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Question
Integrate the following with respect to x :
x(1 – x)17
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Solution
`int x(1 - x)^17 "d"x`
Put 1 – x = u
– dx = du
`int x(1 - x)^17 "d"x = int (1 - "u")"u"^17 xx - "du"`
= `- int ("u"^17 - "u"^18) "du"`
= `- int "u"^17 "du" + int "u"^18 "du"`
= `- ("u"^(17 + 1))/(17 + 1) + ("u"^(18 + 1))/(18 + 1) + "c"`
= `- "u"^18/18 + "u"^19/19 + "c"`
= `- (1 - x)^18/18 + (1 - x)^19/19 + "c"`
`int x(1 - x)^17 "d"x = (1 - x)^19/19 - (1 - x)^18/18 + "c"`
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