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Evaluate: (i) int1/(4x^2+12 x+5)\ dx (ii...

Evaluate: (i) `int1/(4x^2+12 x+5)\ dx` (ii) `int1/(x^2-10 x+34)\ dx`

Text Solution

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(i) `int frac{d x}{4 x^{2}+12 x+5} `
`=frac{1}{4} int frac{d x}{x^{2}+3 x+frac{5}{4}} d x `
`=frac{1}{4} int frac{d x}{(x+frac{3}{2})^{2}-frac{9}{4}+frac{5}{4}} `
`=frac{1}{4} int frac{d x}{(x+frac{3}{2})^{2}-1^{2}} `
`text { let } x+frac{3}{2}=t `
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