Mister Exam

Other calculators

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

Integral of (-1)/(x-1) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  4         
  /         
 |          
 |   -1     
 |  ----- dx
 |  x - 1   
 |          
/           
3
∫34(−1x−1) dx\int\limits_{3}^{4} \left(- \frac{1}{x - 1}\right)\, dx 
Integral(-1/(x - 1), (x, 3, 4))
Detail solution

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

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

    1. Let u=x−1u = x - 1.

      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−1)\log{\left(x - 1 \right)}

    So, the result is: −log⁡(x−1)- \log{\left(x - 1 \right)}

  2. Now simplify:

    −log⁡(x−1)- \log{\left(x - 1 \right)}

  3. Add the constant of integration:

    −log⁡(x−1)+constant- \log{\left(x - 1 \right)}+ \mathrm{constant}

The answer is:

−log⁡(x−1)+constant- \log{\left(x - 1 \right)}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                         
 |                          
 |  -1                      
 | ----- dx = C - log(x - 1)
 | x - 1                    
 |                          
/
∫(−1x−1) dx=C−log⁡(x−1)\int \left(- \frac{1}{x - 1}\right)\, dx = C - \log{\left(x - 1 \right)}
Simplify
The graph
3.004.003.103.203.303.403.503.603.703.803.90-2.00.0
Plot the graph f(x)
The answer [src] 
-log(3) + log(2)
−log⁡(3)+log⁡(2)- \log{\left(3 \right)} + \log{\left(2 \right)} 
=
= 
-log(3) + log(2)
−log⁡(3)+log⁡(2)- \log{\left(3 \right)} + \log{\left(2 \right)} 
-log(3) + log(2)
Numerical answer [src] 
-0.405465108108164
-0.405465108108164

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

    © Mister Exam – Calculator