Advertisements
Advertisements
प्रश्न
For `int ("x - 1")/("x + 1")^3 "e"^"x" "dx" = "e"^"x"` f(x) + c, f(x) = (x + 1)2.
पर्याय
True
False
Advertisements
उत्तर
This statement is false.
Explanation:
Let I =`(("x" - 1))/(("x" + 1)^3) * "e"^"x"` dx
`= int "e"^"x" [(("x" + 1) - 2)/("x"+ 1)^3]` dx
`= int "e"^"x" [1/("x" + 1)^2 - 2/("x" + 1)^3]` dx
`= int "e"^"x" [("x" + 1)^-2 - 2("x" + 1)^-3]` dx
Put f(x) = (x + 1)-2
∴ f '(x) = − 2 (x + 1)−3
∴ I = `"e"^"x" ["f"("x") + "f" '("x")]` dx
`= "e"^"x" * "f"("x")` + c
`= "e"^"x" * ("x + 1")^-2` + c
∴ f(x) = (x + 1)−2
संबंधित प्रश्न
Evaluate : `int x^2/((x^2+2)(2x^2+1))dx`
Integrate the rational function:
`x/((x-1)(x- 2)(x - 3))`
Integrate the rational function:
`(x^3 + x + 1)/(x^2 -1)`
Integrate the rational function:
`1/(x^4 - 1)`
`int (xdx)/((x - 1)(x - 2))` equals:
Evaluate : `∫(x+1)/((x+2)(x+3))dx`
Integrate the following w.r.t. x : `(2x)/((2 + x^2)(3 + x^2)`
Integrate the following w.r.t. x: `(1)/(sinx + sin2x)`
Integrate the following w.r.t. x : `(1)/(sinx*(3 + 2cosx)`
Integrate the following with respect to the respective variable : `(6x + 5)^(3/2)`
Integrate the following w.r.t.x : `(1)/(2cosx + 3sinx)`
Integrate the following w.r.t.x : `(1)/(sinx + sin2x)`
`int 1/(x(x^3 - 1)) "d"x`
`int sqrt((9 + x)/(9 - x)) "d"x`
`int sec^2x sqrt(tan^2x + tanx - 7) "d"x`
`int "e"^(sin^(-1_x))[(x + sqrt(1 - x^2))/sqrt(1 - x^2)] "d"x`
`int "e"^x ((1 + x^2))/(1 + x)^2 "d"x`
`int (x^2 + x -1)/(x^2 + x - 6) "d"x`
`int x^3tan^(-1)x "d"x`
`int 1/x^3 [log x^x]^2 "d"x` = p(log x)3 + c Then p = ______
`int x/((x - 1)^2 (x + 2)) "d"x`
`int 1/(4x^2 - 20x + 17) "d"x`
Evaluate the following:
`int x^2/(1 - x^4) "d"x` put x2 = t
Evaluate the following:
`int (x^2 "d"x)/((x^2 + "a"^2)(x^2 + "b"^2))`
Find: `int x^2/((x^2 + 1)(3x^2 + 4))dx`
Evaluate: `int_-2^1 sqrt(5 - 4x - x^2)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 (5x^2 - 6x + 3) / (2x -3) dx`
Value of ∫ `(x^2 + 1)/((x − 1)(x − 2))`dx is ______.
A proper rational function can be expressed as a sum of simpler rational functions called what?
