Question

integrate

[(tanx)1/2/sinxcosx ]dx

Answer 1

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SOLUTION:--

multiply the denominator and numerator by cosx. 

take the cosx in numerator as a sub-denominator to the present denominator. 

and multiply the the other cosx to the present cosx  making it cos^2 x

  I = tanx ^1/2  /     sinx/cosx . cos^2x dx  ( changing cos to sec )

= tanx ^1/2 / tanx   x      sec^2x   dx( cutting tanx )

= sec^2x / tanx dx

take tanx = t

then sec^2x . dx . = dt  therefore subsitutuing the values ... I = integral dt / t = log t + c = log (tanx ) + c  

Answer 2

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