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Evaluate the following: d∫dxxx4-1 (Hint: Put x2 = sec θ) - Mathematics

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Question

Evaluate the following:

`int ("d"x)/(xsqrt(x^4 - 1))` (Hint: Put x² = sec θ)

Sum

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Solution

Let I = `int ("d"x)/(xsqrt(x^4 - 1))`

= `int (x"d"x)/(x^2sqrt(x^4 - 1))`

Put x² = sec θ

∴ 2x dx = sec θ tan θ dθ

x dx = `1/2 sec theta tan theta "d"theta`

∴ I = `1/2 int (sec theta tan theta)/(sec theta sqrt(sec^2theta - 1)) "d"theta`

= `1/2 int (sectheta tan theta)/(sectheta * tan theta) "d"theta`

= `1/2 int 1 "d"theta`

= `1/2 theta + "C"`

So I = `1/2 sec^-1x^2 + "C"`

Hence, I = `1/2 sec^-1 x^2 + "C"`.

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Evaluation of Simple Integrals of the Following Types and Problems

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Chapter 7: Integrals - Exercise [Page 165]

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NCERT Exemplar Mathematics [English] Class 12

Chapter 7 Integrals
Exercise | Q 26 | Page 165

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