Advertisements
Advertisements
प्रश्न
Integrate the following with respect to x:
`(x + 2)/sqrt(x^2 - 1)`
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
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.
Integrate the following functions with respect to x :
`(x^3 + 4x^2 - 3x + 2)/x^2`
Integrate the following functions with respect to x :
`[sqrt(x) + 1/sqrt(x)]^2`
Integrate the following functions with respect to x :
`(3 + 4cosx)/(sin^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 :
`(3x - 9)/((x - 1)(x + 2)(x^2 + 1))`
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:
27x2e3x
Integrate the following with respect to x:
`"e"^(2x) sinx`
Integrate the following with respect to x:
`"e"^(- 3x) sin 2x`
Integrate the following with respect to x:
`"e"^x (tan x + log sec x)`
Find the integrals of the following:
`1/(9x^2 - 4)`
Find the integrals of the following:
`1/sqrt(9 + 8x - 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(81 + (2x + 1)^2`
Choose the correct alternative:
If `int 3^(1/x)/x^2 "d"x = "k"(3^(1/x)) + "c"`, then the value of k is
Choose the correct alternative:
`int sin^2x "d"x` is
Choose the correct alternative:
`int sqrt((1 - x)/(1 + x)) "d"x` is
