Mister Exam

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Identical expressions
sqrtx(lnx^ two)
square root of x(lnx squared )
square root of x(lnx to the power of two)
√x(lnx^2)
sqrtx(lnx2)
sqrtxlnx2
sqrtx(lnx²)
sqrtx(lnx to the power of 2)
sqrtxlnx^2
sqrtx(lnx^2)dx
Similar expressions
sqrt(x)*(lnx^2)*x

Integral of sqrtx(lnx^2) dx

The solution

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  1                
  /                
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 |             2   
 |         2       
 |  t*x*log (x)  dx
 |                 
/                  
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

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

$\int t x \left(\log{\left(x \right)}^{2}\right)^{2}\, dx = t \int x \left(\log{\left(x \right)}^{2}\right)^{2}\, dx$
1. Don't know the steps in finding this integral.
  
  But the integral is
  
  $\frac{x^{2} \log{\left(x \right)}^{4}}{2} - x^{2} \log{\left(x \right)}^{3} + \frac{3 x^{2} \log{\left(x \right)}^{2}}{2} - \frac{3 x^{2} \log{\left(x \right)}}{2} + \frac{3 x^{2}}{4}$
So, the result is: $t \left(\frac{x^{2} \log{\left(x \right)}^{4}}{2} - x^{2} \log{\left(x \right)}^{3} + \frac{3 x^{2} \log{\left(x \right)}^{2}}{2} - \frac{3 x^{2} \log{\left(x \right)}}{2} + \frac{3 x^{2}}{4}\right)$
Now simplify:

$\frac{t x^{2} \cdot \left(2 \log{\left(x \right)}^{4} - 4 \log{\left(x \right)}^{3} + 6 \log{\left(x \right)}^{2} - 6 \log{\left(x \right)} + 3\right)}{4}$
Add the constant of integration:

$\frac{t x^{2} \cdot \left(2 \log{\left(x \right)}^{4} - 4 \log{\left(x \right)}^{3} + 6 \log{\left(x \right)}^{2} - 6 \log{\left(x \right)} + 3\right)}{4}+ \mathrm{constant}$

The answer is:

$\frac{t x^{2} \cdot \left(2 \log{\left(x \right)}^{4} - 4 \log{\left(x \right)}^{3} + 6 \log{\left(x \right)}^{2} - 6 \log{\left(x \right)} + 3\right)}{4}+ \mathrm{constant}$

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      /
/

$$\int t x \left(\log{\left(x \right)}^{2}\right)^{2}\, dx = C + t \left(\frac{x^{2} \log{\left(x \right)}^{4}}{2} - x^{2} \log{\left(x \right)}^{3} + \frac{3 x^{2} \log{\left(x \right)}^{2}}{2} - \frac{3 x^{2} \log{\left(x \right)}}{2} + \frac{3 x^{2}}{4}\right)$$

Simplify

The answer [src]

3*t
---
 4

$$\frac{3 t}{4}$$

3*t
---
 4

$$\frac{3 t}{4}$$

Упростить

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

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Identical expressions

Similar expressions

Integral of sqrtx(lnx^2) dx

Limits of integration:

The graph:

Piecewise:

The solution