If I_n denotes

MATHEMATICS · Subjective · A Level · Mathematics · Integration · Integration

Problem

If InI_n denotes ∫zne1/zdz\int z^n e^{1/z} dz , then show that (n+1)!In=I0+e1/z(1!z2+2!z3+...+n!zn+1)(n+1)! I_n = I_0 + e^{1/z} (1! z^2 + 2! z^3 + ... + n! z^{n+1}) .

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