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Integartiondx/3sinx+cosx+2

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Integartiondx/3sinx+cosx+2

    • Posted by Azhar Uddin 4 years, 4 months ago

    CBSE > Class 12 > Mathematics
    • 1 answers

    8D Bass Nation 4 years, 4 months ago

    I = ʃ dx / (2sin x + cos x + 3) = ʃ dx / [2(sin x + 1) + (cos x + 1)] = ʃ dx / [2{cos (x / 2) + sin (x / 2)}^2 + 2 {cos (x / 2)}^2] = (1 / 2)*ʃ dx / [{cos (x / 2) + sin (x / 2)}^2 + {cos (x / 2)}^2] = (1 / 2)*ʃ {sec (x / 2)^2}*dx / [1 + [1 + {tan (x / 2)}^2]] Multiplying both numerator and denominator by {sec (x/2)^2}. Let, z = [1 + tan (x/2)]; so, dz = (1 / 2)*[{sec (x/2)}^2]*dx So, I = ʃ dz / {1 + (z^2)} = tan -1 z + K = tan -1 {1 + tan (x / 2)} + K

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