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Integration of√cotx+√tanx

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Integration of√cotx+√tanx

    • Posted by Vaibhav Panchal 4 years, 3 months ago

    CBSE > Class 12 > Mathematics
    • 1 answers

    Gayatri Guntreddi 4 years, 3 months ago

    Write tanx as sinx/cosx and cotx as cosx/sinx I= ✓((sin^2x/sinxcosx) + ✓(cos^2x/sinxcosx))dx I= (sinx+cosx dx)/✓(sinxcosx) sinx-cosx=t (sinx+cosx)dx=dt (sinx-cosx)^2=t^2 1–2sinxcosx=t^2 sinxcosx=(1-t^2)/2 Therefore, I=dt/✓((1-t^2)/2) I=(✓2)sin^-1(t) + C I=(✓2)sin^-1(sinx-cosx) + C

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