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Integrate the functions{e}^{{{3}{{{x}}}}}{({x}^{{4}}+{1})}^{{-

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Integrate the functions $e^{3 l o g x} (x^{4} + 1)^{- 1}$

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Integrate the functions

e^{3 l o g x} (x^{4} + 1)^{- 1}

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Text solutionVerified

Solution: I

= \int e^{3 l o g x} (x^{2} + 1)^{- 1} d x

= \int e^{l o g x^{3}} \frac{1}{x ^{2} + 1} d x

= \frac{x ^{3}}{x ^{4} + 1} d x

let

x^{4} + 1 = t

4 x^{3} d x = d t

x^{3} d x = \frac{d t}{4}

\int \frac{\frac{d t}{4}}{t}

= \frac{1}{4} \int \frac{d t}{t}

= \frac{1}{4} lo g ∣ t ∣

= \frac{1}{4} lo g ∣ ∣ x^{4} + 1 ∣ ∣ + c

answer

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Question Text	Integrate the functions $e^{3 l o g x} (x^{4} + 1)^{- 1}$
Answer Type	Text solution:1
Upvotes	150