Advertisements
Advertisements
Question
Integrate the function `1/sqrt((x -1)(x - 2))`
Advertisements
Solution
Let `I = 1/sqrt((x - 1) (x - 2)) dx`
`= int dx/sqrt(x^2 - 3x + 2)`
`= int dx/sqrt((x^2 - 2 * 3/2 x + 9/4) + 2 - 9/4)`
`= int dx/sqrt((x - 3/2)^2 - 1/4)`
`= int dx/sqrt((x - 3/2)^2 - (1/2)^2)`
`= log abs ((x - 3/2) + sqrt ((x - 3/2)^2 - (1/2)^2)) + C` `...[∵ int dx/ sqrt(x^2 - a^2) = log |x + sqrt (x^2 - a^2)| + C]`
`= log |(x - 3/2) + sqrt((x - 1) (x - 2))| + C`
APPEARS IN
RELATED QUESTIONS
Evaluate:
`int((x+3)e^x)/((x+5)^3)dx`
Integrate the function `1/sqrt(1+4x^2)`
Integrate the function `1/sqrt(9 - 25x^2)`
Integrate the function `(3x)/(1+ 2x^4)`
Integrate the function `(x - 1)/sqrt(x^2 - 1)`
Integrate the function `x^2/sqrt(x^6 + a^6)`
Integrate the function `1/sqrt(x^2 +2x + 2)`
Integrate the function `1/sqrt(7 - 6x - x^2)`
Integrate the function `1/sqrt((x - a)(x - b))`
Integrate the function `(x + 2)/sqrt(x^2 -1)`
Integrate the function `(5x - 2)/(1 + 2x + 3x^2)`
Integrate the function `(x + 2)/sqrt(4x - x^2)`
Integrate the function `(x+2)/sqrt(x^2 + 2x + 3)`
Integrate the function `(5x + 3)/sqrt(x^2 + 4x + 10)`
Integrate the function:
`sqrt(x^2 + 4x +1)`
Integrate the function:
`sqrt(1+ 3x - x^2)`
Integrate the function:
`sqrt(x^2 + 3x)`
`int sqrt(1+ x^2) dx` is equal to ______.
If θ f(x) = `int_0^x t sin t dt` then `f^1(x)` is
Find `int (dx)/sqrt(4x - x^2)`
`int (a^x - b^x)^2/(a^xb^x)dx` equals ______.
Evaluate \[\int \frac{dx}{a^2-x^2}\].
Evaluate \[\int \frac{dx}{\sqrt{a^2-x^2}}\].
Evaluate \[\int \frac{dx}{\sqrt{x^2+a^2}}\].
Which factorization is used before applying partial fractions to \[\frac{1}{x^2-a^2}\]?
Which trigonometric substitution is suitable for \[x^2-a^2\] and \[\sqrt{x^2-a^2}\]?
Which method transforms \[\int\frac{dx}{ax^2+bx+c}\] or \[\int\frac{dx}{\sqrt{ax^2+bx+c}}\] into an expression compatible with standard formulae?
Which expression is the general transformation obtained by completing the square?
For \[x+2=A(4x+6)+B\], what are the values of \[A\] and \[B\]?
