Question

Integration of (log x)/x^2

Answer 1

Answer:

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Step-by-step explanation:

I=∫∞1log(x)x2⋅dx  

Integrating it by parts

=∣∣log(x)∫1x2⋅dx∣∣∞1−∫∞1(1x∫1x2⋅dx)⋅dx

=∣∣∣log(x)∫1x2⋅dx∣∣∣∞1+∫∞11x2⋅dx

=−∣∣∣log(x)1x∣∣∣∞1−∣∣∣1x∣∣∣∞1

=∣∣∣log(x)x∣∣∣1∞+∣∣∣1x∣∣∣1∞

−[log(x)x]x→∞+[log(x)x]x=1−[1x]x→∞+[1x]x=1

=0+0−0+1=1