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  • Integrate the functions in Exercises 1 to 24. 16 e^3 logx (x^4 + 1)^-1

Integrate the functions in Exercises 1 to 24.

    Q16.    e^{3\log x} (x^4 + 1)^{-1}

Answers (1)

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Given the function to be integrated as

e^{3\log x} (x^4 + 1)^{-1}
= e^{\log x^3}(x^4 + 1)^{-1} = \frac{x^3}{x^4 + 1}

Let I = \int e^{3\log x} (x^4 + 1)^{-1}

Let x^4 = t \implies 4x^3 dx = dt

I = \int e^{3\log x} (x^4 + 1)^{-1} = \int \frac{x^3}{x^4 + 1}

\implies I = \frac{1}{4}\log(x^4 +1) + C

Posted by

HARSH KANKARIA

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