Advertisements
Advertisements
प्रश्न
Find : `int (2x^2 + 3)/(x^2(x^2 + 9))dx; x ≠ 0`.
Advertisements
उत्तर
We have, `(2x^2 + 3)/(x^2(x^2 + 9))`
Now, let x2 = t
So, `(2t + 3)/(t(t + 9)) = A/t + B/(t + 9)`, we get A = `1/3` and B = `5/3`
`int (2x^2 + 3)/(x^2(x^2 + 9))dx = 1/3 int dx/x^2 + 5/3 int dx/(x^2 + 9)`
= `-1/(3x) + 5/9 tan^-1 (x/3) + c`, where 'c' is an arbitrary constant of integration.
APPEARS IN
संबंधित प्रश्न
Evaluate : `int x^2/((x^2+2)(2x^2+1))dx`
Find: `I=intdx/(sinx+sin2x)`
Integrate the rational function:
`(1 - x^2)/(x(1-2x))`
Integrate the rational function:
`(3x + 5)/(x^3 - x^2 - x + 1)`
Integrate the rational function:
`(5x)/((x + 1)(x^2 - 4))`
`int (dx)/(x(x^2 + 1))` equals:
Find `int (2cos x)/((1-sinx)(1+sin^2 x)) dx`
Integrate the following w.r.t. x : `(x^2 + 2)/((x - 1)(x + 2)(x + 3)`
Integrate the following w.r.t. x : `x^2/((x^2 + 1)(x^2 - 2)(x^2 + 3))`
Integrate the following w.r.t. x : `(3x - 2)/((x + 1)^2(x + 3)`
Integrate the following w.r.t. x : `(1)/(x(1 + 4x^3 + 3x^6)`
Integrate the following w.r.t. x : `(1)/(sin2x + cosx)`
Integrate the following w.r.t. x : `(5*e^x)/((e^x + 1)(e^(2x) + 9)`
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 w.r.t.x : `sec^2x sqrt(7 + 2 tan x - tan^2 x)`
Evaluate: `int 1/("x"("x"^5 + 1))` dx
`int "dx"/(("x" - 8)("x" + 7))`=
`int "e"^(3logx) (x^4 + 1)^(-1) "d"x`
`int x^7/(1 + x^4)^2 "d"x`
`int "e"^x ((1 + x^2))/(1 + x)^2 "d"x`
`int (x + sinx)/(1 - cosx) "d"x`
`int ("d"x)/(x^3 - 1)`
`int ((2logx + 3))/(x(3logx + 2)[(logx)^2 + 1]) "d"x`
Evaluate `int x^2"e"^(4x) "d"x`
If `int 1/((x^2 + 4)(x^2 + 9))dx = A tan^-1 x/2 + B tan^-1(x/3) + C`, then A – B = ______.
A proper rational function can be expressed as a sum of simpler rational functions called what?
Why is \[\frac{x^{2}+1}{x^{2}-5x+6}\] not a proper rational function?
For \[\frac{5x-5}{(x-2)(x-3)}=\frac{\mathrm{A}}{x-2}+\frac{\mathrm{B}}{x-3}\], which equation results after clearing denominators?
