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Math Help - Definite Integral

  1. #1
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    Definite Integral

    integral dx/1+(tanx)^sqrt(2) from x=0 to x=pi/2
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  2. #2
    Senior Member pankaj's Avatar
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    I=\int_{0}^{\frac{\pi}{2}}\frac{dx}{1+tan^{\sqrt{2  }}x}

    I=\int_{0}^{\frac{\pi}{2}}\frac{dx}{1+tan^{\sqrt{2  }}\big(\frac{\pi}{2}-x\big)}=\int_{0}^{\frac{\pi}{2}}\frac{dx}{1+cot^{\  sqrt{2}}x}=\int_{0}^{\frac{\pi}{2}}\frac{\tan^{\sq  rt{2}} x dx}{1+tan^{\sqrt{2}}x}

    Thus

    2I=\int_{0}^{\frac{\pi}{2}}1 dx=\frac{\pi}{2}

    I=\frac{\pi}{4}
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