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Integrate (tan x)^1/2

Asked by Soham 19th March 2018, 12:26 AM
Answered by Expert
Answer:
begin mathsize 16px style straight I equals integral square root of tanx dx
Put space tanx equals straight t squared
straight x equals tan to the power of negative 1 end exponent straight t squared
dx equals fraction numerator 1 over denominator 1 plus straight t to the power of 4 end fraction cross times 2 tdt
straight I equals integral square root of straight t squared end root space cross times fraction numerator 2 straight t over denominator 1 plus straight t to the power of 4 end fraction dt
straight I equals integral fraction numerator 2 straight t squared over denominator 1 plus straight t to the power of 4 end fraction dt
straight I equals integral fraction numerator straight t squared plus 1 plus straight t squared minus 1 over denominator 1 plus straight t to the power of 4 end fraction dt
straight I equals integral open parentheses fraction numerator straight t squared plus 1 over denominator straight t to the power of 4 plus 1 end fraction plus fraction numerator straight t squared minus 1 over denominator straight t to the power of 4 plus 1 end fraction close parentheses dt
straight I equals integral open parentheses fraction numerator 1 plus begin display style 1 over straight t squared end style over denominator straight t squared plus begin display style 1 over straight t squared end style end fraction plus fraction numerator 1 minus begin display style 1 over straight t squared end style over denominator straight t squared plus begin display style 1 over straight t squared end style end fraction close parentheses dt
Take space straight t minus 1 over straight t equals straight y space for space the space first space integral space and space straight t plus 1 over straight t equals straight z space for space the space second space integral.
Solve space it space further. space
end style
Answered by Expert 19th March 2018, 10:02 AM
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