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Integrate the following functions x tan^...

Integrate the following functions `x tan^-1x`

Text Solution

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`int x tan^-1x dx`
=`tan^-1x xx x^2/2 - int 1/(1+x^2) x^2/2 dx`
=`x^2/2 tan^-1 x- 1/2 int (1+x^2-1)/(1+x^2) dx`
`x^2/2 tan^-1 x-1/2 int (1-1/(1+x^2)) dx`
=`x^2/2 tan^-1 x- 1/2(x-tan^-1 x)+c`
=`x^2/2 tan^-1 -x/2 +1/2 tan^-1 x+c`
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