Advertisements
Advertisements
प्रश्न
Find the integrals of the following:
`1/sqrt(x^2 - 4x + 5)`
Advertisements
उत्तर
`int ("d"x)/sqrt(x^2 - 4x + 5) = int ("d"x)/sqrt((x - 2)^2 - 2^2 + 5)`
= `int ("d"x)/sqrt((x - 2)^2 - 4 + 5)`
= `int ("d"x)/sqrt((x - 2)^2 + 1)`
Put x – 2 = t
dx = dt
`int ("d"x)/sqrt(x^2 - 4x + 5) = int ("d"x)/sqrt("t"^2 + 1^2)`
`int ("d"x)/sqrt(x^2 + "a"^2) = log |x + sqrt(x^2 + "a"^2)| + "c"`
= `log|"t" + sqrt("t"^2 + 1^2)| + "c"`
= `log|(x - 2) + sqrt((x - 2)^2 + 1)| + "c"`
= `log|(x - 2) + sqrt(x^2 - 4x + 4x +1)| + "c"`
`int ("d"x)/sqrt(x^2 - 4x + 5) = log |(x - 2) + sqrt(x^2 - 4x + 5)| + "c"`
APPEARS IN
संबंधित प्रश्न
Evaluate : `∫_0^(pi/2) (sinx.cosx)/(1 + sin^4x)`.dx
Evaluate : `int _0^1 ("x" . ("sin"^-1 "x")^2)/sqrt (1 - "x"^2)` dx
Integrate the following functions with respect to x :
`(3x + 4) sqrt(3x + 7)`
Integrate the following with respect to x :
`("e"^x - "e"^-x)/("e"^x + "e"^-x)`
Integrate the following with respect to x :
sin5x cos3x
Integrate the following with respect to x:
x3 sin x
Integrate the following with respect to x:
`tan^-1 ((8x)/(1 - 16x^2))`
Integrate the following with respect to x:
`sin^-1 ((2x)/(1 + x^2))`
Integrate the following with respect to x:
`"e"^(-x) cos 2x`
Integrate the following with respect to x:
`"e"^x ((2 + sin 2x)/(1 + cos 2x))`
Find the integrals of the following:
`1/(25 - 4x^2)`
Find the integrals of the following:
`1/sqrt(xx^2 + 4x + 2)`
Integrate the following functions with respect to x:
`sqrt(x^2 + 2x + 10)`
Integrate the following functions with respect to x:
`sqrt(81 + (2x + 1)^2`
Choose the correct alternative:
`int sin^2x "d"x` is
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^2x)/(x^2 + 1) "cosec"^2 x/("d"x)` is
Choose the correct alternative:
`int x^2 cos x "d"x` is
