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Identical expressions
t^2ln(x)dt
t squared ln(x)dt
t2ln(x)dt
t2lnxdt
t²ln(x)dt
t to the power of 2ln(x)dt
t^2lnxdt
t^2ln(x)dtdx

Integral of t^2ln(x)dt dx

The solution

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  1             
  /             
 |              
 |   2          
 |  t *log(x) dt
 |              
/               
0

$$\int\limits_{0}^{1} t^{2} \log{\left(x \right)}\, dt$$

Integral(t^2*log(x), (t, 0, 1))

Detail solution

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

$\int t^{2} \log{\left(x \right)}\, dt = \log{\left(x \right)} \int t^{2}\, dt$
1. The integral of $t^{n}$ is $\frac{t^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int t^{2}\, dt = \frac{t^{3}}{3}$
So, the result is: $\frac{t^{3} \log{\left(x \right)}}{3}$
Add the constant of integration:

$\frac{t^{3} \log{\left(x \right)}}{3}+ \mathrm{constant}$

The answer is:

$\frac{t^{3} \log{\left(x \right)}}{3}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                            
 |                     3       
 |  2                 t *log(x)
 | t *log(x) dt = C + ---------
 |                        3    
/

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

Simplify

The answer [src]

log(x)
------
  3

$$\frac{\log{\left(x \right)}}{3}$$

log(x)
------
  3

$$\frac{\log{\left(x \right)}}{3}$$

log(x)/3

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

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Identical expressions

Integral of t^2ln(x)dt dx

Limits of integration:

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Piecewise:

The solution