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Question ∫ x^(n)x^(m)e^(-x) from the range [0, infinity] My question is how to solve this integral? also, when i type it into an integral calculator i get the answer: −Γ(m+n+1,x) what does this represent and how do i use this? the reason im doing this integral is because of this problem;  Construct from the set (x^n); n = 0, 1, …..; using the Gram-Schmidt process, the first five orthogonal polynomials, Ln (x) ; n = 0; 1; 2; 3; 4, where the weight function is w (x) = e^(-x) and the range of variable x is [0; infinity]. Let the coefficient of the highest power of x be (-1)^(n) / n! and normalize the polynomials to 1.

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Question

∫ x^(n)x^(m)e^(-x) from the range [0, infinity]
My

question is how to solve this integral?

also, when i type it into an integral calculator i get the answer: −Γ(m+n+1,x) what does this represent and how do i use this?

the reason im doing this integral is because of this problem;

 Construct from the set (x^n); n = 0, 1, …..; using the Gram-Schmidt process, the first five orthogonal polynomials, Ln (x) ; n = 0; 1; 2; 3; 4, where the weight function is w (x) = e^(-x) and the range of variable x is [0; infinity]. Let the coefficient of the highest power of x be (-1)^(n) / n! and normalize the polynomials to 1. 

 
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