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Numerade Educator

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Problem 44 Hard Difficulty

Evaluate the indefinite integral.

$ \displaystyle \int \frac{x}{1 + x^4} \, dx $

Answer

$\frac{1}{2} \tan ^{-1}\left(x^{2}\right)+\mathrm{C}$

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Video Transcript

okay, Given the problem, the first thing you know you could do is we can rewrite the denominator as one plus ax squared squared D backs. Now we know that you is equivalent to x squared, which means that de X is equivalent to one divide by two acts d'you, which means now we have the integral of one over one plus u squared times one over two acts d'you, which means factoring out the 1/2. We know we have 1/2 times inverse tangent because this is inverse tangent plus c. And then remember what you is x squared plus C.