Advertisements
Advertisements
प्रश्न
Integrate the following functions with respect to x:
`sqrt((x + 1)^2 - 4)`
Advertisements
उत्तर
`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
संबंधित प्रश्न
Evaluate : `int1/(x(3+logx))dx`
Evaluate : `int _0^1 ("x" . ("sin"^-1 "x")^2)/sqrt (1 - "x"^2)` dx
Integrate the following functions with respect to x :
(2x – 5)(3x + 4x)
Integrate the following functions with respect to x :
`(sin^2x)/(1 + cosx)`
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 :
`x^2/(1 + x^6)`
Integrate the following with respect to x :
`("e"^x - "e"^-x)/("e"^x + "e"^-x)`
Integrate the following with respect to x :
`sqrt(x)/(1 + sqrt(x))`
Integrate the following with respect to x :
`tan x sqrt(sec x)`
Integrate the following with respect to x:
x log x
Integrate the following with respect to x:
`"e"^(tan^-1 x) ((1 + x + x^2)/(1 + x^2))`
Find the integrals of the following:
`1/(4 - x^2)`
Find the integrals of the following:
`1/(25 - 4x^2)`
Integrate the following with respect to x:
`(5x - 2)/(2 + 2x + x^2)`
Integrate the following with respect to x:
`(2x + 3)/sqrt(x^2 + 4x + 1)`
Choose the correct alternative:
`int x^2 cos x "d"x` is
Choose the correct alternative:
`int (x + 2)/sqrt(x^2 - 1) "d"x` is
