Advertisements
Advertisements
Question
Integrate the function `1/sqrt(7 - 6x - x^2)`
Advertisements
Solution
Let `I = int 1/sqrt(7 - 6x - x^2) dx`
`= dx/sqrt(7 - (x^2 + 6x))`
`= int dx/sqrt(7 - (x^2 + 6x + 9) + 9)`
`= int dx/sqrt(16 - (x + 3)^2)`
`= int dx/sqrt(4^2 - (x + 3)^2)`
`= sin^-1 ((x + 3)/4) + C` `...[because 1/sqrt(a^2 - x^2) dx = sin^-1 x/a + C]`
APPEARS IN
RELATED QUESTIONS
Evaluate: `int(5x-2)/(1+2x+3x^2)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 `(x - 1)/sqrt(x^2 - 1)`
Integrate the function `x^2/sqrt(x^6 + a^6)`
Integrate the function `(5x - 2)/(1 + 2x + 3x^2)`
Integrate the function `(6x + 7)/sqrt((x - 5)(x - 4))`
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(x^2 + 3x)`
Integrate the function:
`sqrt(1+ x^2/9)`
`int sqrt(x^2 - 8x + 7) dx` is equal to ______.
Evaluate : `int_2^3 3^x dx`
Find `int (2x)/(x^2 + 1)(x^2 + 2)^2 dx`
\[\int\frac{8x + 13}{\sqrt{4x + 7}} \text{ dx }\]
If θ f(x) = `int_0^x t sin t dt` then `f^1(x)` is
Evaluate \[\int \frac{dx}{x^2+a^2}\].
For \[\int\frac{px+q}{ax^2+bx+c}\,dx\], how is \[px+q\] written in relation to the derivative of the denominator?
What is the completed-square form of \[3x^2+13x-10\]?
Evaluate \[\int\frac{dx}{3x^2+13x-10}\].
For \[x+2=A(4x+6)+B\], what are the values of \[A\] and \[B\]?
Evaluate \[\int\frac{x+2}{2x^2+6x+5}\,dx\].
