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 : `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 :
`(sin^2x)/(1 + cosx)`
Integrate the following functions with respect to x :
cos 3x cos 2x
Integrate the following functions with respect to x :
`x^3/((x - 1)(x - 2))`
Integrate the following with respect to x :
`("e"^x - "e"^-x)/("e"^x + "e"^-x)`
Integrate the following with respect to x :
`(sin sqrt(x))/sqrt(x)`
Integrate the following with respect to x :
`tan x sqrt(sec x)`
Integrate the following with respect to x :
x(1 – x)17
Integrate the following with respect to x:
`tan^-1 ((8x)/(1 - 16x^2))`
Find the integrals of the following:
`1/((x + 1)^2 - 25)`
Find the integrals of the following:
`1/sqrt(x^2 - 4x + 5)`
Integrate the following with respect to x:
`(2x - 3)/(x^2 + 4x - 12)`
Integrate the following with respect to x:
`(2x + 3)/sqrt(x^2 + 4x + 1)`
Integrate the following functions with respect to x:
`sqrt(9 - (2x + 5)^2`
Integrate the following functions with respect to x:
`sqrt(81 + (2x + 1)^2`
Integrate the following functions with respect to x:
`sqrt((x + 1)^2 - 4)`
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
