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((3x-2)÷√(3+2x-4x^2))
Solving integrals/ ((3x-2)÷√(3+2x-4x^2))

You entered:

((3x-2)÷√(3+2x-4x^2))

What you mean?

(3*x - 1*2)/(sqrt(3 + 2*x - 4*x^2))
 
(3*x - 1*2)/((sqrt(3 + 2*x - 4*x)*2))
 
(3*x - 1*2)/((sqrt(3 + 2*x - 4*x))^2)
 
(3*x - 1*2)/((sqrt(3 + 2*x - 1*4)*x^2))
 
(3*x - 1*2)/(sqrt(3 + 2*x) - 4*x^2)
 
(3*x - 1*2)/(sqrt(3 + 2)*x - 4*x^2)
 
3*x - 2*(3 + 2*x - 4*x^2)/(sqrt(x))

Integral of ((3x-2)÷√(3+2x-4x^2)) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                       
  /                       
 |                        
 |        3*x - 2         
 |  ------------------- dx
 |     ________________   
 |    /              2    
 |  \/  3 + 2*x - 4*x     
 |                        
/                         
0
$$\int\limits_{0}^{1} \frac{3 x - 2}{\sqrt{- 4 x^{2} + 2 x + 3}}\, dx$$
Simplify
The answer (Indefinite) [src] 
                                      /    ____           \                        
  /                                   |4*\/ 13 *(-1/4 + x)|        ________________
 |                              5*asin|-------------------|       /        2       
 |       3*x - 2                      \         13        /   3*\/  3 - 4*x  + 2*x 
 | ------------------- dx = C - --------------------------- - ---------------------
 |    ________________                       8                          4          
 |   /              2                                                              
 | \/  3 + 2*x - 4*x                                                               
 |                                                                                 
/
$${{5\,\arcsin \left({{2-8\,x}\over{2\,\sqrt{13}}}\right)}\over{8}}- {{3\,\sqrt{-4\,x^2+2\,x+3}}\over{4}}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
            /  ____\         /    ____\          
            |\/ 13 |         |3*\/ 13 |          
      5*asin|------|   5*asin|--------|       ___
  3         \  13  /         \   13   /   3*\/ 3 
- - - -------------- - ---------------- + -------
  4         8                 8              4
$$-{{5\,\arcsin \left({{3}\over{\sqrt{13}}}\right)+5\,\arcsin \left( {{1}\over{\sqrt{13}}}\right)-2\,3^{{{3}\over{2}}}+6}\over{8}}$$ 
=
= 
            /  ____\         /    ____\          
            |\/ 13 |         |3*\/ 13 |          
      5*asin|------|   5*asin|--------|       ___
  3         \  13  /         \   13   /   3*\/ 3 
- - - -------------- - ---------------- + -------
  4         8                 8              4
$$- \frac{3}{4} - \frac{5 \operatorname{asin}{\left(\frac{3 \sqrt{13}}{13} \right)}}{8} - \frac{5 \operatorname{asin}{\left(\frac{\sqrt{13}}{13} \right)}}{8} + \frac{3 \sqrt{3}}{4}$$
Simplify
Numerical answer [src] 
-0.240854784792181
-0.240854784792181
The graph
Integral of ((3x-2)÷√(3+2x-4x^2)) dx

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

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