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Integrate step by step solution in Wolfram|Alpha

Posted 9 years ago
5 Replies
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Hello i would like to get a step by step solution to this  integrate x^2[e^(x*y)]dx dy, x=0 to x/2, y=0 to 2 but i cant find the way how to do it..Im using WolframAlpha to my mobile.Any ideas?
POSTED BY: Loukas Pyrg
5 Replies
 In[1]:= Integrate[x^2 Exp[x*y], {x, 0, 1}, {y, 0, 2}]
 Out[1]= 1/4 (-1 + E^2)
 In[2]:= i1 = Integrate[x^2 Exp[x*y], {y, 0, 2}]
 Out[2]= (-1 + E^(2 x)) x
 In[3]:= Integrate[i1, {x, 0, 1}]

Out[3]= 1/4 (-1 + E^2)
The only hard integral is x*exp(2*x) which Wolfram Alpha can show step by step:
Take the integral:
integral e^(2 x) x dx
For the integrand e^(2 x) x, integrate by parts,  integral f dg = f g- integral g df, where
f = x,     dg = e^(2 x)  dx,
df =   dx,     g = e^(2 x)/2:
  =  1/2 e^(2 x) x-1/2 integral e^(2 x)  dx
For the integrand e^(2 x), substitute u = 2 x and  du = 2  dx:
  =  1/2 e^(2 x) x-1/4 integral e^u  du
The integral of e^u is e^u:
  =  1/2 e^(2 x) x-e^u/4+constant
Substitute back for u = 2 x:
  =  1/2 e^(2 x) x-e^(2 x)/4+constant
Which is equal to:
Answer: | 
|   =  1/4 e^(2 x) (2 x-1)+constant

I wasn't joking when I said "Integrate by Parts"
POSTED BY: Frank Kampas
Posted 9 years ago
Mathematica and WolframAlpha use very powerful and complicated methods to integrate.
The methods used do not have any steps that a student would use or understand.
There is no way to display the steps used.
POSTED BY: Bill Simpson
When in doubt, integrate by parts.
POSTED BY: Frank Kampas
How can the upper limit of x be x/2 ?
POSTED BY: Frank Kampas
Posted 9 years ago
ok lets say that we have to solve this   integrate x^2[e^(x*y)]dx dy, x=0 to 1, y=0 to 2  Is it possible to display in WolframAlpha the
solution of integral equation step by step? Not only the final solution. If yes, how to do it?
POSTED BY: Loukas Pyrg
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