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Question
Integrate the function `(3x)/(1+ 2x^4)`
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Solution
Let `I = int (3x)/ (1 + 2x^4) dx`
Put x2 = t
⇒ 2x dx = dt
⇒ `x dx = dt/2`
∴ `I = 3/2 int dt/(1 + 2t^2 )`
`= 3/4 int dt/ (1/2 + t^2)`
`= 3/4 int dt/ ((1/sqrt2)^2 + t^2)` `....[∵ int dx/(a^2+x^2) = 1/a tan^-1 x/a + C]`
`3/4* 1/ (1/sqrt2) tan^-1 (t/(1/sqrt2)) + C`
`3/(2sqrt2) tan^-1 sqrt2t + C`
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