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Integrate the functions1/(sqrt(1+4x^2))...

Integrate the functions`1/(sqrt(1+4x^2))`

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` int (1)/(sqrt(1+4x^(2)))dx`
` =(1)/(2) int (1)/(sqrt(x^(2) +((1)/(2))^(2)))dx`
` =(1)/(2)log |x+sqrt(x^(2)+((1)/(2))^(2))|+c_(1)`
`=(1)/(2) log |(2x+ sqrt(4x^(2)+1))/(2)|+c_(1)`
`=(1)/(2)log |2x+sqrt(4x^(2)+1)|-(1)/(2) log 2+c_(1)`
`=(1)/(2) log|2x+sqrt(4x^(2)+1)|+c`
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