Advertisements
Advertisements
Question
Integrate the function `1/sqrt((x - a)(x - b))`
Advertisements
Solution
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
RELATED QUESTIONS
find : `int(3x+1)sqrt(4-3x-2x^2)dx`
Integrate the function `1/sqrt(1+4x^2)`
Integrate the function `x^2/(1 - x^6)`
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((x -1)(x - 2))`
Integrate the function `(4x+ 1)/sqrt(2x^2 + x - 3)`
Integrate the function `(5x - 2)/(1 + 2x + 3x^2)`
Integrate the function `(6x + 7)/sqrt((x - 5)(x - 4))`
Integrate the function `(x + 2)/sqrt(4x - x^2)`
Integrate the function `(x + 3)/(x^2 - 2x - 5)`
Integrate the function:
`sqrt(1-4x - x^2)`
Integrate the function:
`sqrt(x^2 + 4x - 5)`
Integrate the function:
`sqrt(1+ 3x - x^2)`
Integrate the function:
`sqrt(1+ x^2/9)`
Evaluate : `int_2^3 3^x dx`
Find `int (2x)/(x^2 + 1)(x^2 + 2)^2 dx`
\[\int\frac{8x + 13}{\sqrt{4x + 7}} \text{ dx }\]
\[\int\frac{1 + x + x^2}{x^2 \left( 1 + x \right)} \text{ dx}\]
Find : \[\int\left( 2x + 5 \right)\sqrt{10 - 4x - 3 x^2}dx\] .
If θ f(x) = `int_0^x t sin t dt` then `f^1(x)` is
Find: `int (dx)/(x^2 - 6x + 13)`
`int (a^x - b^x)^2/(a^xb^x)dx` equals ______.
