Advertisements
Advertisements
Question
Integrate the following w.r.t.x : `x^2/sqrt(1 - x^6)`
Advertisements
Solution
Let I = `int x^2/sqrt(1 - x^6)*dx`
Put x3 = t
∴ 3x2dx = dt
∴ x2dx = `(1)/(3)*dt`
∴ I = `(1)/(3) int 1/sqrt(1 - t^2)*dt`
= `(1)/(3)sin^-1 (t) + c`
= `(1)/(3)sin^-1 (x^3) + c`.
APPEARS IN
RELATED QUESTIONS
Integrate the rational function:
`1/(x^2 - 9)`
Integrate the rational function:
`(2x)/(x^2 + 3x + 2)`
Integrate the rational function:
`(3x -1)/(x + 2)^2`
Integrate the rational function:
`1/(x^4 - 1)`
Integrate the rational function:
`1/(x(x^n + 1))` [Hint: multiply numerator and denominator by xn − 1 and put xn = t]
Integrate the rational function:
`((x^2 +1)(x^2 + 2))/((x^2 + 3)(x^2+ 4))`
Integrate the rational function:
`(2x)/((x^2 + 1)(x^2 + 3))`
`int (xdx)/((x - 1)(x - 2))` equals:
Find :
`∫ sin(x-a)/sin(x+a)dx`
Integrate the following w.r.t. x : `(x^2 + 2)/((x - 1)(x + 2)(x + 3)`
Integrate the following w.r.t. x : `(3x - 2)/((x + 1)^2(x + 3)`
Integrate the following w.r.t. x : `(5*e^x)/((e^x + 1)(e^(2x) + 9)`
Integrate the following w.r.t. x : `(2log x + 3)/(x(3 log x + 2)[(logx)^2 + 1]`
Choose the correct options from the given alternatives :
If `int tan^3x*sec^3x*dx = (1/m)sec^mx - (1/n)sec^n x + c, "then" (m, n)` =
Integrate the following with respect to the respective variable : `(cos 7x - cos8x)/(1 + 2 cos 5x)`
Integrate the following w.r.t.x : `(1)/((1 - cos4x)(3 - cot2x)`
Integrate the following w.r.t.x : `sec^2x sqrt(7 + 2 tan x - tan^2 x)`
Evaluate: `int "3x - 2"/(("x + 1")^2("x + 3"))` dx
Evaluate: `int 1/("x"("x"^"n" + 1))` dx
`int "dx"/(("x" - 8)("x" + 7))`=
For `int ("x - 1")/("x + 1")^3 "e"^"x" "dx" = "e"^"x"` f(x) + c, f(x) = (x + 1)2.
`int (2x - 7)/sqrt(4x- 1) dx`
`int "e"^(3logx) (x^4 + 1)^(-1) "d"x`
`int (7 + 4x + 5x^2)/(2x + 3)^(3/2) dx`
`int 1/(2 + cosx - sinx) "d"x`
`int sec^3x "d"x`
`int (x^2 + x -1)/(x^2 + x - 6) "d"x`
`int ("d"x)/(2 + 3tanx)`
`int (3x + 4)/sqrt(2x^2 + 2x + 1) "d"x`
`int x sin2x cos5x "d"x`
`int xcos^3x "d"x`
Choose the correct alternative:
`int (x + 2)/(2x^2 + 6x + 5) "d"x = "p"int (4x + 6)/(2x^2 + 6x + 5) "d"x + 1/2 int 1/(2x^2 + 6x + 5)"d"x`, then p = ?
`int 1/x^3 [log x^x]^2 "d"x` = p(log x)3 + c Then p = ______
Evaluate `int x^2"e"^(4x) "d"x`
`int x/((x - 1)^2 (x + 2)) "d"x`
Verify the following using the concept of integration as an antiderivative
`int (x^3"d"x)/(x + 1) = x - x^2/2 + x^3/3 - log|x + 1| + "C"`
Evaluate the following:
`int x^2/(1 - x^4) "d"x` put x2 = t
The numerator of a fraction is 4 less than its denominator. If the numerator is decreased by 2 and the denominator is increased by 1, the denominator becomes eight times the numerator. Find the fraction.
Find: `int x^2/((x^2 + 1)(3x^2 + 4))dx`
If f(x) = `int(3x - 1)x(x + 1)(18x^11 + 15x^10 - 10x^9)^(1/6)dx`, where f(0) = 0, is in the form of `((18x^α + 15x^β - 10x^γ)^δ)/θ`, then (3α + 4β + 5γ + 6δ + 7θ) is ______. (Where δ is a rational number in its simplest form)
`int 1/(x^2 + 1)^2 dx` = ______.
Evaluate: `int (2x^2 - 3)/((x^2 - 5)(x^2 + 4))dx`
Evaluate:
`int x/((x + 2)(x - 1)^2)dx`
Evaluate:
`int(2x^3 - 1)/(x^4 + x)dx`
Value of ∫ `(x^2 + 1)/((x − 1)(x − 2))`dx is ______.
