Would you help me with this integration? #int ((sqrt(x^4+2+x^(-4)))/x^3)dx#

no need go into details. I need just to see the process. Thanks

1 Answer
George C.
Feb 13, 2018

#int (sqrt(x^4+2+x^(-4))/x^3) dx = ln abs x-1/4x^(-4)+C#

Explanation:

Note that:

#x^4+2+x^(-4) = (x^2+x^(-2))^2#

You can probably fill in the rest:

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

#color(white)(int (sqrt(x^4+2+x^(-4))/x^3) dx) = int x^(-1)+x^(-5) dx#

#color(white)(int (sqrt(x^4+2+x^(-4))/x^3) dx) = ln abs x-1/4x^(-4)+C#

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