Advertisements
Advertisements
प्रश्न
Integrate the following with respect to x:
`"e"^x ((x - 1)/(2x^2))`
Advertisements
उत्तर
Let I =`int "e"^x ((x - 1)/2x^2) "d"x`
= `1/2 int "e"^x (x/x^2 - 1/x^2) "d"x`
= `1/2 int "e"^x (1/x - 1/x^2) "d"x`
Take f(x) = `1/x`
f'(x) = `- 1/x^2`
`[int "e"^x ["f"(x) + "f"(x)] "d"x = "e"^x "f"(x) + "c"]`
∴ I = `1/2 "e"^x 1/x + "c"`
I = `"e"^x/(2x) + "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 _0^1 ("x" . ("sin"^-1 "x")^2)/sqrt (1 - "x"^2)` dx
Integrate the following functions with respect to x :
`[sqrt(x) + 1/sqrt(x)]^2`
Integrate the following functions with respect to x :
(2x – 5)(3x + 4x)
Integrate the following functions with respect to x :
sin2 5x
Integrate the following functions with respect to x :
`(3x - 9)/((x - 1)(x + 2)(x^2 + 1))`
Integrate the following with respect to x :
`(sin 2x)/("a"^2 + "b"^2 sin^2x)`
Integrate the following with respect to x :
`tan x sqrt(sec x)`
Integrate the following with respect to x:
`(2x - 3)/(x^2 + 4x - 12)`
Integrate the following functions with respect to x:
`sqrt(x^2 + 2x + 10)`
Integrate the following functions with respect to x:
`sqrt(x^2 - 2x - 3)`
Integrate the following functions with respect to x:
`sqrt((x + 1)^2 - 4)`
Choose the correct alternative:
`int ("e"^x (1 + x))/(cos^2(x"e"^x)) "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 sqrt((1 - x)/(1 + x)) "d"x` is
Choose the correct alternative:
`int "e"^(- 4x) cos "d"x` is
Choose the correct alternative:
`int 1/(x sqrt(log x)^2 - 5) "d"x` is
