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November 27th, 2017, 12:07 PM  #1 
Newbie Joined: Nov 2017 From: San Diego Posts: 1 Thanks: 0  How to solve this integral without Jacobian method?
How to solve this integral without Jacobian method?

November 27th, 2017, 01:42 PM  #2 
Senior Member Joined: Feb 2016 From: Australia Posts: 1,830 Thanks: 648 Math Focus: Yet to find out. 
It might be useful to typeset your equations to improve readability. Could you confirm if the following translation is correct (I can't tell if that's an $n$ or an $x$ in the numerator of the exponential..)? $$\int_{2}^{1} \int_{0}^{y+2} \exp \left({\dfrac{x + y}{x  y}}\right) dx \ dy$$ 
November 28th, 2017, 03:48 AM  #3 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 
Looking at the integrand, I would be inclined to let u= x y. Then x= u+ y so that dx= du and x+ y= u+ 2y. When x= 0, u= y and when x= y+ 2, u= 2. The integral becomes $\displaystyle \int_{2}^{1}\int_y^2 \frac{u+ 2y}{u}dudy= \int_{2}^{1}\int_y^2 1+ 2\frac{y}{u} dudy$. 

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integral, jacobian, method, mrthod, solve 
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