Question

please answer my ques​

Answer 1

find the answer in the attachment

Answer 2

Answer:

We need    ∫logxdx  

It can be done by using integration by parts,

i.e.,  ∫udv=uv−∫vdu  

By ILATE, log function should have more priority than algebraic function,

So,  u=logx,  

dv=dx⇒v=x  

So,  ∫logxdx=logx.(x)−∫x.(logx)′  

⇒xlogx−∫x.1xdx  

⇒xlogx−∫dx  

⇒xlogx−x+C  

∴∫logxdx=xlogx−x+C  

Where  C  is the integration constant.

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