Advertisements
Advertisements
Question
Integrate the following functions with respect to x:
`sqrt((x + 1)^2 - 4)`
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
Find the volume of solid generated by rotating the area bounded by x2+y2 =36 and the lines x = 0, x = 3 about X -axis.
Find the volume of the solid generated by the complete revolution of the ellipse `"x"^2/36 + "y"^2/25 = 1` about Y-axis.
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 :
`(sin4x)/sinx`
Integrate the following functions with respect to x :
cos 3x cos 2x
Integrate the following functions with respect to x :
`"e"^(x log "a") "e"^x`
Integrate the following functions with respect to x :
`(3x + 4) sqrt(3x + 7)`
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(1 – x)17
Integrate the following with respect to x:
x sin 3x
Integrate the following with respect to x:
x sec x tan x
Integrate the following with respect to x:
x log x
Integrate the following with respect to x:
`sin^-1 ((2x)/(1 + x^2))`
Integrate the following with respect to x:
`"e"^(-x) cos 2x`
Choose the correct alternative:
`int ("e"^(6 log x) - "e"^(5logx))/("e"^(4logx) - "e"^(3logx)) "d"x` is
Choose the correct alternative:
`int secx/sqrt(cos2x) "d"x` is
Choose the correct alternative:
`int x^2 cos x "d"x` is
