Advertisements
Advertisements
प्रश्न
Find: `int (dx)/(x^2 - 6x + 13)`
Advertisements
उत्तर
Given integral is I = `int (dx)/(x^2 - 6x + 13)`
= `int (dx)/((x - 3)^2 + 13 - 9)`
= `int (dx)/((x - 3)^2 + 4)`
= `int (dx)/((x - 3)^2 + 2^2)`
= `1/2 tan^-1 ((x - 3)/2) + C` ...`["Using" int 1/(x^2 + a^2) dx = 1/a tan^-1 x/a + C]`
APPEARS IN
संबंधित प्रश्न
Evaluate : ` int x^2/((x^2+4)(x^2+9))dx`
Integrate the function `1/sqrt(1+4x^2)`
Integrate the function `1/sqrt(9 - 25x^2)`
Integrate the function `(3x)/(1+ 2x^4)`
Integrate the function `x^2/sqrt(x^6 + a^6)`
Integrate the function `(x + 2)/sqrt(x^2 -1)`
Integrate the function `(5x - 2)/(1 + 2x + 3x^2)`
Integrate the function:
`sqrt(1- 4x^2)`
Integrate the function:
`sqrt(x^2 + 4x +1)`
Integrate the function:
`sqrt(x^2 + 3x)`
Integrate the function:
`sqrt(1+ x^2/9)`
`int sqrt(1+ x^2) dx` is equal to ______.
`int sqrt(x^2 - 8x + 7) dx` is equal to ______.
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)/sqrt(4x - x^2)`
Which factorization is used before applying partial fractions to \[\frac{1}{x^2-a^2}\]?
Which trigonometric substitution is suitable for \[a^2-x^2\] and \[\sqrt{a^2-x^2}\]?
Which trigonometric substitution is suitable for \[x^2-a^2\] and \[\sqrt{x^2-a^2}\]?
