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

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  • Identical expressions

  • (x^ two *dx)/(three + two *x^ two)
  • (x squared multiply by dx) divide by (3 plus 2 multiply by x squared )
  • (x to the power of two multiply by dx) divide by (three plus two multiply by x to the power of two)
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  • (x^2*dx) divide by (3+2*x^2)

  • Similar expressions

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

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

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                 
  /                 
 |                  
 |   2      1       
 |  x *1*-------- dx
 |              2   
 |       3 + 2*x    
 |                  
/                   
-1
$$\int\limits_{-1}^{1} x^{2} \cdot 1 \cdot \frac{1}{2 x^{2} + 3}\, dx$$ 
Integral(x^2*1/(3 + 2*x^2), (x, -1, 1))
Detail solution

  1. Rewrite the integrand:

  2. Integrate term-by-term:

    1. The integral of a constant is the constant times the variable of integration:

    1. The integral of a constant times a function is the constant times the integral of the function:

      1. The integral of is .

      So, the result is:

    The result is:

  3. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
                                        /    ___\
  /                             ___     |x*\/ 6 |
 |                            \/ 6 *atan|-------|
 |  2      1              x             \   3   /
 | x *1*-------- dx = C + - - -------------------
 |             2          2            4         
 |      3 + 2*x                                  
 |                                               
/
$$\int x^{2} \cdot 1 \cdot \frac{1}{2 x^{2} + 3}\, dx = C + \frac{x}{2} - \frac{\sqrt{6} \operatorname{atan}{\left(\frac{\sqrt{6} x}{3} \right)}}{4}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
              /  ___\
      ___     |\/ 6 |
    \/ 6 *atan|-----|
              \  3  /
1 - -----------------
            2
$$-{{\sqrt{6}\,\arctan \left({{\sqrt{6}}\over{3}}\right)-2}\over{2}}$$ 
=
= 
              /  ___\
      ___     |\/ 6 |
    \/ 6 *atan|-----|
              \  3  /
1 - -----------------
            2
$$- \frac{\sqrt{6} \operatorname{atan}{\left(\frac{\sqrt{6}}{3} \right)}}{2} + 1$$
Упростить
Numerical answer [src] 
0.161393667779618
0.161393667779618
The graph
Integral of (x^2*dx)/(3+2*x^2) dx

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

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