Advertisements
Advertisements
प्रश्न
For `int ("x - 1")/("x + 1")^3 "e"^"x" "dx" = "e"^"x"` f(x) + c, f(x) = (x + 1)2.
विकल्प
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: `∫8/((x+2)(x^2+4))dx`
Integrate the rational function:
`1/(x^2 - 9)`
Integrate the rational function:
`(2x)/(x^2 + 3x + 2)`
Integrate the rational function:
`(5x)/((x + 1)(x^2 - 4))`
Integrate the rational function:
`((x^2 +1)(x^2 + 2))/((x^2 + 3)(x^2+ 4))`
Integrate the rational function:
`1/(x(x^4 - 1))`
Find `int(e^x dx)/((e^x - 1)^2 (e^x + 2))`
Find `int (2cos x)/((1-sinx)(1+sin^2 x)) dx`
Integrate the following w.r.t. x : `(1)/(x(x^5 + 1)`
Integrate the following w.r.t. x : `(2log x + 3)/(x(3 log x + 2)[(logx)^2 + 1]`
Integrate the following w.r.t. x: `(x^2 + 3)/((x^2 - 1)(x^2 - 2)`
Evaluate: `int (5"x"^2 + 20"x" + 6)/("x"^3 + 2"x"^2 + "x")` dx
`int "dx"/(("x" - 8)("x" + 7))`=
Evaluate: `int ("3x" - 1)/("2x"^2 - "x" - 1)` dx
`int "e"^(3logx) (x^4 + 1)^(-1) "d"x`
`int sqrt((9 + x)/(9 - x)) "d"x`
`int sin(logx) "d"x`
`int "e"^x ((1 + x^2))/(1 + x)^2 "d"x`
`int (x + sinx)/(1 - cosx) "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 = ?
Choose the correct alternative:
`int ((x^3 + 3x^2 + 3x + 1))/(x + 1)^5 "d"x` =
If `int(sin2x)/(sin5x sin3x)dx = 1/3log|sin 3x| - 1/5log|f(x)| + c`, then f(x) = ______
Evaluate the following:
`int (x^2"d"x)/(x^4 - x^2 - 12)`
Evaluate the following:
`int (x^2 "d"x)/((x^2 + "a"^2)(x^2 + "b"^2))`
Evaluate the following:
`int sqrt(tanx) "d"x` (Hint: Put tanx = t2)
`int 1/(x^2 + 1)^2 dx` = ______.
Evaluate:
`int (x + 7)/(x^2 + 4x + 7)dx`
