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

Find the integrals of the following:

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

योग

`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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अध्याय 11: Integral Calculus - Exercise 11.10 [पृष्ठ २१९]

अध्याय 11 Integral Calculus
Exercise 11.10 | Q 3. (ii) | पृष्ठ २१९

Find the volume of the solid generated by the complete revolution of the ellipse `"x"^2/36 + "y"^2/25 = 1` about Y-axis.

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`(cos 2x)/(sin^2x cos^2x)`

Integrate the following functions with respect to x :

`(sin^2x)/(1 + cosx)`

Integrate the following functions with respect to x :

cos 3x cos 2x

Integrate the following with respect to x :

`(10x^9 + 10^x log_"e" 10)/(10^x + x^10)`

Integrate the following with respect to x :

`alpha beta x^(alpha - 1) "e"^(- beta x^alpha)`

Integrate the following with respect to x :

sin⁵x cos³x