Advertisements
Advertisements
Question
Integrate the function `1/sqrt(8+3x - x^2)`
Advertisements
Solution
Let `I = int 1/sqrt(8 + 3x - x^2) dx`
`= int dx/sqrt(8 - (x^2 - 3x))`
`= int dx/sqrt(8 - (x^2 - 2 * 3/2 x + 9/4) + 9/4)`
`= int dx/sqrt(41/4 - (x - 3/2)^2)`
`= int dx/sqrt((sqrt41/2)^2 - (x - 3/2)^2)` `...[∵ int dx/sqrt (a^2 - x^2) = sin^-1 x/a + C]`
`= sin^-1 ((x - 3/2)/(sqrt41/2)) + C`
`= sin^-1 ((2x - 3)/sqrt41) + C`
APPEARS IN
RELATED QUESTIONS
find : `int(3x+1)sqrt(4-3x-2x^2)dx`
Find:
`int(x^3-1)/(x^3+x)dx`
Integrate the function `1/sqrt(9 - 25x^2)`
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 -1)(x - 2))`
Integrate the function `(x + 2)/sqrt(x^2 -1)`
Integrate the function `(6x + 7)/sqrt((x - 5)(x - 4))`
Integrate the function `(x + 2)/sqrt(4x - x^2)`
Integrate the function `(x+2)/sqrt(x^2 + 2x + 3)`
`int dx/(x^2 + 2x + 2)` equals:
`int dx/sqrt(9x - 4x^2)` equals:
Integrate the function:
`sqrt(1- 4x^2)`
Integrate the function:
`sqrt(x^2 + 4x +1)`
Integrate the function:
`sqrt(x^2 + 4x - 5)`
Integrate the function:
`sqrt(1+ 3x - x^2)`
Integrate the function:
`sqrt(x^2 + 3x)`
Integrate the function:
`sqrt(1+ x^2/9)`
`int sqrt(x^2 - 8x + 7) dx` is equal to ______.
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_(-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 ______.
