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
Integrate the rational function:
`1/(x^2 - 9)`
Integrate the rational function:
`(1 - x^2)/(x(1-2x))`
Integrate the rational function:
`2/((1-x)(1+x^2))`
Find :
`∫ sin(x-a)/sin(x+a)dx`
Integrate the following w.r.t. x:
`(6x^3 + 5x^2 - 7)/(3x^2 - 2x - 1)`
Integrate the following w.r.t. x : `(1)/(x(x^5 + 1)`
Integrate the following w.r.t. x : `(1)/(x^3 - 1)`
Integrate the following w.r.t. x : `((3sin - 2)*cosx)/(5 - 4sin x - cos^2x)`
Integrate the following w.r.t.x : `x^2/sqrt(1 - x^6)`
Integrate the following w.r.t.x:
`x^2/((x - 1)(3x - 1)(3x - 2)`
Integrate the following w.r.t.x : `sqrt(tanx)/(sinx*cosx)`
`int "e"^(3logx) (x^4 + 1)^(-1) "d"x`
`int ((x^2 + 2))/(x^2 + 1) "a"^(x + tan^(-1_x)) "d"x`
`int sqrt((9 + x)/(9 - x)) "d"x`
`int 1/(2 + cosx - sinx) "d"x`
`int (3x + 4)/sqrt(2x^2 + 2x + 1) "d"x`
`int x^3tan^(-1)x "d"x`
`int x^2/((x^2 + 1)(x^2 - 2)(x^2 + 3)) "d"x`
`int ("d"x)/(x^3 - 1)`
Choose the correct alternative:
`int sqrt(1 + x) "d"x` =
Evaluate `int x^2"e"^(4x) "d"x`
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 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))`
If f(x) = `int(3x - 1)x(x + 1)(18x^11 + 15x^10 - 10x^9)^(1/6)dx`, where f(0) = 0, is in the form of `((18x^α + 15x^β - 10x^γ)^δ)/θ`, then (3α + 4β + 5γ + 6δ + 7θ) is ______. (Where δ is a rational number in its simplest form)
`int 1/(x^2 + 1)^2 dx` = ______.
Find: `int x^4/((x - 1)(x^2 + 1))dx`.
Evaluate:
`int 2/((1 - x)(1 + x^2))dx`
Evaluate:
`int (x + 7)/(x^2 + 4x + 7)dx`
