Advertisements
Advertisements
प्रश्न
Integrate the function `1/sqrt((x - a)(x - b))`
Advertisements
उत्तर
Let `I = int dx/sqrt((x - a) (x - b))`
`= int dx/sqrt(x^2 - (a + b)x + ab)`
`= int dx/{[x^2 - 2 ((a + b)/2) x + ((a + b)/2)^2] + ab - ((a + b)/2)^2`
`= int dx/sqrt((x - (a + b)/2)^2 - ((a - b)/2)^2)`
`= log [(x - (a + b)/2) + sqrt((x - (a + b)/2)^2 - ((a - b)/2)^2)] + C` `...[∵ int dx/ sqrt (x^2 - a^2) = log |x + sqrt (x^2 - a^2)| + C]`
`= log [x - (a + b)/2 + sqrt((x - a)(x - b))] + C`
APPEARS IN
संबंधित प्रश्न
Evaluate : ` int x^2/((x^2+4)(x^2+9))dx`
find : `int(3x+1)sqrt(4-3x-2x^2)dx`
Find:
`int(x^3-1)/(x^3+x)dx`
Integrate the function `(3x^2)/(x^6 + 1)`
Integrate the function `1/sqrt(1+4x^2)`
Integrate the function `1/sqrt((2-x)^2 + 1)`
Integrate the function `(3x)/(1+ 2x^4)`
Integrate the function `(sec^2 x)/sqrt(tan^2 x + 4)`
Integrate the function `1/sqrt(7 - 6x - x^2)`
Integrate the function `1/sqrt((x -1)(x - 2))`
Integrate the function `(x + 2)/sqrt(x^2 -1)`
Integrate the function `(x + 3)/(x^2 - 2x - 5)`
`int dx/(x^2 + 2x + 2)` equals:
Integrate the function:
`sqrt(4 - x^2)`
Integrate the function:
`sqrt(1- 4x^2)`
Integrate the function:
`sqrt(1-4x - x^2)`
`int sqrt(x^2 - 8x + 7) dx` is equal to ______.
\[\int\frac{8x + 13}{\sqrt{4x + 7}} \text{ dx }\]
Find:
`int_(-pi/4)^0 (1+tan"x")/(1-tan"x") "dx"`
If θ f(x) = `int_0^x t sin t dt` then `f^1(x)` is
`int (a^x - b^x)^2/(a^xb^x)dx` equals ______.
What is a standard integral?
Evaluate \[\int \frac{dx}{x^2-a^2}\].
Evaluate \[\int \frac{dx}{\sqrt{a^2-x^2}}\].
Which trigonometric substitution is suitable for \[x^2+a^2\] and \[\sqrt{x^2+a^2}\]?
Which trigonometric substitution is suitable for \[x^2-a^2\] and \[\sqrt{x^2-a^2}\]?
Which expression is the general transformation obtained by completing the square?
What is the completed-square form of \[x^2-6x+13\]?
For \[x+2=A(4x+6)+B\], what are the values of \[A\] and \[B\]?
Evaluate \[\int\frac{x+2}{2x^2+6x+5}\,dx\].
