Evaluate the definite integrals `int_0^1(2x+3"")/(5x^2+1)dx`

Explanation

`I=int_{0}^{1} frac{2 x+3}{5 x^{2}+1} d x`
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I=int_{0}^{1} frac{2 x}{5 x^{2}+1} d x+int_{0}^{1} frac{3}{5 x^{2}+1} {dx}`
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I=frac{1}{5} int_{0}^{1} frac{10 x}{5 x^{2}+1} d x+3 int_{0}^{1} frac{1}{(sqrt{5} x)^{2}+1} d x`
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I=frac{1}{5}[log (5 x^{2}+1)] 0^{1}+frac{3}{sqrt{5}}[tan ^{-1} frac{sqrt{5} x}{1}]_{0}^{1}`
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I=frac{1}{5}(log 6-log 1)+frac{3}{sqrt{5}} tan ^{-1} sqrt{5}`
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I=frac{1}{5} log 6+frac{3}{sqrt{5}} tan -1 sqrt{5}`
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