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How do you find the antiderivative of #(x^(3) + 2x)/(x^(4) + 4x^(2) +2)#?

1 Answer

Jun 29, 2018

#int(x^3+2x)/(x^4+4x^2+2)dx=1/4ln|x^4+4x^2+2|+c#

Explanation:

Here,

#I=int(x^3+2x)/(x^4+4x^2+2)dx#

#=1/4int(4x^3+8x)/(x^4+4x^2+2)dx#

#=1/4int(d(x^4+4x^2+2))/(x^4+4x^2+2)dx#

#=1/4ln|x^4+4x^2+2|+c#

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