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-1/t
Solving integrals/ -1/t

Integral of -1/t dt

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src] 
  1       
  /       
 |        
 |  -1    
 |  --- dt
 |   t    
 |        
/         
0
∫01(−1t) dt\int\limits_{0}^{1} \left(- \frac{1}{t}\right)\, dt 
Integral(-1/t, (t, 0, 1))
Detail solution

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

    ∫(−1t) dt=−∫1t dt\int \left(- \frac{1}{t}\right)\, dt = - \int \frac{1}{t}\, dt

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

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

  2. Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src] 
  /                   
 |                    
 | -1                 
 | --- dt = C - log(t)
 |  t                 
 |                    
/
∫(−1t) dt=C−log⁡(t)\int \left(- \frac{1}{t}\right)\, dt = C - \log{\left(t \right)}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.90-1000010000
Plot the graph f(x)
The answer [src] 
-oo
−∞-\infty 
=
= 
-oo
−∞-\infty 
-oo
Numerical answer [src] 
-44.0904461339929
-44.0904461339929
The graph
Integral of -1/t dt

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

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