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Evaluate the following integrals: int (2x+3)/(5x^2+1)

Answer»

Solution :`(2X+13/(5x^2+1) = (2x)/(5x^2+1) + 3/(5x^2 +1) `
` =1/5 (10x)/(5x^2+1) + 3/((sqrt5x)^2 +1)`
THEREFORE` int_0^1 (2x+3)/(5x^2+1) dx`
=`[1/5 log|5x^2+1| +3/sqrt5 tan^-1 (sqrt5x)]_0^1`
`(1/5 log6 +3/sqrt5 tan^-1 sqrt5)-(1/5 LOG1 + 3/sqrt5 tan^-1 0)`
=`1/5 log6 +3/sqrt5 tan^-1 sqrt5`


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