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Integration of (x-one)/(x^2+one)

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Integration of (x-one)/(x^2+one)

    • Posted by Aman Grewal 3 years, 9 months ago

    CBSE > Class 12 > Mathematics
    • 2 answers

    Twinkle . 3 years, 9 months ago

    (x-1/x²+1)dx = (x/x²+1)dx - (1/x²+1)dx Let (x/x²+1)dx be I1 and (1/x²+1)dx be I2 I2=tan-¹x I1=(x/x²+1)dx Let x²=u 2xdx=du On substitution, I1=(1/2)(1/u+1)du =log|u+1|/2 =log|x²+1|/2 Ans. I1-I2 = log|x²+1|/2 - tan-¹x

    0Thank You

    Adarsh Ninja 3 years, 9 months ago

    1/2 log|x²+1| - tan—¹x

    0Thank You

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