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Evaluate: intx/((x^2+4)sqrt(x^2+1))dx...

Evaluate: `intx/((x^2+4)sqrt(x^2+1))dx`

Text Solution

Verified by Experts

The correct Answer is:
`(1)/(sqrt(3))"tan"^(-1)sqrt((x^(2)+1)/(3))+C`
`I=int(x)/((x^(2)+4)sqrt(x^(2)+1))dx`
` " Let " x^(2)+1=t^(2) " or " xdx=t dt `
`:. I=int(tdt)/((t^(2)+3)t)=(1)/(sqrt(3))"tan"^(-1)(t)/(sqrt(3))+C`
`=(1)/(sqrt(3))"tan"^(-1)sqrt((x^(2)+1)/(3))+C`
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