Advertisements
Advertisements
Question
Find the integrals of the following:
`1/sqrt(xx^2 + 4x + 2)`
Solution
`int ("d"x)/sqrt(x^2 + 4x + 2) = int ("d"x)/sqrt((x + 2)^2 - 2^2 + 2)`
= `int ("d"x)/sqrt((x + 2)^2 - 4 + 2)`
= `int ("d"x)/sqrt((x + 2)^2 - 2)`
= `int ("d"x)/sqrt((x + 2)^2 - (sqrt(2))^2`
Put x + 2 = t
dx = dt
= `int ("d"x)/sqrt("t"^2 - (sqrt(2))^2`
`int ("d"x)/sqrt(x^2 - "a"^2) = log|x + sqrt(x^2 - "a"^2)| + "c"`
= `log |"t" + sqrt("t"^2 - (sqrt(2))^2)| + "c"`
= `log |(x + 2) + sqrt((x + 2)^2 - 2)| + "c"`
= `log |(x + 2) + sqrt(x^2 + 4x + 4 - 2)| + "c"`
`int ("d"x)/sqrt(x^2 + 4x + 2) = log|(x + 2) + sqrt(x^2 + 4x + 2)| + "c"`
APPEARS IN
RELATED QUESTIONS
Find the volume of the solid generated by the complete revolution of the ellipse `"x"^2/36 + "y"^2/25 = 1` about Y-axis.
Evaluate : `int _0^1 ("x" . ("sin"^-1 "x")^2)/sqrt (1 - "x"^2)` dx
Integrate the following functions with respect to x :
sin2 5x
Integrate the following functions with respect to x :
`"e"^(x log "a") "e"^x`
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 :
`cosx/(cos(x - "a"))`
Integrate the following with respect to x:
x sin 3x
Integrate the following with respect to x:
`(x sin^-1 x)/sqrt(1 - x^2)`
Integrate the following with respect to x:
x5ex2
Integrate the following with respect to x:
`sin^-1 ((2x)/(1 + x^2))`
Integrate the following with respect to x:
`"e"^(2x) sinx`
Find the integrals of the following:
`1/(9x^2 - 4)`
Find the integrals of the following:
`1/sqrt((2 + x)^2 - 1)`
Integrate the following with respect to x:
`(2x + 1)/sqrt(9 + 4x - x^2)`
Integrate the following functions with respect to x:
`sqrt(9 - (2x + 5)^2`
Choose the correct alternative:
`int (x + 2)/sqrt(x^2 - 1) "d"x` is
Choose the correct alternative:
`int sin sqrt(x) "d"x` is
