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x*2^(3x-1)
Solving integrals/ x*2^(3x-1)

Integral of x*2^(3x-1) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1              
  /              
 |               
 |     3*x - 1   
 |  x*2        dx
 |               
/                
0
$$\int\limits_{0}^{1} 2^{3 x - 1} x\, dx$$ 
Integral(x*2^(3*x - 1*1), (x, 0, 1))
Detail solution

  1. Rewrite the integrand:

  2. 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:

  3. Now simplify:

  4. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                          
 |                      3*x                  
 |    3*x - 1          2   *(-1 + 3*x*log(2))
 | x*2        dx = C + ----------------------
 |                                 2         
/                            18*log (2)
$${{\left(3\,\log 2\,x-1\right)\,e^{3\,\log 2\,x}}\over{18\,\left( \log 2\right)^2}}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
    1        4*(-1 + 3*log(2))
---------- + -----------------
      2               2       
18*log (2)       9*log (2)
$${{12\,\log 2-4}\over{9\,\left(\log 2\right)^2}}+{{1}\over{18\, \left(\log 2\right)^2}}$$ 
=
= 
    1        4*(-1 + 3*log(2))
---------- + -----------------
      2               2       
18*log (2)       9*log (2)
$$\frac{1}{18 \log{\left(2 \right)}^{2}} + \frac{4 \left(-1 + 3 \log{\left(2 \right)}\right)}{9 \log{\left(2 \right)}^{2}}$$
Simplify
Numerical answer [src] 
1.11417211746088
1.11417211746088
The graph
Integral of x*2^(3x-1) dx

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

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