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

Integral of 1/(3x-4) dx

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src] 
  1             
  /             
 |              
 |       1      
 |  1*------- dx
 |    3*x - 4   
 |              
/               
0
∫011⋅13x−4 dx\int\limits_{0}^{1} 1 \cdot \frac{1}{3 x - 4}\, dx
Simplify
Detail solution

  1. Let u=3x−4u = 3 x - 4.

    Then let du=3dxdu = 3 dx and substitute du3\frac{du}{3}:

    ∫19u du\int \frac{1}{9 u}\, du

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

      ∫13u du=∫1u du3\int \frac{1}{3 u}\, du = \frac{\int \frac{1}{u}\, du}{3}

      1. The integral of 1u\frac{1}{u} is log⁡(u)\log{\left(u \right)}.

      So, the result is: log⁡(u)3\frac{\log{\left(u \right)}}{3}

    Now substitute uu back in:

    log⁡(3x−4)3\frac{\log{\left(3 x - 4 \right)}}{3}

  2. Now simplify:

    log⁡(3x−4)3\frac{\log{\left(3 x - 4 \right)}}{3}

  3. Add the constant of integration:

    log⁡(3x−4)3+constant\frac{\log{\left(3 x - 4 \right)}}{3}+ \mathrm{constant}

The answer is:

log⁡(3x−4)3+constant\frac{\log{\left(3 x - 4 \right)}}{3}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                               
 |                                
 |      1             log(3*x - 4)
 | 1*------- dx = C + ------------
 |   3*x - 4               3      
 |                                
/
log⁡(3 x−4)3{{\log \left(3\,x-4\right)}\over{3}}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.90-2.00.0
Plot the graph f(x)
The answer [src] 
-log(4) 
--------
   3
−log⁡43-{{\log 4}\over{3}} 
=
= 
-log(4) 
--------
   3
−log⁡(4)3- \frac{\log{\left(4 \right)}}{3}
Simplify
Numerical answer [src] 
-0.462098120373297
-0.462098120373297
The graph
Integral of 1/(3x-4) dx

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

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