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# Integrate step by step solution in Wolfram|Alpha

Posted 10 years ago
 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?
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Posted 10 years ago
 In:= Integrate[x^2 Exp[x*y], {x, 0, 1}, {y, 0, 2}]  Out= 1/4 (-1 + E^2)  In:= i1 = Integrate[x^2 Exp[x*y], {y, 0, 2}]  Out= (-1 + E^(2 x)) x  In:= Integrate[i1, {x, 0, 1}]Out= 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 dxFor 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)  dxFor the integrand e^(2 x), substitute u = 2 x and  du = 2  dx:  =  1/2 e^(2 x) x-1/4 integral e^u  duThe integral of e^u is e^u:  =  1/2 e^(2 x) x-e^u/4+constantSubstitute back for u = 2 x:  =  1/2 e^(2 x) x-e^(2 x)/4+constantWhich is equal to:Answer: |  |   =  1/4 e^(2 x) (2 x-1)+constantI wasn't joking when I said "Integrate by Parts"
Posted 10 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 10 years ago
 When in doubt, integrate by parts.
Posted 10 years ago
 How can the upper limit of x be x/2 ?
Posted 10 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 thesolution of integral equation step by step? Not only the final solution. If yes, how to do it?