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Math Help - Integration...Please check my solution

  1. #1
    Newbie
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    Mar 2010
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    Integration...Please check my solution

    Hi ,
    Could you please help me with Integration : [sec sqrt(x)]^2 / 2 sqrt (x) ( 1+[tan sqrt(x)]^2]

    First i simplified it :
    sec sqrt(x)]^2 is equivalent to 1+[tan sqrt(x)]^2] I cancel them out.
    1/2 sqrt(x) would remain.
    Then the integration is equal to :
    1/2 Integral x^ -1/2
    The final answer is :
    ( x^1/2)
    Please let me know if my answer is correct.
    I would really appreciate it if you show me the correct solution.
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  2. #2
    Super Member

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    Lexington, MA (USA)
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    Hello, alireza64851

    \int \frac{\sec^2\!\sqrt{x} }{2\sqrt{x}(1+\tan^2\!\sqrt{x})}\,dx


    First i simplified it :

    . . \sec^2\!\sqrt{x} \:=\:1+\tan^2\!\sqrt{x} . . . I cancelled them out.

    Then: . \frac{1}{2\sqrt{x}} would remain.

    Then the integration is equal to: . \tfrac{1}{2}\int x^{-\frac{1}{2}}dx

    The final answer is: . x^{\frac{1}{2}} + C

    Please let me know if my answer is correct.

    Absolutely correct! . . . Nice work!

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