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Integral of sqrtx(lnx^2) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1                
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 |             2   
 |         2       
 |  t*x*log (x)  dx
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0                  
$$\int\limits_{0}^{1} t x \left(\log{\left(x \right)}^{2}\right)^{2}\, dx$$
Integral(t*x*(log(x)^2)^2, (x, 0, 1))
Detail solution
  1. The integral of a constant times a function is the constant times the integral of the function:

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

      But the integral is

    So, the result is:

  2. Now simplify:

  3. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                                                                     
 |                                                                                      
 |            2            /   2    2    4                      2             2    2   \
 |        2                |3*x    x *log (x)    2    3      3*x *log(x)   3*x *log (x)|
 | t*x*log (x)  dx = C + t*|---- + ---------- - x *log (x) - ----------- + ------------|
 |                         \ 4         2                          2             2      /
/                                                                                       
$$\int t x \left(\log{\left(x \right)}^{2}\right)^{2}\, dx = C + t \left(\frac{x^{2} \log{\left(x \right)}^{4}}{2} - x^{2} \log{\left(x \right)}^{3} + \frac{3 x^{2} \log{\left(x \right)}^{2}}{2} - \frac{3 x^{2} \log{\left(x \right)}}{2} + \frac{3 x^{2}}{4}\right)$$
The answer [src]
3*t
---
 4 
$$\frac{3 t}{4}$$
=
=
3*t
---
 4 
$$\frac{3 t}{4}$$

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