Advertisements
Advertisements
प्रश्न
Integrate the following with respect to x :
`x^2/(1 + x^6)`
Advertisements
उत्तर
`int x^2/(1 + x^6) "d"x = int x^2/(1 + (x^3)^2) "d"x`
Put x3 = u
3x2 dx = du
x2 dx = `1/3 "du"`
`int x^2/(1 + x^6) "d"x = int (1/3 "du")/(1 + "u"^2)`
= `1/3 int "du"/(1 + "u"^2)`
= `1/3 tan^-1 ("u") + "c"`
`int x^2/(1 + x^6) "d"x = 1/3 tan^-1 (x^3) + "c"`
APPEARS IN
संबंधित प्रश्न
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 :
`x^3/((x - 1)(x - 2))`
Integrate the following with respect to x :
`("e"^x - "e"^-x)/("e"^x + "e"^-x)`
Integrate the following with respect to x :
`(sin^-1 x)/sqrt(1 - x^2)`
Integrate the following with respect to x:
9xe3x
Integrate the following with respect to x:
x sec x tan x
Integrate the following with respect to x:
x log x
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"^x (tan x + log sec x)`
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:
`(3x + 1)/(2x^2 - 2x + 3)`
Integrate the following functions with respect to x:
`sqrt((x + 1)^2 - 4)`
Choose the correct alternative:
The gradient (slope) of a curve at any point (x, y) is `(x^2 - 4)/x^2`. If the curve passes through the point (2, 7), then the equation of the curve is
Choose the correct alternative:
`int sqrt((1 - x)/(1 + x)) "d"x` is
Choose the correct alternative:
`int (x + 2)/sqrt(x^2 - 1) "d"x` is
