Integrate the following functions w.r.t. x : (2x+1)x+2 - Mathematics and Statistics

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Sum

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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Chapter 3: Indefinite Integration - Exercise 3.2 (A) [Page 110]

APPEARS IN

Balbharati Mathematics and Statistics 2 (Arts and Science) 12th Standard HSC Maharashtra State Board
Chapter 3 Indefinite Integration
Exercise 3.2 (A) | Q 1.19 | Page 110

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