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Question
Find `int dx/(5 - 8x - x^2)`
Solution
Let `I = int dx/(5-8x-x^2) dx`
`= int dx/(5 + 16 - 16 - 8x - x^2) dx`
`= int dx/(21 - (x+4)^2) dx`
`=int dx/((sqrt(21))^2 - (x + 4)^2) dx`
`= 1/(2xxsqrt(21)) log|(sqrt21+x + 4)/(sqrt21 - x - 4)| + C`
`= 1/(2sqrt(21)) log |(sqrt21 + 4 + x)/(sqrt21 - 4 - x)|+C`
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