Integrate the following functions w.r.t. x : x.sec2(x2)tan3(x2) - Mathematics and Statistics

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Sum

Integrate the following functions w.r.t. x : `(x.sec^2(x^2))/sqrt(tan^3(x^2)`

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Solution

Let I = `int (x.sec^2(x^2))/sqrt(tan^3(x^2)).dx`

Put tan(x2) = t

∴ sec2(x2) x 2x dx = dt

∴ `x.sec^2(x^2)dx = dt/(2)`

∴ I = `int (1)/sqrt(t^3).dt/(2)`

= `(1)/(2) int t^(-3/2)dt`

= `(1)/(2).(t^(-1/2))/(-1/2) + c`

= `(-1)/sqrt(t) + c`

= `(-1)/sqrt(tan(x^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 1.04 | Page 110

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