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
Evaluate : `∫_0^(pi/2) (sinx.cosx)/(1 + sin^4x)`.dx
Find the volume of the solid obtained by revolving about the X-axis, the region bounded by the curve `"x"^2/4 - "y"^2/9 = 1` and the lines x = 2 , x = 4.
Integrate the following functions with respect to x :
cot2x + tan2x
Integrate the following functions with respect to x :
cos 3x cos 2x
Integrate the following functions with respect to x :
`"e"^(x log "a") "e"^x`
Integrate the following functions with respect to x :
`1/((x - 1)(x + 2)^2`
Integrate the following with respect to x :
`x/sqrt(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 :
`sqrt(x)/(1 + sqrt(x))`
Integrate the following with respect to x :
`tan x sqrt(sec x)`
Integrate the following with respect to x:
x sec x tan x
Integrate the following with respect to x:
`"e"^(tan^-1 x) ((1 + x + x^2)/(1 + x^2))`
Find the integrals of the following:
`1/sqrt(xx^2 + 4x + 2)`
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)`
Choose the correct alternative:
`int (x^2 + cos^2x)/(x^2 + 1) "cosec"^2 x/("d"x)` is
Choose the correct alternative:
`int x^2 cos x "d"x` is
Choose the correct alternative:
`int ("d"x)/("e"^x - 1)` is
Choose the correct alternative:
`int 1/(x sqrt(log x)^2 - 5) "d"x` is
