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



Asked on

1 Answer | Add Yours

sciencesolve's profile pic

Posted on (Answer #1)

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.`

We’ve answered 287,863 questions. We can answer yours, too.

Ask a question