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

Find the integrals of the following:

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

Sum

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

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

Evaluate:`int(tansqrtx)/sqrtxdx`

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`x/sqrt(1 + x^2)`

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`(sin^-1 x)/sqrt(1 - x^2)`

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`cosx/(cos(x - "a"))`