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

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Answer 1 · 2018-06-29T07:24:59

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

Here,

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

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

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

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

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