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x tan^(-1) x |
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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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