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dy/e^y
Solving integrals/ dy/e^y

Integral of dy/e^y dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1      
  /      
 |       
 |  1    
 |  -- dy
 |   y   
 |  E    
 |       
/        
0
∫011ey dy\int\limits_{0}^{1} \frac{1}{e^{y}}\, dy 
Integral(1/(E^y), (y, 0, 1))
Detail solution

  1. Let u=eyu = e^{y}.

    Then let du=eydydu = e^{y} dy and substitute dudu:

    ∫1u2 du\int \frac{1}{u^{2}}\, du

    1. The integral of unu^{n} is un+1n+1\frac{u^{n + 1}}{n + 1} when n≠−1n \neq -1:

      ∫1u2 du=−1u\int \frac{1}{u^{2}}\, du = - \frac{1}{u}

    Now substitute uu back in:

    −e−y- e^{- y}

  2. Add the constant of integration:

    −e−y+constant- e^{- y}+ \mathrm{constant}

The answer is:

−e−y+constant- e^{- y}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /               
 |                
 | 1            -y
 | -- dy = C - e  
 |  y             
 | E              
 |                
/
∫1ey dy=C−e−y\int \frac{1}{e^{y}}\, dy = C - e^{- y}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.902-2
Plot the graph f(x)
The answer [src] 
     -1
1 - e
1−e−11 - e^{-1} 
=
= 
     -1
1 - e
1−e−11 - e^{-1} 
1 - exp(-1)
Numerical answer [src] 
0.632120558828558
0.632120558828558
The graph
Integral of dy/e^y dx

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

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