MHB Shortcuts for Solving Multiple Integrals: Is There a Faster Way?

Click For Summary
Solving multiple integrals can be cumbersome, especially when treating one variable as a constant. The proposed method of rewriting the integrand as 1 - (2x5)/(x1+x2+x3+x4+x5) offers some simplification. However, after initial steps, the process becomes lengthy due to logarithmic functions and integration by parts. The goal is to find a quicker method to solve the integral in 2-3 minutes. Efficient techniques or shortcuts are needed to streamline the process.
DaalChawal
Messages
85
Reaction score
0
1624918141288.png

I'm having a problem solving this, My approach is solving $x_1$ as a variable and rest as constants first and then going on further. But it is getting too lengthy. Is there any short method?
 
Physics news on Phys.org
Would it help writing the integrand as $\displaystyle \begin{align*} 1 - \frac{2\,x_5}{x_1+x_2+x_3+x_4+x_5} \end{align*}$?
 
Yes, it does help but after the first two steps log comes, and then using by parts it becomes quite lengthy. I was looking for a short approach so that this question can be solved in 2-3 minutes. Btw thanks for your help 🙂
 

Similar threads

I Express the limit as a definite integral
Replies
16
Views
4K
I Question about Integrals to Determine Volume vs Surface Area
Replies
5
Views
3K
I Is There a Better Way to Solve Integrals Than Symbolab and Mathematica?
Replies
9
Views
3K
I How to evaluate the enclosed area of this implicit curve?
Replies
2
Views
3K
I The Basic Area Problem (introduction to the topic of integrals)
Replies
24
Views
3K
A Integral of 2 Bessel functions of different orders
Replies
3
Views
2K
I Integration of ##e^{-x^2}## with respect to ##x##
Replies
4
Views
3K
Integrating ##d\psi=(x+y)dx +x_0dy##
Replies
9
Views
2K
I What would a calculus author have to say on ##\int r^2dm##?
Replies
11
Views
2K
MHB Few beginner doubts about differential equations ?
Replies
8
Views
2K