Let Q(x) =n∏k=1(the product of k=1 to n of) (x-αk)a polynomial of degree n, where αi ≠αj if i ≠j.Verify the following formula: ∫dx/Q(X)= n Σk=1 (the sum of k=1 to n of) (ln(x-αk))/Q'(αk) note: use the principle of mathematical induction to demonstrate equality and do not use numerical examples.
Let Q(x) =n∏k=1(the product of k=1 to n of) (x-αk)a polynomial of degree n, where αi ≠αj if i ≠j.Verify the following formula: ∫dx/Q(X)= n Σk=1 (the sum of k=1 to n of) (ln(x-αk))/Q'(αk) note: use the principle of mathematical induction to demonstrate equality and do not use numerical examples.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Let Q(x) =n∏k=1(the product of k=1 to n of) (x-αk)a polynomial of degree n, where αi ≠αj if i ≠j.Verify the following formula:
∫dx/Q(X)= n Σk=1 (the sum of k=1 to n of) (ln(x-αk))/Q'(αk)
note: use the principle of mathematical induction to demonstrate equality and do not use numerical examples.
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