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Question
Integrate the following functions with respect to x :
`(3x + 4) sqrt(3x + 7)`
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Solution
`int (3x + 4) sqrt(3x + 7) "d"x = int (3x + 7 - 3) sqrt(3x + 7) "d"x`
= `int [(3x + 7) sqrt(3x + 7) - 3sqrt(3x + 7)] "d"x`
= `int (3x + 7) sqrt(3x + 7) "d"x - int 3sqrt(3x + 7) "d"x`
= `int (3x + 7)^(3/2) "d"x - 3int (3x + 7)^(1/2) "d"x`
= `1/3 (3x + 7)^(3/2 + 1)/(3/2 + 1) - 3(3x + 7)^(1/2 + 1)/(1/2 + 1) + "c"`
= `1/3 (3x + 7)^(5/2)/(5/2) - 3 xx 1/3 (3x + 7)^(3/2)/(3/2) + "c"`
= `1/3 xx 2/5 (3x + 7)^(5/2) - 2/3 (3x + 7)^(3/2) + "c"`
= `2/15 (3x + 7)^(5/2) - 2/3 (3x + 7)^(3/2) + "c"`
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