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Question
Evaluate the following.
`int ("e"^"x" + "e"^(- "x"))^2 ("e"^"x" - "e"^(-"x"))`dx
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Solution
Let I = `int ("e"^"x" + "e"^(- "x"))^2 * ("e"^"x" - "e"^(-"x"))`dx
Put `"e"^"x" + "e"^(- "x")` = t
∴ `"e"^"x" - "e"^(- "x")`dx = dt
∴ I = `int "t"^2 . "dt"`
∴ I = `(t^(2 + 1))/(2 + 1) + c`
∴ I = `(t^3)/(3) + c`
∴ I = `[("e"^"x" + "e"^(- "x"))^3]/(3) + c`
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