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
Integrate the following functions with respect to x :
`(3 + 4cosx)/(sin^2x)`
Integrate the following functions with respect to x :
`(sin4x)/sinx`
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 :
`alpha beta x^(alpha - 1) "e"^(- beta x^alpha)`
Integrate the following with respect to x:
`"e"^(2x) sinx`
Integrate the following with respect to x:
`"e"^(- 3x) cos x`
Integrate the following with respect to x:
`"e"^x (tan x + log sec x)`
Integrate the following with respect to x:
`"e"^x sec x(1 + tan x)`
Integrate the following with respect to x:
`"e"^x ((2 + sin 2x)/(1 + cos 2x))`
Find the integrals of the following:
`1/sqrt(x^2 - 4x + 5)`
Integrate the following with respect to x:
`(x + 2)/sqrt(x^2 - 1)`
Integrate the following with respect to x:
`(2x + 3)/sqrt(x^2 + 4x + 1)`
Integrate the following functions with respect to x:
`sqrt((6 - x)(x - 4))`
Choose the correct alternative:
`int ("e"^x (1 + x))/(cos^2(x"e"^x)) "d"x` is
Choose the correct alternative:
`int (x^2 + cos^2x)/(x^2 + 1) "cosec"^2 x/("d"x)` is
Choose the correct alternative:
`int x^2 cos x "d"x` is
Choose the correct alternative:
`int sqrt((1 - x)/(1 + x)) "d"x` is
Choose the correct alternative:
`int 1/(x sqrt(log x)^2 - 5) "d"x` is
