___\
-4*asinh(2) - 3*\/ 2  + 3*\/ 5  + 4*log\1 + \/ 2 /
$$-4\,{\rm asinh}\; 2+4\,{\rm asinh}\; 1+3\,\sqrt{5}-3\,\sqrt{2}$$ 
=
= 
                  ___       ___        /      ___\
-4*asinh(2) - 3*\/ 2  + 3*\/ 5  + 4*log\1 + \/ 2 /
$$- 4 \operatorname{asinh}{\left(2 \right)} - 3 \sqrt{2} + 4 \log{\left(1 + \sqrt{2} \right)} + 3 \sqrt{5}$$
Упростить
Numerical answer [src] 
0.216515692743015
0.216515692743015
The graph
Integral of (3*x-1)/((x^2+2*x+2)^1/2) dx

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

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