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Question
Evaluate the following.
`int 1/(sqrt("x"^2 + 4"x"+ 29))` dx
Solution
Let I = `int 1/(sqrt("x"^2 + 4"x"+ 29))` dx
`= int 1/sqrt("x"^2 + 2 * 2"x" + 4 - 4 + 29)` dx
`= int 1/(sqrt(("x + 2")^2 + 25)` dx
`= int "dx"/(sqrt(("x + 2")^2 + 5^2)`
`= log |("x + 2") + sqrt(("x + 2")^2 + 5^2)|`+ c
∴ I = `= log |("x + 2") + sqrt("x"^2 + "4x" + 29)|` + c
Notes
The answer in the textbook is incorrect.
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