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-0,1/e^xdx
Solving integrals/ -0,1/e^xdx

Integral of -0,1/e^xdx dx

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src] 
 11/5             
   /              
  |               
  |        1      
  |  -1/10*--*1 dx
  |         x     
  |        e      
  |               
 /                
 2/5
∫25115((−110)1ex1) dx\int\limits_{\frac{2}{5}}^{\frac{11}{5}} \left(\left(- \frac{1}{10}\right) \frac{1}{e^{x}} 1\right)\, dx 
Integral(-1/10*1/E^x, (x, 2/5, 11/5))
Detail solution

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

    ∫((−110)1ex1) dx=−∫1ex dx10\int \left(\left(- \frac{1}{10}\right) \frac{1}{e^{x}} 1\right)\, dx = - \frac{\int \frac{1}{e^{x}}\, dx}{10}

    1. Let u=exu = e^{x}.

      Then let du=exdxdu = e^{x} dx 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−x- e^{- x}

    So, the result is: e−x10\frac{e^{- x}}{10}

  2. Add the constant of integration:

    e−x10+constant\frac{e^{- x}}{10}+ \mathrm{constant}

The answer is:

e−x10+constant\frac{e^{- x}}{10}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                       
 |                      -x
 |       1             e  
 | -1/10*--*1 dx = C + ---
 |        x             10
 |       e                
 |                        
/
e−x10{{e^ {- x }}\over{10}}
Simplify
The graph
0.42.20.60.81.01.21.41.61.82.00.1-0.1
Plot the graph f(x)
The answer [src] 
   -2/5    -11/5
  e       e     
- ----- + ------
    10      10
−e−25−e−11510-{{e^ {- {{2}\over{5}} }-e^ {- {{11}\over{5}} }}\over{10}} 
=
= 
   -2/5    -11/5
  e       e     
- ----- + ------
    10      10
−110e25+110e115- \frac{1}{10 e^{\frac{2}{5}}} + \frac{1}{10 e^{\frac{11}{5}}}
Упростить
Numerical answer [src] 
-0.0559516887673305
-0.0559516887673305
The graph
Integral of -0,1/e^xdx dx

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

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