Find the integrals of the following: 1x2-4x+5

Question

Find the integrals of the following:

`1/sqrt(x^2 - 4x + 5)`

Sum

Solution

`int ("d"x)/sqrt(x^2 - 4x + 5) = int ("d"x)/sqrt((x - 2)^2 - 2^2 + 5)`

= `int ("d"x)/sqrt((x - 2)^2 - 4 + 5)`

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

Put x – 2 = t

dx = dt

`int ("d"x)/sqrt(x^2 - 4x + 5) = int ("d"x)/sqrt("t"^2 + 1^2)`

`int ("d"x)/sqrt(x^2 + "a"^2) = log |x + sqrt(x^2 + "a"^2)| + "c"`

= `log|"t" + sqrt("t"^2 + 1^2)| + "c"`

= `log|(x - 2) + sqrt((x - 2)^2 + 1)| + "c"`

= `log|(x - 2) + sqrt(x^2 - 4x + 4x +1)| + "c"`

`int ("d"x)/sqrt(x^2 - 4x + 5) = log |(x - 2) + sqrt(x^2 - 4x + 5)| + "c"`

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Indefinite Integration with Standard Indefinite Integral Formulae - Methods of Integration

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Q 3. (ii)Q 3. (i)Q 3. (iii)

Chapter 11: Integral Calculus - Exercise 11.10 [Page 219]

APPEARS IN

Samacheer Kalvi Mathematics - Volume 1 and 2 [English] Class 11 TN Board

Chapter 11 Integral Calculus
Exercise 11.10 | Q 3. (ii) | Page 219

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