Advertisements
Advertisements
प्रश्न
Integrate the following with respect to x :
`alpha beta x^(alpha - 1) "e"^(- beta x^alpha)`
Advertisements
उत्तर
`int alpha beta x^(alpha - 1) "e"^(- beta x^alpha)`
Put β xα = u
α β xα-1 dx = du
`int alpha beta x^(alpha - 1) "e"^(- beta x^alpha) * "d"x = int "e"^(- betax^alpha) (alpha beta) x^(alpha - 1) * "d"x`
= `int "e"^(- "u") * "du"`
= `("e"^(- "u"))/(- 1) + "c"`
`int alpha beta x^(alpha - 1) "e"^(- beta x^alpha) * "d"x = - "e"^(- beta x^alpha) + "c"`
APPEARS IN
संबंधित प्रश्न
Evaluate : `int1/(x(3+logx))dx`
Integrate the following functions with respect to x :
`(sin^2x)/(1 + cosx)`
Integrate the following functions with respect to x :
`(1 + cos 4x)/(cos x - tan x)`
Integrate the following with respect to x :
`x^2/(1 + x^6)`
Integrate the following with respect to x :
`(sin^-1 x)/sqrt(1 - x^2)`
Integrate the following with respect to x :
`tan x sqrt(sec x)`
Integrate the following with respect to x :
sin5x cos3x
Integrate the following with respect to x:
x sin 3x
Integrate the following with respect to x:
25xe–5x
Integrate the following with respect to x:
x2 cos x
Integrate the following with respect to x:
`(x sin^-1 x)/sqrt(1 - x^2)`
Integrate the following with respect to x:
`"e"^(- 3x) sin 2x`
Integrate the following with respect to x:
`"e"^x (tan x + log sec x)`
Integrate the following with respect to x:
`(2x - 3)/(x^2 + 4x - 12)`
Integrate the following with respect to x:
`(2x + 1)/sqrt(9 + 4x - x^2)`
Integrate the following functions with respect to x:
`sqrt((6 - x)(x - 4))`
Choose the correct alternative:
If `int 3^(1/x)/x^2 "d"x = "k"(3^(1/x)) + "c"`, then the value of k 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
