Advertisements
Advertisements
प्रश्न
Integrate the function in `x^2e^x`.
Advertisements
उत्तर
Let `I = int x^2 e^x dx`
Put u = x2, v = ex
`int uv dx = u int v dx - int( (du)/dx int v dx) dx`
`= x^2 int e^x dx - int (2x).e^x dx`
`= x^2 e^x - 2 int xe^x dx`
We define the first function by integrating multiple parts.
`I = x^2 e^x - 2 [x int e^x dx - int (d/dx x. int e^x dx)]`
`= x^2 e^x - 2 [xe^x - 2 int 1.e^x dx]`
`= x^2 e^x - 2x e^x + 2e^x + C`
`= e^x (x^2 - 2x + 2) + C`
APPEARS IN
संबंधित प्रश्न
If u and v are two functions of x then prove that
`intuvdx=uintvdx-int[du/dxintvdx]dx`
Hence evaluate, `int xe^xdx`
Integrate the function in x log 2x.
Integrate the function in x2 log x.
Integrate the function in x cos-1 x.
Integrate the function in `(x cos^(-1) x)/sqrt(1-x^2)`.
Integrate the function in x (log x)2.
Integrate the function in e2x sin x.
Evaluate the following:
`int sec^3x.dx`
Evaluate the following : `int(sin(logx)^2)/x.log.x.dx`
Integrate the following functions w.r.t. x : `e^(2x).sin3x`
Integrate the following functions w.r.t. x:
sin (log x)
Integrate the following functions w.r.t. x : `x^2 .sqrt(a^2 - x^6)`
Integrate the following functions w.r.t. x: `sqrt(x^2 + 2x + 5)`.
Choose the correct options from the given alternatives :
`int tan(sin^-1 x)*dx` =
Integrate the following w.r.t.x : sec4x cosec2x
Evaluate the following.
`int x^3 e^(x^2)`dx
Evaluate the following.
`int e^x (1/x - 1/x^2)`dx
Choose the correct alternative:
`intx^(2)3^(x^3) "d"x` =
`int log x * [log ("e"x)]^-2` dx = ?
The value of `int "e"^(5x) (1/x - 1/(5x^2)) "d"x` is ______.
`int "e"^x [x (log x)^2 + 2 log x] "dx"` = ______.
Evaluate the following:
`int (sin^-1 x)/((1 - x)^(3/2)) "d"x`
Evaluate the following:
`int_0^pi x log sin x "d"x`
Evaluate: `int_0^(pi/4) (dx)/(1 + tanx)`
Find: `int e^x.sin2xdx`
Find: `int (2x)/((x^2 + 1)(x^2 + 2)) dx`
Solve: `int sqrt(4x^2 + 5)dx`
`int1/sqrt(x^2 - a^2) dx` = ______
`intsqrt(1+x) dx` = ______
Evaluate the following:
`intx^3e^(x^2)dx`
Evaluate `int (1 + x + x^2/(2!))dx`
If f'(x) = 4x3 - 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x)
Evaluate the following.
`int x^3 e^(x^2) dx`
Evaluate the following.
`intx^2e^(4x)dx`
Evaluate the following.
`intx^3 e^(x^2)dx`
Which function is an example under priority \(I\) in the LIATE rule?
Which pair is listed as Trigonometric in the LIATE rule?
When applying integration by parts to \(\log x\) and inverse trig, what should they be multiplied by?
