Advertisements
Advertisements
प्रश्न
Integrate the following with respect to x:
`(x + 2)/sqrt(x^2 - 1)`
Advertisements
उत्तर
Let x + 2 = `"A" "d"/("d"x) (x^2 - 1) + "B"`
x + 2 = A(2x) + B
2A = 1
⇒ A = `1/2`
B = 2
x + 2 = `1/2 (2x) + 2`
`int (x + 2)/sqrt(x^2 - 1) "d"x = int (1/2 (2x) + 2)/sqrt(x^2 - 1) "d"x`
= `1/2 int (2x)/sqrt(x^2 - 1) "d"x + 2 int ("d"x)/sqrt(x^2 - 1)`
Put `x^2 - 1` = t
2x dx = dt
= `1/2 int "dt"/"t" + 2 int ("d"x)/sqrt(x^2 - 1^2)`
= `1/2 "t"^(- 1/2) "dt" + 2 log |x + sqrt(x^2 - 1^2)| + "c"`
= `1/2 ("t"^(- 1/2 + 1))/(- 1/2 + 1) + 2 log |x + sqrt(x^2 - 1)| + "c"`
= `1/2 ("t"^(1/2))/(1/2) + 2 log |x + sqrt(x^2 - 1)| + "c"`
`int (x + 2)/sqrt(x^2 - 1) "d"x = sqrt(x^2 - 1) + 2 log |x + sqrt(x^2 - 1)| + "c"`
APPEARS IN
संबंधित प्रश्न
Integrate the following functions with respect to x :
`(cos2x - cos 2 alpha)/(cosx - cos alpha)`
Integrate the following functions with respect to x :
`(cos 2x)/(sin^2x cos^2x)`
Integrate the following functions with respect to x :
cos 3x cos 2x
Integrate the following functions with respect to x :
`(1 + cos 4x)/(cos x - tan x)`
Integrate the following functions with respect to x :
`x^3/((x - 1)(x - 2))`
Integrate the following with respect to x :
`cosx/(cos(x - "a"))`
Integrate the following with respect to x:
`"e"^x ((2 + sin 2x)/(1 + cos 2x))`
Integrate the following with respect to x:\
`logx/(1 + log)^2`
Find the integrals of the following:
`1/(9x^2 - 4)`
Find the integrals of the following:
`1/(6x - 7 - x^2)`
Find the integrals of the following:
`1/((x + 1)^2 - 25)`
Integrate the following with respect to x:
`(2x - 3)/(x^2 + 4x - 12)`
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)`
Integrate the following functions with respect to x:
`sqrt(x^2 + 2x + 10)`
Choose the correct alternative:
The gradient (slope) of a curve at any point (x, y) is `(x^2 - 4)/x^2`. If the curve passes through the point (2, 7), then the equation of the curve 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
Choose the correct alternative:
`int "e"^(- 4x) cos "d"x` is
