Mister Exam

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Integral of d{x}:
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Integral of dx/sinxcosx
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Integral of 1/(1-cos(x))
Identical expressions
x(inx)^ two / one
x(inx) squared divide by 1
x(inx) to the power of two divide by one
x(inx)2/1
xinx2/1
x(inx)²/1
x(inx) to the power of 2/1
xinx^2/1
x(inx)^2 divide by 1
x(inx)^2/1dx

Integral of x(inx)^2/1 dx

The solution

You have entered [src]

 oo             
  /             
 |              
 |       2      
 |  x*log (x)   
 |  --------- dx
 |      1       
 |              
/               
E

$$\int\limits_{e}^{\infty} \frac{x \log{\left(x \right)}^{2}}{1}\, dx$$

Integral((x*log(x)^2)/1, (x, E, oo))

Detail solution

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

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

$\frac{x^{2} \left(2 \log{\left(x \right)}^{2} - 2 \log{\left(x \right)} + 1\right)}{4}$
Add the constant of integration:

$\frac{x^{2} \left(2 \log{\left(x \right)}^{2} - 2 \log{\left(x \right)} + 1\right)}{4}+ \mathrm{constant}$

The answer is:

$\frac{x^{2} \left(2 \log{\left(x \right)}^{2} - 2 \log{\left(x \right)} + 1\right)}{4}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                              
 |                                               
 |      2              2    2    2       2       
 | x*log (x)          x    x *log (x)   x *log(x)
 | --------- dx = C + -- + ---------- - ---------
 |     1              4        2            2    
 |                                               
/

$$\int \frac{x \log{\left(x \right)}^{2}}{1}\, dx = C + \frac{x^{2} \log{\left(x \right)}^{2}}{2} - \frac{x^{2} \log{\left(x \right)}}{2} + \frac{x^{2}}{4}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

oo

$$\infty$$

oo

$$\infty$$

oo

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

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Identical expressions

Integral of x(inx)^2/1 dx

Limits of integration:

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Piecewise:

The solution