Integral of xln(4)x dx

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 |  x*log(4)*x dx
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$$\int\limits_{0}^{1} x x \log{\left(4 \right)}\, dx$$

Integral((x*log(4))*x, (x, 0, 1))

Detail solution

Rewrite the integrand:

$x x \log{\left(4 \right)} = 2 x^{2} \log{\left(2 \right)}$
The integral of a constant times a function is the constant times the integral of the function:

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

$\frac{2 x^{3} \log{\left(2 \right)}}{3}+ \mathrm{constant}$

The answer is:

$\frac{2 x^{3} \log{\left(2 \right)}}{3}+ \mathrm{constant}$

The answer (Indefinite) [src]

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

2*log(2)
--------
   3

$$\frac{2 \log{\left(2 \right)}}{3}$$

2*log(2)
--------
   3

$$\frac{2 \log{\left(2 \right)}}{3}$$

2*log(2)/3

Numerical answer [src]

0.462098120373297

0.462098120373297

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