Advertisements
Advertisements
Question
Find the integrals of the following:
`1/(9x^2 - 4)`
Advertisements
Solution
`int ("d"x)/(9x^2 - 4) = 1/9 int ("d"x)/(x^2 - 4/9)`
= `1/9 int ("d"x)/(x^2 - (2/3)^2`
`int ("d"x)/(x^2 - "a"^2) = 1/(2"a") log |(x - "a")/(x + "a")| + "c"`
= `1/9 xx 1/(2 xx (2/3)) log |(x - 2/3)/(x + 2/3)| + "c"`
= `1/9 xx 1/(4/3) log |((3x - 2)/3)/((3x + 2)/3)| + "c"`
= `1/9 xx 3/4 log |(3x - 2)/(3x + 2)| + "c"`
= `1/12 log |(3x - 2)/(3x + 2)| + "c"`
APPEARS IN
RELATED QUESTIONS
Evaluate : `int (1+logx)/(x(2+logx)(3+logx))dx`
Integrate the following functions with respect to x :
`(sin^2x)/(1 + cosx)`
Integrate the following functions with respect to x :
`(1 + cos 4x)/(cos x - tan x)`
Integrate the following functions with respect to x :
`(x + 1)/((x + 2)(x + 3))`
Integrate the following with respect to x :
`(sin sqrt(x))/sqrt(x)`
Integrate the following with respect to x :
`tan x sqrt(sec x)`
Integrate the following with respect to x:
`(x sin^-1 x)/sqrt(1 - x^2)`
Integrate the following with respect to x:
x5ex2
Integrate the following with respect to x:
`"e"^("a"x) cos"b"x`
Integrate the following with respect to x:
`"e"^(-x) cos 2x`
Integrate the following with respect to x:
`"e"^(- 3x) sin 2x`
Integrate the following with respect to x:
`"e"^x ((2 + sin 2x)/(1 + cos 2x))`
Find the integrals of the following:
`1/sqrt(9 + 8x - x^2)`
Integrate the following with respect to x:
`(2x + 1)/sqrt(9 + 4x - x^2)`
Integrate the following functions with respect to x:
`sqrt((x + 1)^2 - 4)`
Choose the correct alternative:
If `int 3^(1/x)/x^2 "d"x = "k"(3^(1/x)) + "c"`, then the value of k is
Choose the correct alternative:
`int 2^(3x + 5) "d"x` is
Choose the correct alternative:
`int "e"^(- 7x) sin 5x "d"x` is
Choose the correct alternative:
`int sin sqrt(x) "d"x` is
