1.

x tan^(-1) x

Answer»

Solution :` INT X. tan^(-1) x dx`
` =tan^(-1) x int x dx - int {(d)/(dx) tan^(-1) x int x dx }dx`
` =(x^(2))/(2) tan^(-1) x- int (1)/(1+x^(2)) .(x^(2))/(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)+1)/(2)) tan^(-1) x-(1)/(2) x+c`


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