_{[0 ]}^{[pie/2 ]} log(tanx).dx

 

 

_{[0 ]}^{[ pie/2]} logsinx -_{[ 0]}^{[ pie/2]} logcosx

 

 

_{[ 0]}^{[ pie/2]} log sin(pi/2-x) - _{[0 ]}^{[ pi/2]} logcosx

 

 

_{[ ]}^{[ ]} log cosx -_{[ ]}^{[ ]} log cosx

 

this is using propeties of defenite integrals then we get the ans

as

answer is 0

 

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