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`
Evaluate : `∫_0^(pi/2) (sinx.cosx)/(1 + sin^4x)`.dx
Find the volume of the solid generated by the complete revolution of the ellipse `"x"^2/36 + "y"^2/25 = 1` about Y-axis.
Find the volume of the solid obtained by revolving about the X-axis, the region bounded by the curve `"x"^2/4 - "y"^2/9 = 1` and the lines x = 2 , x = 4.
Integrate the following functions with respect to x :
(2x – 5)(3x + 4x)
Integrate the following functions with respect to x :
`(cos2x - cos 2 alpha)/(cosx - cos alpha)`
Integrate the following functions with respect to x :
`(sin4x)/sinx`
Integrate the following functions with respect to x :
sin2 5x
Integrate the following functions with respect to x :
`1/((x - 1)(x + 2)^2`
Integrate the following with respect to x :
`cot x/(log(sin x))`
Integrate the following with respect to x :
`1/(x log x log (log x))`
Integrate the following with respect to x:
x sec x tan x
Integrate the following with respect to x:
x2 cos x
Integrate the following with respect to x:
x3 sin x
Find the integrals of the following:
`1/(6x - 7 - x^2)`
Integrate the following with respect to x:
`(2x - 3)/(x^2 + 4x - 12)`
Integrate the following with respect to x:
`(5x - 2)/(2 + 2x + x^2)`
Choose the correct alternative:
`int ("e"^(6 log x) - "e"^(5logx))/("e"^(4logx) - "e"^(3logx)) "d"x` is
Choose the correct alternative:
`int sin sqrt(x) "d"x` is
