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How to solve ∫ (x/(1+x^4)) dx ?

Question

How to solve ∫ (x/(1+x^4)) dx ?
How to solve ∫ (x/(1+x^4)) dx ?

Answers

#intx/(1+x^4)dx = 1/2tan^(-1)(x^2) + C#

Explanation:

Given that #int1/(x^2+1)dx = tan^(-1)(x) + C#

we will proceed by substitution.

Let #u = x^2 => du = 2xdx#

Then

#intx/(1+x^4)dx = 1/2int1/(1+(x^2)^2)*2xdx#

#= 1/2int1/(1+u^2)du#

#= 1/2tan^(-1)(u) + C#

#= 1/2tan^(-1)(x^2) + C#


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