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4/(3x-1)^3
Solving integrals/ 4/(3x-1)^3

Integral of 4/(3x-1)^3 dx

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src] 
  1              
  /              
 |               
 |      4        
 |  ---------- dx
 |           3   
 |  (3*x - 1)    
 |               
/                
0
∫014(3x−1)3 dx\int\limits_{0}^{1} \frac{4}{\left(3 x - 1\right)^{3}}\, dx 
Integral(4/((3*x - 1*1)^3), (x, 0, 1))
Detail solution

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

    ∫4(3x−1)3 dx=4∫1(3x−1)3 dx\int \frac{4}{\left(3 x - 1\right)^{3}}\, dx = 4 \int \frac{1}{\left(3 x - 1\right)^{3}}\, dx

    1. Don't know the steps in finding this integral.

      But the integral is

      −154x2−36x+6- \frac{1}{54 x^{2} - 36 x + 6}

    So, the result is: −454x2−36x+6- \frac{4}{54 x^{2} - 36 x + 6}

  2. Now simplify:

    −227x2−18x+3- \frac{2}{27 x^{2} - 18 x + 3}

  3. Add the constant of integration:

    −227x2−18x+3+constant- \frac{2}{27 x^{2} - 18 x + 3}+ \mathrm{constant}

The answer is:

−227x2−18x+3+constant- \frac{2}{27 x^{2} - 18 x + 3}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                                    
 |                                     
 |     4                      4        
 | ---------- dx = C - ----------------
 |          3                         2
 | (3*x - 1)           6 - 36*x + 54*x 
 |                                     
/
−23 (3 x−1)2-{{2}\over{3\,\left(3\,x-1\right)^2}}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.90-50000000000005000000000000
Plot the graph f(x)
The answer [src] 
nan
12{{1}\over{2}} 
=
= 
nan
NaN\text{NaN}
Simplify
Numerical answer [src] 
1898216623.51506
1898216623.51506
The graph
Integral of 4/(3x-1)^3 dx

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

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