Advertisements
Advertisements
प्रश्न
Evaluate: `int "e"^"x" (1 + "x")/(2 + "x")^2` dx
Advertisements
उत्तर
Let I = `int "e"^"x" (1 + "x")/(2 + "x")^2` dx
`= int "e"^"x" [((2 + "x") - 1)/(2 + "x")^2]` dx
`= int "e"^"x" [1/(2 + "x") - 1/(2 + "x")^2]`dx
Let f(x) = `1/(2 + "x")`
∴ f '(x) = `(-1)/(2 +"x")^2`
∴ I = `int "e"^"x" ["f"("x") + "f" '("x")]` dx
`= "e"^"x" * "f"("x") + "c"`
`= "e"^"x" * 1/(2 + "x")` + c
∴ I = `"e"^"x"/(2 + "x")` + c
APPEARS IN
संबंधित प्रश्न
Find `int((3sintheta-2)costheta)/(5-cos^2theta-4sin theta)d theta`.
Integrate the functions:
`1/(x(log x)^m), x > 0, m ne 1`
Integrate the functions:
`(2cosx - 3sinx)/(6cos x + 4 sin x)`
Integrate the functions:
`1/(1 - tan x)`
Write a value of
Write a value of
Write a value of\[\int\frac{1}{1 + 2 e^x} \text{ dx }\].
Write a value of\[\int\frac{\left( \tan^{- 1} x \right)^3}{1 + x^2} dx\]
Write a value of\[\int\frac{\sec^2 x}{\left( 5 + \tan x \right)^4} dx\]
Find : ` int (sin 2x ) /((sin^2 x + 1) ( sin^2 x + 3 ) ) dx`
Integrate the following functions w.r.t. x : `(1)/(x(x^3 - 1)`
Integrate the following functions w.r.t. x : `(3e^(2x) + 5)/(4e^(2x) - 5)`
Evaluate the following : `int (1)/(1 + x - x^2).dx`
Evaluate the following integrals:
`int (7x + 3)/sqrt(3 + 2x - x^2).dx`
Evaluate the following.
`int "x"^3/sqrt(1 + "x"^4)` dx
Evaluate the following.
`int "x"^5/("x"^2 + 1)`dx
Evaluate the following.
`int 1/(7 + 6"x" - "x"^2)` dx
`int sqrt(1 + "x"^2) "dx"` =
`int sin^-1 x`dx = ?
`int(5x + 2)/(3x - 4) dx` = ______
`int (sin (5x)/2)/(sin x/2)dx` is equal to ______. (where C is a constant of integration).
`int cos^3x dx` = ______.
Evaluate `int(1 + x + x^2/(2!) )dx`
Evaluate the following.
`int x sqrt(1 + x^2) dx`
Evaluate:
`int sqrt((a - x)/x) dx`
Evaluate the following
`int x^3 e^(x^2) ` dx
Evaluate `int(5x^2-6x+3)/(2x-3)dx`
If f'(x) = 4x3 - 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
Evaluate the following.
`intx^3/sqrt(1 + x^4) dx`
