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(5x-2)/(1+2x+3x^2)dx`
Evaluate : ` int x^2/((x^2+4)(x^2+9))dx`
find : `int(3x+1)sqrt(4-3x-2x^2)dx`
Evaluate:
`int((x+3)e^x)/((x+5)^3)dx`
Integrate the function `(3x^2)/(x^6 + 1)`
Integrate the function `1/sqrt(9 - 25x^2)`
Integrate the function `(3x)/(1+ 2x^4)`
Integrate the function `x^2/(1 - x^6)`
Integrate the function `(x - 1)/sqrt(x^2 - 1)`
Integrate the function `(sec^2 x)/sqrt(tan^2 x + 4)`
Integrate the function `1/sqrt(x^2 +2x + 2)`
Integrate the function `1/sqrt((x -1)(x - 2))`
Integrate the function `1/sqrt(8+3x - x^2)`
Integrate the function `(4x+ 1)/sqrt(2x^2 + x - 3)`
`int dx/(x^2 + 2x + 2)` equals:
Integrate the function:
`sqrt(1- 4x^2)`
Integrate the function:
`sqrt(x^2 + 4x +1)`
Integrate the function:
`sqrt(1+ 3x - x^2)`
`int sqrt(x^2 - 8x + 7) dx` is equal to ______.
Find `int (2x)/(x^2 + 1)(x^2 + 2)^2 dx`
Integration of \[\frac{1}{1 + \left( \log_e x \right)^2}\] with respect to loge x is
\[\int\frac{8x + 13}{\sqrt{4x + 7}} \text{ dx }\]
Find:
`int_(-pi/4)^0 (1+tan"x")/(1-tan"x") "dx"`
Find: `int (dx)/(x^2 - 6x + 13)`
`int (a^x - b^x)^2/(a^xb^x)dx` equals ______.
