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

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

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The solution

You have entered [src] 
  1         
  /         
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 |   -1     
 |  ----- dx
 |  x + 1   
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0
∫01(−1x+1) dx\int\limits_{0}^{1} \left(- \frac{1}{x + 1}\right)\, dx 
Integral(-1/(x + 1), (x, 0, 1))
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] 
  /                         
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 |  -1                      
 | ----- dx = C - log(x + 1)
 | x + 1                    
 |                          
/
−log⁡(x+1)-\log \left(x+1\right)
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.901-2
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+1) dx

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

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