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Solving integrals/ x/x^2

Integral of x/x^2 dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
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∫01xx2 dx\int\limits_{0}^{1} \frac{x}{x^{2}}\, dx 
Integral(x/(x^2), (x, 0, 1))
Detail solution

  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}

  2. Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src] 
  /                   
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∫xx2 dx=C+log⁡(x2)2\int \frac{x}{x^{2}}\, dx = C + \frac{\log{\left(x^{2} \right)}}{2}
Simplify
The answer [src] 
oo
∞\infty 
=
= 
oo
∞\infty
Упростить
Numerical answer [src] 
44.0904461339929
44.0904461339929

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

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