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
Evaluate : `∫_0^(pi/2) (sinx.cosx)/(1 + sin^4x)`.dx
Evaluate : `int_0^1 "x" . "tan"^-1 "x" "dx"`
Evaluate:`int(tansqrtx)/sqrtxdx`
Integrate the following functions with respect to x :
`(sin^2x)/(1 + cosx)`
Integrate the following with respect to x :
`x/sqrt(1 + x^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:
25xe–5x
Integrate the following with respect to x:
`(x sin^-1 x)/sqrt(1 - x^2)`
Integrate the following with respect to x:
`"e"^(-x) cos 2x`
Integrate the following with respect to x:
`"e"^(- 3x) sin 2x`
Find the integrals of the following:
`1/(6x - 7 - x^2)`
Find the integrals of the following:
`1/sqrt(x^2 - 4x + 5)`
Integrate the following with respect to x:
`(3x + 1)/(2x^2 - 2x + 3)`
Integrate the following functions with respect to x:
`sqrt((6 - x)(x - 4))`
Integrate the following functions with respect to x:
`sqrt(81 + (2x + 1)^2`
Choose the correct alternative:
`int ("d"x)/("e"^x - 1)` is
Choose the correct alternative:
`int (sec^2x)/(tan^2 x - 1) "d"x`
Choose the correct alternative:
`int x^2 "e"^(x/2) "d"x` is
Choose the correct alternative:
`int "e"^(sqrt(x)) "d"x` is
