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Question
Integrate the following with respect to x.
`x^3/sqrt(x^8 - 1)`
Solution
`int x^3/sqrt(x^8 - 1) "d"x = int (x^3 "d"x)/sqrt((x^4)^2 - 1^2)`
Let x4 = t
Then 4x3dx = dt
= `1/4 int "dt"/sqrt("t"^2 - 1)`
= `1/4 log|"t" + sqrt("t"^2 - 1)| + "c"`
= `1/4 log|x^4 + sqrt(x^8 - 1)| + "c"`
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