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How integrate y = x/(x^4+1)?

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yapayapa | (Level 2) Honors

Posted July 10, 2013 at 4:13 PM via web

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How integrate y = x/(x^4+1)?

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted July 10, 2013 at 4:54 PM (Answer #1)

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You need to use substitution technique, hence, you should come up with the following substitution, such that:

`x^2 = t => 2xdx = dt => xdx = (dt)/2`

Replacing the variable, yields:

`int x/(x^4+1)dx = int ((dt)/2)/(t^2 + 1)`

`int ((dt)/2)/(t^2 + 1) = (1/2)tan^(-1) t + c`

Replacing back `x^2` for `t` yields:

`int x/(x^4+1)dx = (1/2)tan^(-1) x^2 + c`

Hence, evaluating the indefinite integral of the given function, using substitution technique, yields `int x/(x^4+1)dx = (1/2)tan^(-1) x^2 + c.`

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