Advertisements
Advertisements
प्रश्न
Find the integrals of the following:
`1/(9x^2 - 4)`
Advertisements
उत्तर
`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
संबंधित प्रश्न
Evaluate : `∫_0^(pi/2) (sinx.cosx)/(1 + sin^4x)`.dx
Integrate the following functions with respect to x :
`(cos 2x)/(sin^2x cos^2x)`
Integrate the following functions with respect to x :
`(1 + cos 4x)/(cos x - tan x)`
Integrate the following functions with respect to x :
`(3x - 9)/((x - 1)(x + 2)(x^2 + 1))`
Integrate the following functions with respect to x :
`x^3/((x - 1)(x - 2))`
Integrate the following with respect to x :
`("e"^x - "e"^-x)/("e"^x + "e"^-x)`
Integrate the following with respect to x :
`alpha beta x^(alpha - 1) "e"^(- beta x^alpha)`
Integrate the following with respect to x:
x sec x tan x
Integrate the following with respect to x:
x3 sin x
Integrate the following with respect to x:
x5ex2
Integrate the following with respect to x:
`"e"^(- 3x) cos x`
Find the integrals of the following:
`1/(4 - x^2)`
Integrate the following with respect to x:
`(3x + 1)/(2x^2 - 2x + 3)`
Integrate the following functions with respect to x:
`sqrt(x^2 + 2x + 10)`
Integrate the following functions with respect to x:
`sqrt(x^2 - 2x - 3)`
Integrate the following functions with respect to x:
`sqrt(81 + (2x + 1)^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 secx/sqrt(cos2x) "d"x` is
Choose the correct alternative:
`int 1/(x sqrt(log x)^2 - 5) "d"x` is
