Advertisements
Advertisements
प्रश्न
Integrate the following w.r.t.x : `x^2/sqrt(1 - x^6)`
Advertisements
उत्तर
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
संबंधित प्रश्न
Find : `int x^2/(x^4+x^2-2) dx`
Evaluate:
`int x^2/(x^4+x^2-2)dx`
Evaluate: `∫8/((x+2)(x^2+4))dx`
Integrate the rational function:
`(3x + 5)/(x^3 - x^2 - x + 1)`
Integrate the rational function:
`(2x - 3)/((x^2 -1)(2x + 3))`
Integrate the rational function:
`(5x)/((x + 1)(x^2 - 4))`
Integrate the rational function:
`(x^3 + x + 1)/(x^2 -1)`
Integrate the rational function:
`(cos x)/((1-sinx)(2 - sin x))` [Hint: Put sin x = t]
Integrate the following w.r.t. x : `(1)/(x(x^5 + 1)`
Integrate the following w.r.t. x : `(1)/(x(1 + 4x^3 + 3x^6)`
Integrate the following w.r.t. x : `(1)/(sinx*(3 + 2cosx)`
Integrate the following w.r.t. x : `(5*e^x)/((e^x + 1)(e^(2x) + 9)`
Integrate the following w.r.t. x: `(x^2 + 3)/((x^2 - 1)(x^2 - 2)`
Integrate the following with respect to the respective variable : `cot^-1 ((1 + sinx)/cosx)`
Integrate the following w.r.t.x : `(1)/((1 - cos4x)(3 - cot2x)`
Integrate the following w.r.t.x : `(1)/(2cosx + 3sinx)`
Integrate the following w.r.t.x : `(1)/(sinx + sin2x)`
Evaluate: `int "3x - 2"/(("x + 1")^2("x + 3"))` dx
`int "dx"/(("x" - 8)("x" + 7))`=
Evaluate: `int (2"x"^3 - 3"x"^2 - 9"x" + 1)/("2x"^2 - "x" - 10)` dx
`int sqrt(4^x(4^x + 4)) "d"x`
`int 1/(2 + cosx - sinx) "d"x`
`int sec^3x "d"x`
`int sec^2x sqrt(tan^2x + tanx - 7) "d"x`
`int x^3tan^(-1)x "d"x`
`int x sin2x cos5x "d"x`
`int x^2/((x^2 + 1)(x^2 - 2)(x^2 + 3)) "d"x`
`int ((2logx + 3))/(x(3logx + 2)[(logx)^2 + 1]) "d"x`
Evaluate `int x^2"e"^(4x) "d"x`
If `intsqrt((x - 7)/(x - 9)) dx = Asqrt(x^2 - 16x + 63) + log|x - 8 + sqrt(x^2 - 16x + 63)| + c`, then A = ______
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: `int (dx)/(2 + cos x - sin x)`
Find: `int x^2/((x^2 + 1)(3x^2 + 4))dx`
If `int 1/((x^2 + 4)(x^2 + 9))dx = A tan^-1 x/2 + B tan^-1(x/3) + C`, then A – B = ______.
Find: `int x^4/((x - 1)(x^2 + 1))dx`.
Find : `int (2x^2 + 3)/(x^2(x^2 + 9))dx; x ≠ 0`.
Evaluate:
`int x/((x + 2)(x - 1)^2)dx`
When is a rational function called improper?
Integration by partial fractions is a method used to integrate which functions?
Which partial-fraction decomposition is appropriate for \[\frac{\mathrm{p}x+\mathrm{q}}{(x-\mathrm{a})(x-\mathrm{b})}\]?
What is done after long division, before writing the appropriate partial-fraction decomposition?
What is the result of dividing \[x^{2}+1\] by \[x^{2}-5x+6\]?
For \[\frac{5x-5}{(x-2)(x-3)}=\frac{\mathrm{A}}{x-2}+\frac{\mathrm{B}}{x-3}\], which equation results after clearing denominators?
Which decomposition is correct for \[\frac{x^{2}+1}{x^{2}-5x+6}\]?
