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x/sqrt(5+x-x^2)
Solving integrals/ x/sqrt(5+x-x^2)

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

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src] 
  1                   
  /                   
 |                    
 |         x          
 |  --------------- dx
 |     ____________   
 |    /          2    
 |  \/  5 + x - x     
 |                    
/                     
0
$$\int\limits_{0}^{1} \frac{x}{\sqrt{- x^{2} + x + 5}}\, dx$$ 
Integral(x/(sqrt(5 + x - x^2)), (x, 0, 1))
The answer (Indefinite) [src] 
                                /    ____           \                  
  /                             |2*\/ 21 *(-1/2 + x)|                  
 |                          asin|-------------------|      ____________
 |        x                     \         21        /     /          2 
 | --------------- dx = C + ------------------------- - \/  5 + x - x  
 |    ____________                      2                              
 |   /          2                                                      
 | \/  5 + x - x                                                       
 |                                                                     
/
$$-\sqrt{-x^2+x+5}-{{\arcsin \left({{1-2\,x}\over{\sqrt{21}}}\right) }\over{2}}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
    /  ____\
    |\/ 21 |
asin|------|
    \  21  /
$${{\arcsin \left({{1}\over{\sqrt{21}}}\right)+2\,\sqrt{5}}\over{2}}+ {{\arcsin \left({{1}\over{\sqrt{21}}}\right)-2\,\sqrt{5}}\over{2}}$$ 
=
= 
    /  ____\
    |\/ 21 |
asin|------|
    \  21  /
$$\operatorname{asin}{\left(\frac{\sqrt{21}}{21} \right)}$$
Упростить
Numerical answer [src] 
0.219987977395459
0.219987977395459
The graph
Integral of x/sqrt(5+x-x^2) dx

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

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