Advertisements
Advertisements
प्रश्न
Integrate the following with respect to x:
25xe–5x
Advertisements
उत्तर
`int 5x"e"^(-5x) "d"x = int 5x"e"^(- 5x) "d"x`
`int "u" "dv" = "uv" - "u""'""v"_2 + "u""'""v"_2 - "u""'""v"_3 +` .........(1)
u = x
u' = 1
u" = 0
dv = `"e"^(- 5x) * "d"x`
⇒ v = `int "e"^(- 5x) * d"x`
= `("e"^(- 5x))/(- 5)`
v1 = `int "v" "d"x`
= `- 1/5 int "e"^(-5x) * "d"x`
= `- 1/5 xx ("e"^(- 5x))/(- 5)`
= `+ 1/5^2 "e"^(-5x)`
v2 = `int "v"_1 "d"x`
= `int 1/5^2 "e"^(- 5x) "d"x`
= `1/5^2 xx ("e"^-5x)/(- 5)`
= `- 1/5^3 "e"^(- 5x)`
`int 25x "e"^(- 5x) "d"x = 25[x xx ("e"^(- 5x))/(5x) - 1 xx 1/5^2 "e"^(- 5x) + 0 xx - 1/5^3 "e"^(-5x)]`
= `25[ - x/5 "e"^(- 5x) - 1/5^2 "e"(- 5x)]`
= `- 5x "e"^(-5 x) - "e"^(- 5x)`
`int 25x "e"^(- 5x) "d"x = - "e"^( 5x) (5x + 1 + "c"`
APPEARS IN
संबंधित प्रश्न
Evaluate : `∫_0^(pi/2) (sinx.cosx)/(1 + sin^4x)`.dx
Integrate the following functions with respect to x :
`(x^3 + 4x^2 - 3x + 2)/x^2`
Integrate the following functions with respect to x :
cos 3x cos 2x
Integrate the following functions with respect to x :
`(8^(1 + x) + 4^(1 - x))/2^x`
Integrate the following functions with respect to x :
`(3x - 9)/((x - 1)(x + 2)(x^2 + 1))`
Integrate the following with respect to x :
`cot x/(log(sin x))`
Integrate the following with respect to x :
`(sin 2x)/("a"^2 + "b"^2 sin^2x)`
Integrate the following with respect to x:
`"e"^(- 3x) sin 2x`
Integrate the following with respect to x:
`"e"^(- 3x) cos x`
Find the integrals of the following:
`1/(4 - 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(9 - (2x + 5)^2`
Choose the correct alternative:
`int 2^(3x + 5) "d"x` is
Choose the correct alternative:
`int ("e"^x(x^2 tan^-1x + tan^-1x + 1))/(x^2 + 1) "d"x` is
Choose the correct alternative:
`int sin sqrt(x) "d"x` is
Choose the correct alternative:
`int "e"^(sqrt(x)) "d"x` is
