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Integrate the following functions sin^-1...

Integrate the following functions `sin^-1 ((2x)/(1+x^2))`

Text Solution

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`int sin^-1((2x)/(1+x^2)) dx`
=`int 2 tan^-1x dx = 2int 1 xx tan^-1 x dx`
=`2[tan^-1x xx x-int 1/(1+x^2) dx]`
`2[x tan^-1 x -1/2 int(2x)/(1+x^2) dx]`
=`2 [x tan^-1x -1/2 log (1+x^2)]+c`
=`2 x tan^-1x -log(11+x^2)+c`
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