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Solving integrals/ x/exp3x^2+4

Integral of x/exp3x^2+4 dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                 
  /                 
 |                  
 |  /   x       \   
 |  |------- + 4| dx
 |  |      2    |   
 |  |/ 3*x\     |   
 |  \\e   /     /   
 |                  
/                   
0
∫01(x(e3x)2+4) dx\int\limits_{0}^{1} \left(\frac{x}{\left(e^{3 x}\right)^{2}} + 4\right)\, dx 
Integral(x/exp(3*x)^2 + 4, (x, 0, 1))
Detail solution

  1. Integrate term-by-term:

    1. Don't know the steps in finding this integral.

      But the integral is

      (−6x−1)e−6x36\frac{\left(- 6 x - 1\right) e^{- 6 x}}{36}

    1. The integral of a constant is the constant times the variable of integration:

      ∫4 dx=4x\int 4\, dx = 4 x

    The result is: 4x+(−6x−1)e−6x364 x + \frac{\left(- 6 x - 1\right) e^{- 6 x}}{36}

  2. Now simplify:

    (144xe6x−6x−1)e−6x36\frac{\left(144 x e^{6 x} - 6 x - 1\right) e^{- 6 x}}{36}

  3. Add the constant of integration:

    (144xe6x−6x−1)e−6x36+constant\frac{\left(144 x e^{6 x} - 6 x - 1\right) e^{- 6 x}}{36}+ \mathrm{constant}

The answer is:

(144xe6x−6x−1)e−6x36+constant\frac{\left(144 x e^{6 x} - 6 x - 1\right) e^{- 6 x}}{36}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                                             
 |                                          -6*x
 | /   x       \                (-1 - 6*x)*e    
 | |------- + 4| dx = C + 4*x + ----------------
 | |      2    |                       36       
 | |/ 3*x\     |                                
 | \\e   /     /                                
 |                                              
/
∫(x(e3x)2+4) dx=C+4x+(−6x−1)e−6x36\int \left(\frac{x}{\left(e^{3 x}\right)^{2}} + 4\right)\, dx = C + 4 x + \frac{\left(- 6 x - 1\right) e^{- 6 x}}{36}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.905-5
Plot the graph f(x)
The answer [src] 
         -6
145   7*e  
--- - -----
 36     36
14536−736e6\frac{145}{36} - \frac{7}{36 e^{6}} 
=
= 
         -6
145   7*e  
--- - -----
 36     36
14536−736e6\frac{145}{36} - \frac{7}{36 e^{6}} 
145/36 - 7*exp(-6)/36
Numerical answer [src] 
4.02729579818787
4.02729579818787

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

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