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Integrate the following functions (3x)/(...

Integrate the following functions `(3x)/(1+2x^4)`

Text Solution

Verified by Experts

Let t = `sqrt2 x^2`. Then dt = `2 sqrt2 x dx`
`gt x dx = 1/(2 sqrt2) dt`
therefore` int (3x)/(1+2x^4) dx = int 3/(1+t^2) 1/(2sqrt2) dt`
=`3/(2 sqrt2) tan^-1 t+c`
`3/(2 sqrt2) tan^-1 (sqrt2 x^2)+c`
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