Evaluate: `int"t"a n^(-1)sqrt(x)dx`

Answer

`(x+1)tan^(-1)sqrt(x)-sqrt(x)+C`

Explanation

`int tan^(-1)sqrt(x)*1dx=(tan^(-1)sqrt(x))-int(1)/(1+x)(1)/(2sqrt(x))x dx " (Integrating by parts)" `
`=x tan^(-1)sqrt(x)-(1)/(2)int(sqrt(x)dx)/(1+x)`
`=x tan^(-1)sqrt(x)-(1)/(2)[2(sqrt(x)-tan^(-1)sqrt(x))]+C`
`=x tan^(-1)sqrt(x)-sqrt(x)+tan^(-1)sqrt(x)+C`
`=(x+1)tan^(-1)sqrt(x)-sqrt(x)+C`