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Integral of t*exp(-t/2) dt

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
 oo          
  /          
 |           
 |     -t    
 |     ---   
 |      2    
 |  t*e    dt
 |           
/            
0            
$$\int\limits_{0}^{\infty} t e^{\frac{\left(-1\right) t}{2}}\, dt$$
Integral(t*exp((-t)/2), (t, 0, oo))
Detail solution
  1. Use integration by parts:

    Let and let .

    Then .

    To find :

    1. Let .

      Then let and substitute :

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

        1. The integral of the exponential function is itself.

        So, the result is:

      Now substitute back in:

    Now evaluate the sub-integral.

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

    1. Let .

      Then let and substitute :

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

        1. The integral of the exponential function is itself.

        So, the result is:

      Now substitute back in:

    So, the result is:

  3. Now simplify:

  4. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                 
 |                                  
 |    -t              -t         -t 
 |    ---             ---        ---
 |     2               2          2 
 | t*e    dt = C - 4*e    - 2*t*e   
 |                                  
/                                   
$$\int t e^{\frac{\left(-1\right) t}{2}}\, dt = C - 2 t e^{- \frac{t}{2}} - 4 e^{- \frac{t}{2}}$$
The graph
The answer [src]
4
$$4$$
=
=
4
$$4$$
4

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