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Question
Evaluate the following.
`int 1/(sqrt("x"^2 -8"x" - 20))` dx
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Solution
Let I = `int 1/(sqrt("x"^2 -8"x" - 20))` dx
`= int 1/(sqrt ("x"^2 - 2 * 4"x" + 16 - 16 - 20))` dx
`= int "dx"/sqrt(("x - 4")^2 - 36)` dx
`= int "dx"/(sqrt(("x - 4")^2 - 6^2))` dx
`= log |("x - 4") + sqrt(("x - 4")^2 - 6^2)|` + c
∴ I = `log |("x - 4") + sqrt("x"^2 - 8"x" - 20)|` + c
Notes
The answer in the textbook is incorrect.
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