Advertisements
Advertisements
प्रश्न
Integrate the following functions with respect to x :
`(3x + 4) sqrt(3x + 7)`
Advertisements
उत्तर
`int (3x + 4) sqrt(3x + 7) "d"x = int (3x + 7 - 3) sqrt(3x + 7) "d"x`
= `int [(3x + 7) sqrt(3x + 7) - 3sqrt(3x + 7)] "d"x`
= `int (3x + 7) sqrt(3x + 7) "d"x - int 3sqrt(3x + 7) "d"x`
= `int (3x + 7)^(3/2) "d"x - 3int (3x + 7)^(1/2) "d"x`
= `1/3 (3x + 7)^(3/2 + 1)/(3/2 + 1) - 3(3x + 7)^(1/2 + 1)/(1/2 + 1) + "c"`
= `1/3 (3x + 7)^(5/2)/(5/2) - 3 xx 1/3 (3x + 7)^(3/2)/(3/2) + "c"`
= `1/3 xx 2/5 (3x + 7)^(5/2) - 2/3 (3x + 7)^(3/2) + "c"`
= `2/15 (3x + 7)^(5/2) - 2/3 (3x + 7)^(3/2) + "c"`
APPEARS IN
संबंधित प्रश्न
Evaluate : `int1/(x(3+logx))dx`
Evaluate : `∫_0^(pi/2) (sinx.cosx)/(1 + sin^4x)`.dx
Integrate the following functions with respect to x :
(2x – 5)(3x + 4x)
Integrate the following functions with respect to x :
`(cos 2x)/(sin^2x cos^2x)`
Integrate the following functions with respect to x :
`(3 + 4cosx)/(sin^2x)`
Integrate the following with respect to x :
`("cosec" x)/(log(tan x/2))`
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 :
`cosx/(cos(x - "a"))`
Integrate the following with respect to x:
9xe3x
Integrate the following with respect to x:
x log x
Integrate the following with respect to x:
x5ex2
Integrate the following with respect to x:
`sin^-1 ((2x)/(1 + x^2))`
Integrate the following with respect to x:
`"e"^(- 3x) sin 2x`
Find the integrals of the following:
`1/sqrt((2 + x)^2 - 1)`
Integrate the following with respect to x:
`(5x - 2)/(2 + 2x + x^2)`
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(x^2 tan^-1x + tan^-1x + 1))/(x^2 + 1) "d"x` is
Choose the correct alternative:
`int sqrt((1 - x)/(1 + x)) "d"x` is
