Word Count : 359

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हमारे पास दिया है: $$ I_{m,n} = \int x^m (\log x)^n \, dx $$ इसे आंशिक समाकलन (integration by parts) से हल किया जा सकता है। चरण 1: आंशिक समाकलन लागू करें आंशिक समाकलन का नियम है: $$ \int u \, dv = uv - \int v \, du $$ यहाँ हम चुनते हैं: $$ u = (\log x)^n \implies du = n (\log x)^{n-1} \frac{dx}{x} $$ $$ dv = x^m dx \implies v = \frac{x^{m+1}}{m+1} \quad (m \neq -1) $$ इसे नियम में डालते हैं: $$ I_{m,n} = __________ ____ ______ _______ ______ __________.
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