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Integration of 2cosx-sinx/2sinx+cosx

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Integration of 2cosx-sinx/2sinx+cosx

    • Posted by Anshika Kumari 4 years, 2 months ago

    CBSE > Class 12 > Mathematics
    • 2 answers

    Suryakant Swain 4 years, 2 months ago

    -ln|2sinx+cosx|+c

    0Thank You

    Xyz .. 4 years, 2 months ago

    Take (2sinx + cosx) = t Differentiate both side w.r.t x d/dx(2sinx + cosx)=d/dx(t) 》2cosx - sinx = dt/dx 》》dx= dt/2cosx - sinx Now  I= ∫(2cosx - sinx/2sinx + cosx) dx This can be written as: I=  ∫(2cosx - sinx/t) dt/2cosx - sinx =  ∫1/t dt = log|t|+C = log|2sinx + cosx| +C

    2Thank You

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