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Question
Integrate the following with respect to x :
`alpha beta x^(alpha - 1) "e"^(- beta x^alpha)`
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Solution
`int alpha beta x^(alpha - 1) "e"^(- beta x^alpha)`
Put β xα = u
α β xα-1 dx = du
`int alpha beta x^(alpha - 1) "e"^(- beta x^alpha) * "d"x = int "e"^(- betax^alpha) (alpha beta) x^(alpha - 1) * "d"x`
= `int "e"^(- "u") * "du"`
= `("e"^(- "u"))/(- 1) + "c"`
`int alpha beta x^(alpha - 1) "e"^(- beta x^alpha) * "d"x = - "e"^(- beta x^alpha) + "c"`
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