How to integrate : sec^4(x/2) ?

Integrate : sec^4(x/2)

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  • 10 years ago
    Favorite Answer

    ∫ sec^4 (x/2) dx

    = ∫ sec^2 (x/2) * sec^2 (x/2) dx

    = ∫[1 + tan^2 (x/2)] * sec^2 (x/2) dx

    = ∫ sec^2 (x/2) dx + ∫ tan^2 (x/2) * sec^2 (x/2) dx

    = 2tan(x/2) + ∫ tan^2 (x/2) * sec^2 (x/2) dx

    Let tan(x/2) = u for the second integral

    => (1/2) sec^2 (x/2) dx = du

    => sec^2 (x/2) dx = 2du

    => Integral

    = 2tan(x/2) + 2 ∫ u^2 du

    = 2tan(x/2) + (2/3) u^3 + c

    = 2tan(x/2) + (2/3) tan^3 (x/2) + c.

  • 6 years ago

    its 2

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