`inttan^(-1)sqrt(x) dx` is equal to

1.	`inttan^(-1)sqrt(x) dx` is equal to
Answer» Put `sqrt(x)=t" so that "(1)/(2sqrt(x))dx=dtordx=2tdt`. `:.inttan^(-1)sqrt(x)dx=2int(tan^(-1)t)dt` `=2{:[(tan^(-1)t)(t^(2))/(2)-int{(1)/((1+t^(2)))(t^(2))/(2)-int}dt]:}+C` `=t^(2)(tan^(-1)t)-int(t^(2))/((1+t^(2)))dt+C` `=t^(2)(tan^(-1)t)-int([(1+t^(2))-1])/((1+t^(2)))dt+C` `t^(2)(tan^(-1)t)-intdt+int(1)/((1+t^(2)))dt+C` `=t^(2)(tan^(-1)t)-t+tan^(-1)t+C=(t^(2)+1)tan^(-1)t-t+C` `=(x+1)tan^(-1)sqrt(x)-sqrt(x)+C`.

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