MathematicsFill in the blank:On integration, the function cotxlog sinx   becomes ____

Fill in the blank:


On integration, the function cotxlog sinx   becomes ____


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    Solution:

    The correct answer is: Let f x =cotxlog sinx  
    On integration,
    f x =cotxlog sinx dx  
    Let log(sinx)=t  
    On differentiation,
    d dx log sinx = dt dx 1 sinx .cosx= dt dx dt dx =cotx dt=cotx.dx  
    Using the above equations,
    f x dx=cotxlog sinx dx f x dx= log sinx cotxdx f x dx=tdt  
    f x dx= t 2 2 +C f x dx= log sinx 2 2 +C cotxlog(sinx)= log sinx 2 2 +C  
     
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