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Question
Integrate the function:
`e^(3log x) (x^4 + 1)^(-1)`
Solution
Let `I = int e^(3 log x) (x^4 + 1)^-1 dx`
`= inte^(log x^3) (x^4 + 1)^-1 dx`
`= int x^3 (x^4 + 1)^-1 dx`
`= intx^3/ (x^4 + 1) dx`
put x4 = t
⇒ 4x3 dx = dt
∴ `I = 1/4 int dt/ (t + 1)`
`= 1/4 log (t + 1) + C`
`= 1/4 log (x^4 + 1) + C`
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