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Evaluate: int"t"a n^(-1)xdx...

Evaluate: `int"t"a n^(-1)xdx`

Text Solution

Verified by Experts

The correct Answer is:
`(x+1)tan^(-1)sqrt(x)-sqrt(x)+C`
`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`
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