Advertisements
Advertisements
Question
Integrate the following functions with respect to x:
`sqrt((x + 1)^2 - 4)`
Advertisements
Solution
`int sqrt((x + 1)^2 - 4) "d"x = int sqrt((x + 1)^2 - 2^2) "d"x`
Put x + 1 = t
dx = dt
= `int sqrt("t"^2 - 2^2) "dt"`
= `"t"/2 sqrt("t"^2 - 2^2) - 2^2/2 log |"t" + sqrt("t" - 2^2)| + "c"`
= `((x + 1))/2 sqrt((x + 1)^2 - 2^2) - 2 log|(x + 1) + sqrt((x + 1)^2 - 2^2)| + "c"`
`int sqrt((x + 1)^2 - 4) "d"x = ((x + 1))/2 sqrt((x + 1)^2 - 4) - 2 log |(x + 1) + sqrt((x + 1)^2 - 4)| + "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
Integrate the following functions with respect to x :
(2x – 5)(3x + 4x)
Integrate the following functions with respect to x :
`(cos 2x)/(sin^2x cos^2x)`
Integrate the following functions with respect to x :
`(3x + 4) sqrt(3x + 7)`
Integrate the following functions with respect to x :
`(x + 1)/((x + 2)(x + 3))`
Integrate the following functions with respect to x :
`1/((x - 1)(x + 2)^2`
Integrate the following with respect to x :
`x/sqrt(1 + x^2)`
Integrate the following with respect to x :
`("cosec" x)/(log(tan x/2))`
Integrate the following with respect to x :
`(sin^-1 x)/sqrt(1 - x^2)`
Integrate the following with respect to x :
`1/(x log x log (log x))`
Integrate the following with respect to x:
x sin 3x
Integrate the following with respect to x:
x2 cos x
Integrate the following with respect to x:
`(x sin^-1 x)/sqrt(1 - x^2)`
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:
`(3x + 1)/(2x^2 - 2x + 3)`
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 sqrt((1 - x)/(1 + x)) "d"x` is
