Mister Exam

Other calculators

1/(x-2)
Solving integrals/ 1/(x-2)

Integral of 1/(x-2) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1           
  /           
 |            
 |      1     
 |  1*----- dx
 |    x - 2   
 |            
/             
0
∫011⋅1x−2 dx\int\limits_{0}^{1} 1 \cdot \frac{1}{x - 2}\, dx 
Integral(1/(x - 1*2), (x, 0, 1))
Detail solution

  1. Let u=x−2u = x - 2.

    Then let du=dxdu = dx and substitute dudu:

    ∫1u du\int \frac{1}{u}\, du

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

    Now substitute uu back in:

    log⁡(x−2)\log{\left(x - 2 \right)}

  2. Now simplify:

    log⁡(x−2)\log{\left(x - 2 \right)}

  3. Add the constant of integration:

    log⁡(x−2)+constant\log{\left(x - 2 \right)}+ \mathrm{constant}

The answer is:

log⁡(x−2)+constant\log{\left(x - 2 \right)}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                           
 |                            
 |     1                      
 | 1*----- dx = C + log(x - 2)
 |   x - 2                    
 |                            
/
log⁡(x−2)\log \left(x-2\right)
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.90-1.50.0
Plot the graph f(x)
The answer [src] 
-log(2)
−log⁡2-\log 2 
=
= 
-log(2)
−log⁡(2)- \log{\left(2 \right)}
Упростить
Numerical answer [src] 
-0.693147180559945
-0.693147180559945
The graph
Integral of 1/(x-2) dx

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

    © Mister Exam – Calculator