Advertisements
Advertisements
प्रश्न
Integrate the following functions with respect to x :
`1/(sqrt(x + 3) - sqrt(x - 4))`
Advertisements
उत्तर
`int 1/(sqrt(x + 3) - sqrt(x - 4)) "d"x`
= `int 1/(sqrt(x + 3) - sqrt(x - 4)) xx (sqrt(x + 3) + sqrt(x - 4))/(sqrt(x + 3) + sqrt(x - 4)) "d"x`
= `int (sqrt(x + 3) + sqrt(x - 4))/((x + 3) - (x - 4)) "d"x`
= `int (sqrt(x + 3) + sqrt(x - 4))/(x + 3 - x + 4) "d"x`
= `int (sqrt(x + 3) + sqrt(x - 4))/7 "d"x`
= `int sqrt(x + 3)/7 "d"x + int sqrt(x - 4)/7 "d"x`
= `1/7 int (x + 3)^(1/2) "d"x + 1/7 int (x - 4)^(1/2) "d"x`
= `1/7 (x + 3)^(1/2 + 1)/(1/2 + 1) + 1/7 (x - 4)^(1/2 + 1)/(1/2 + 1) + "c"`
= `1/7 (x + 3)^(3/2)/(3/2) + 1/7 (x - 4)^(3/2)/(3/2) + "c"`
= `1/7 xx 2/3 (x + 3)^(3/2) + 1/7 xx 2/3 (x - 4)^(3/2) + "c"`
= `2/21 [(x + 3)^(3/2) + (x - 4)^(3/2)] + "c"`
APPEARS IN
संबंधित प्रश्न
Evaluate : `int1/(x(3+logx))dx`
Integrate the following functions with respect to x :
(2x – 5)(3x + 4x)
Integrate the following functions with respect to x :
cot2x + tan2x
Integrate the following functions with respect to x :
`(cos 2x)/(sin^2x cos^2x)`
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 :
`("cosec" x)/(log(tan x/2))`
Integrate the following with respect to x :
sin5x cos3x
Integrate the following with respect to x:
`"e"^(2x) sinx`
Integrate the following with respect to x:
`"e"^x ((2 + sin 2x)/(1 + cos 2x))`
Find the integrals of the following:
`1/(9x^2 - 4)`
Find the integrals of the following:
`1/(6x - 7 - x^2)`
Find the integrals of the following:
`1/sqrt(x^2 - 4x + 5)`
Integrate the following with respect to x:
`(5x - 2)/(2 + 2x + x^2)`
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)`
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 ("e"^x (1 + x))/(cos^2(x"e"^x)) "d"x` is
Choose the correct alternative:
`int tan^-1 sqrt((1 - cos 2x)/(1 + cos 2x)) "d"x` is
Choose the correct alternative:
`int ("e"^x(x^2 tan^-1x + tan^-1x + 1))/(x^2 + 1) "d"x` is
