Advertisements
Advertisements
Question
Integrate the following with respect to x :
`x^2/(1 + x^6)`
Advertisements
Solution
`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
RELATED QUESTIONS
Evaluate:`int(tansqrtx)/sqrtxdx`
Integrate the following functions with respect to x :
`(x^3 + 4x^2 - 3x + 2)/x^2`
Integrate the following functions with respect to x :
`(3 + 4cosx)/(sin^2x)`
Integrate the following with respect to x :
`alpha beta x^(alpha - 1) "e"^(- beta x^alpha)`
Integrate the following with respect to x :
x(1 – x)17
Integrate the following with respect to x:
x sin 3x
Integrate the following with respect to x:
`"e"^(2x) sinx`
Integrate the following with respect to x:
`"e"^(-x) cos 2x`
Integrate the following with respect to x:
`"e"^(- 3x) cos x`
Integrate the following with respect to x:
`"e"^(tan^-1 x) ((1 + x + x^2)/(1 + x^2))`
Integrate the following with respect to x:\
`logx/(1 + log)^2`
Find the integrals of the following:
`1/(25 - 4x^2)`
Find the integrals of the following:
`1/sqrt((2 + x)^2 - 1)`
Integrate the following with respect to x:
`(3x + 1)/(2x^2 - 2x + 3)`
Integrate the following with respect to x:
`(2x + 1)/sqrt(9 + 4x - x^2)`
Integrate the following functions with respect to x:
`sqrt((x + 1)^2 - 4)`
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 (x^2 + cos^2x)/(x^2 + 1) "cosec"^2 x/("d"x)` is
