Question
Evaluate .
Answer :
Word Count : 235
We need to evaluate the integral: \[ I = \int \frac{\ln x}{x^2}dx \] ### Step 1: Use Substitution Let: \[ u = \ln x \] Then, differentiating both sides: \[ du = \frac{dx}{x} \] Rewriting the given integral: \[ I = \int \frac{u}{x^2} dx \] Since \( dx = x \, du \), we express \( x^2 \) __________ ________ _______ _____ _________ _________ _______ ___ _______ _________.
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_________ ______ ______ _______ _______ ___ _________ _____ ______.
_____ _________ _____ _______ __________ ____ ________ ______ ________ _______ ______.
_________ _________ ______ _________ ____ _____.
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We need to evaluate the integral: \[ I = \int \frac{\ln x}{x^2}dx \] ### Step 1: Use Substitution Let: \[ u = \ln x \] Then, differentiating both sides: \[ du = \frac{dx}{x} \] Rewriting the given integral: \[ I = \int \frac{u}{x^2} dx \] Since \( dx = x \, du \), we express \( x^2 \) __________ ________ _______ _____ _________ _________ _______ ___ _______ _________.
__________ ___ _________ _________ ________.
_______ ________ ________ _______ _______ _________ __________ ______ __________.
___ __________ __________ ______ __________ _____ _____ ________ ___ ___.
_________ __________ ___ ___ ____ ___ _______ __________ ___ ________ _________.
______ ________ __________ ______ _________.
_______ _____ ______ _______ ___ __________.
___ _________ ___ _________ __________.
___ _______ ___ ____ ______ _____ ___ __________ __________.
______ _________ _______ __________ _________ ________ ___.
____ _______ ________ _______ ___ ______ ___ _______.
______ _____ _________ _____ ____ ________ ___ _______ _____.
________ ______ ____ _____ ____ _______ __________ ____ _______.
_____ ____ ________ ____ _________ _______ __________ ____ __________ ___ ________ _________.
_________ _______ __________ ________ ____ ___.
_________ ______ ________ ____ ___ ________ _____ _____ ______ ___ ______.
_____ _______ _________ _________ ______ ______ ___.
_______ _____ _____ _____ _______ ___ _____ _____ ____ _________ ______ _______.
_________ ______ ______ _______ _______ ___ _________ _____ ______.
_____ _________ _____ _______ __________ ____ ________ ______ ________ _______ ______.
_________ _________ ______ _________ ____ _____.
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