Solving closed-form solution of integral by Matlab!!!

Let a, b, and c are constants. How to solve the closed-form solution of the following integral by Matlab from 0 to infinity

1/(1+y)*1/(a+y)*1/(b+y)*exp(-cy)

Thanks in advance for your kind cooperation

[Steven Lord]

What makes you sure that such a closed-form solution exists?

Consider substituting values in for a, b, and c then numerically integrating using integral.

[Walter Roberson]

Are there any constraints on the constants? Real-valued? Non-negative?

[Walter Roberson]

Under the assumption that none of the values are negative,

(exp(c*a)*(b-1)*Ei(1, c*a)-exp(c*b)*(a-1)*Ei(1, c*b)+exp(c)*Ei(1, c)*(a-b))/((b-1)*(a-1)*(a-b))

where Ei is the Exponential Integral

Answer 1

[David Goodmanson]

Hi kader, This depends on what you consider to be closed form. I assume the factor in front is 1/[(1+y)(a+y)(b+y)]. You can solve for constants F,A,B in partial fractions

1/((1+y)(a+y)(b+y)) = F/(1+y) +A/(a+y) +B/(b+y)

Then e.g,

   A Int{0,inf} exp(-cy)/(a+y) dy
 = A exp(ac) Int{ac,inf} exp(-z)/z dz
 = A exp(ac) E1(ac)

where E1 is the exponential integral, which Matlab has.