Advertisements
Advertisements
प्रश्न
Integrate the rational function:
`1/(x^2 - 9)`
Advertisements
उत्तर
Let `1/(x^2 - 9) = 1/((x - 3)(x + 3))`
`= A/(x - 3) + B/(x + 3)`
⇒ 1 ≡ A(x + 3) + B(x - 3)
Put x = 3
1 = A (3 + 3)
⇒ A `= 1/6`
again, put x = -3
1 = B(3 - 3)
⇒ B `= -1/6`
`therefore 1/(x^2 - 9) = 1/6 [1/(x - 3) - 1/(x + 3)]`
`=> int 1/(x^2 - 9) = 1/6 int (1/(x - 3) - 1/(x + 3))` dx
`= 1/6 [log abs (x - 3) - log abs (x + 3)] + C`
`= 1/6 log abs ((x - 3)/(x + 3)) + C`
APPEARS IN
संबंधित प्रश्न
Evaluate:
`int x^2/(x^4+x^2-2)dx`
Integrate the rational function:
`x/((x + 1)(x+ 2))`
Integrate the rational function:
`(3x - 1)/((x - 1)(x - 2)(x - 3))`
Integrate the rational function:
`x/((x-1)(x- 2)(x - 3))`
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 :
`∫ sin(x-a)/sin(x+a)dx`
Integrate the following w.r.t. x : `(12x + 3)/(6x^2 + 13x - 63)`
Integrate the following w.r.t. x:
`(6x^3 + 5x^2 - 7)/(3x^2 - 2x - 1)`
Integrate the following w.r.t. x : `(2x)/((2 + x^2)(3 + x^2)`
Integrate the following w.r.t. x : `2^x/(4^x - 3 * 2^x - 4`
Integrate the following w.r.t. x : `(1)/(x(1 + 4x^3 + 3x^6)`
Integrate the following w.r.t.x:
`x^2/((x - 1)(3x - 1)(3x - 2)`
Evaluate: `int 1/("x"("x"^"n" + 1))` dx
Evaluate: `int (5"x"^2 + 20"x" + 6)/("x"^3 + 2"x"^2 + "x")` dx
State whether the following statement is True or False.
If `int (("x - 1") "dx")/(("x + 1")("x - 2"))` = A log |x + 1| + B log |x - 2| + c, then A + B = 1.
Evaluate: `int (2"x"^3 - 3"x"^2 - 9"x" + 1)/("2x"^2 - "x" - 10)` dx
If f'(x) = `x - 3/x^3`, f(1) = `11/2` find f(x)
`int (7 + 4x + 5x^2)/(2x + 3)^(3/2) dx`
`int x^3tan^(-1)x "d"x`
`int x sin2x cos5x "d"x`
`int (x + sinx)/(1 - cosx) "d"x`
`int ("d"x)/(x^3 - 1)`
`int xcos^3x "d"x`
`int (sin2x)/(3sin^4x - 4sin^2x + 1) "d"x`
`int ((2logx + 3))/(x(3logx + 2)[(logx)^2 + 1]) "d"x`
Choose the correct alternative:
`int sqrt(1 + x) "d"x` =
Choose the correct alternative:
`int ((x^3 + 3x^2 + 3x + 1))/(x + 1)^5 "d"x` =
State whether the following statement is True or False:
For `int (x - 1)/(x + 1)^3 "e"^x"d"x` = ex f(x) + c, f(x) = (x + 1)2
Evaluate the following:
`int x^2/(1 - x^4) "d"x` put x2 = t
Evaluate the following:
`int_"0"^pi (x"d"x)/(1 + sin x)`
Evaluate: `int (dx)/(2 + cos x - sin x)`
Find: `int x^2/((x^2 + 1)(3x^2 + 4))dx`
If `intsqrt((x - 5)/(x - 7))dx = Asqrt(x^2 - 12x + 35) + log|x| - 6 + sqrt(x^2 - 12x + 35) + C|`, then A = ______.
Evaluate: `int (2x^2 - 3)/((x^2 - 5)(x^2 + 4))dx`
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 2/((1 - x)(1 + x^2))dx`
