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Evaluate the following. ∫1x2-8x-20 dx - Mathematics and Statistics

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Sum

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

[Note: Answer in the textbook is incorrect.]

Concept: Methods of Integration: Integration by Substitution
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