Advertisements
Advertisements
प्रश्न
Integrate the following with respect to x.
`"e"^x [(x - 1)/(x + 1)^3]`
उत्तर
`"e"^x [(x - 1)/(x + 1)^3] = "e"^x [(x + 1 - 1 - 1)/(x + 1)^3]`
= `"e"^x [(x + 1)/(x + 1)^3 - 2/(x + 1)^3]`
= `"e"^x [1/(x + 1)^2 - 2/(x + 1)^3]`
Ler f(x) = `1/(x + 1)^2`
f'(x) = `(- 2)/(x + 1)^3`
So `int ("e"^x (x - 1))/(x + 1)^3 "d"x = int "e"^x ["f"(x) + "f'"(x)] "d"x`
= `"e"^x "f"(x) + "c"`
= `"e"^x/(x + 1)^2 + "c"`
APPEARS IN
संबंधित प्रश्न
Integrate the following with respect to x.
If f'(x) = `1/x` and f(1) = `pi/4`, then find f(x)
Integrate the following with respect to x.
`"e"^(xlog"a") + "e"^("a"log"a") - "e"^("n"logx)`
Integrate the following with respect to x.
ex(1 + x) log(xex)
Integrate the following with respect to x.
`1/(x^2(x^2 + 1))`
Integrate the following with respect to x.
`1/sqrt(x^2 - 3x + 2)`
Integrate the following with respect to x.
`sqrt(1 + x + x^2)`
Choose the correct alternative:
`int (sin2x)/(2sinx) "d"x` is
Choose the correct alternative:
`int "e"^x/("e"^x + 1) "d"x` is
Choose the correct alternative:
`int (2x + 3)/sqrt(x^2 + 3x + 2) "d"x` is
Choose the correct alternative:
`int_0^(pi/3) tan x "d"x` is
