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 : `int (1+logx)/(x(2+logx)(3+logx))dx`
Find the elasticity of demand if the marginal revenue is ₹ 50 and price is ₹ 75.
Evaluate:`int(tansqrtx)/sqrtxdx`
Integrate the following functions with respect to x :
cot2x + tan2x
Integrate the following with respect to x :
`("e"^x - "e"^-x)/("e"^x + "e"^-x)`
Integrate the following with respect to x :
`(sin sqrt(x))/sqrt(x)`
Integrate the following with respect to x :
`("cosec" x)/(log(tan x/2))`
Integrate the following with respect to x:
x sin 3x
Integrate the following with respect to x:
27x2e3x
Integrate the following with respect to x:
x2 cos x
Integrate the following with respect to x:
`sin^-1 ((2x)/(1 + x^2))`
Integrate the following with respect to x:
`"e"^(2x) sinx`
Find the integrals of the following:
`1/(4 - x^2)`
Find the integrals of the following:
`1/((x + 1)^2 - 25)`
Find the integrals of the following:
`1/sqrt((2 + x)^2 - 1)`
Find the integrals of the following:
`1/sqrt(x^2 - 4x + 5)`
Integrate the following with respect to x:
`(2x + 1)/sqrt(9 + 4x - x^2)`
Integrate the following with respect to x:
`(2x + 3)/sqrt(x^2 + 4x + 1)`
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
