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Question
Integrate the following functions w.r.t. x : `(2x + 1)sqrt(x + 2)`
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Solution
Let I = `ff(2x + 1)sqrt(x + 2).dx`
Put x + 2 = t
∴ dx = dt
Also, x = t – 2
∴ 2x + 1 = 2(t – 2) + 1 = 2t – 3
∴ I = `int (2t - 3)sqrt(t) dt`
= `int (2t^(3/2) - 3t^(1/2))dt`
= `2int t^(3/2)dt - 3 intt^(1/2)dt`
= `2.(t^5/2)/((5/2)) - 3 . (t^(3/2))/((3/2)) + c`
= `(4)/(5)(x + 2)^(5/2) - 2(x + 2)^(3/2) + c`.
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