`int_(0)^(1)(2x+3)/(5x^(2)+1)dx`

Explanation

`int_(0)^(1)(2x+3)/(5x^(2)+1)dx`
`=int_(0)^(1)(2x)/(5x^(2)+1)dx+int_(0)^(1)(3)/(5x^(2)+1)dx`
`=(1)/(5)int_(0)^(1)(10x)/(5x^(2)+1)Dx+3int_(0)^(1)(1)/((sqrt5.x)^(2)+1)dx`
`=(1)/(5)[log|5x^(2)+1|]_(0)^(1)+(3)/(sqrt5)[tan^(-1)(sqrt5x)]_(0)^(1)`
`=(1)/(5)[log6-log1]+(3)/(sqrt5)(tan^(-1)sqrt5-tan^(-1)0)`
`=(1)/(5)log6+(3)/(sqrt5)tan^(-1)sqrt5`