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Solving integrals/ xdx/x^2+2

You entered:

xdx/x^2+2

What you mean?

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

Integral of xdx/x^2+2 dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                
  /                
 |                 
 |  /    1     \   
 |  |x*1*-- + 2| dx
 |  |     2    |   
 |  \    x     /   
 |                 
/                  
0
∫01(x1⋅1x2+2) dx\int\limits_{0}^{1} \left(x 1 \cdot \frac{1}{x^{2}} + 2\right)\, dx 
Integral(x*1/x^2 + 2, (x, 0, 1))
Detail solution

  1. Integrate term-by-term:

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

      ∫1x dx=∫2x dx2\int \frac{1}{x}\, dx = \frac{\int \frac{2}{x}\, dx}{2}

      1. Let u=x2u = x^{2}.

        Then let du=2xdxdu = 2 x dx and substitute du2\frac{du}{2}:

        ∫12u du\int \frac{1}{2 u}\, du

        1. Don't know the steps in finding this integral.

          But the integral is

          log⁡(u)\log{\left(u \right)}

        Now substitute uu back in:

        log⁡(x2)\log{\left(x^{2} \right)}

      So, the result is: log⁡(x2)2\frac{\log{\left(x^{2} \right)}}{2}

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

      ∫2 dx=2x\int 2\, dx = 2 x

    The result is: 2x+log⁡(x2)22 x + \frac{\log{\left(x^{2} \right)}}{2}

  2. Add the constant of integration:

    2x+log⁡(x2)2+constant2 x + \frac{\log{\left(x^{2} \right)}}{2}+ \mathrm{constant}

The answer is:

2x+log⁡(x2)2+constant2 x + \frac{\log{\left(x^{2} \right)}}{2}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                                   
 |                          / 2\      
 | /    1     \          log\x /      
 | |x*1*-- + 2| dx = C + ------- + 2*x
 | |     2    |             2         
 | \    x     /                       
 |                                    
/
log⁡x+2 x\log x+2\,x
Simplify
The answer [src] 
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Simplify
Numerical answer [src] 
46.0904461339929
46.0904461339929

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

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