Advertisements
Advertisements
प्रश्न
Integrate the following functions w.r.t. x : `e^x .(1/x - 1/x^2)`
Advertisements
उत्तर
Let I = `int e^x .(1/x - 1/x^2).dx`
Let f(x) = `(1)/x`
∴ f'(x) = `-(1)/x^2`
∴ I = `int e^x[f(x) + f'(x)].dx`
= ex f(x) + c
= `e^x . (1)/x + 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 sin 3x.
Integrate the function in `x^2e^x`.
Integrate the function in x log x.
Integrate the function in x2 log x.
Integrate the function in x cos-1 x.
Integrate the function in x sec2 x.
Integrate the function in `e^x (1/x - 1/x^2)`.
`intx^2 e^(x^3) dx` equals:
Find :
`∫(log x)^2 dx`
Evaluate the following:
`int sec^3x.dx`
Evaluate the following : `int x^3.logx.dx`
Evaluate the following : `int e^(2x).cos 3x.dx`
Evaluate the following : `int x.cos^3x.dx`
Evaluate the following:
`int x.sin 2x. cos 5x.dx`
Integrate the following functions w.r.t. x : `e^(2x).sin3x`
Integrate the following w.r.t. x: `(1 + log x)^2/x`
Integrate the following w.r.t.x : `sqrt(x)sec(x^(3/2))*tan(x^(3/2))`
Evaluate the following.
`int "e"^"x" "x - 1"/("x + 1")^3` dx
`int ("x" + 1/"x")^3 "dx"` = ______
Evaluate: `int "dx"/("x"[(log "x")^2 + 4 log "x" - 1])`
Evaluate:
∫ (log x)2 dx
Evaluate `int 1/(x(x - 1)) "d"x`
Evaluate `int 1/(x log x) "d"x`
Evaluate `int 1/(4x^2 - 1) "d"x`
`int [(log x - 1)/(1 + (log x)^2)]^2`dx = ?
∫ log x · (log x + 2) dx = ?
`int log x * [log ("e"x)]^-2` dx = ?
Evaluate the following:
`int_0^pi x log sin x "d"x`
`int "dx"/(sin(x - "a")sin(x - "b"))` is equal to ______.
If `int (f(x))/(log(sin x))dx` = log[log sin x] + c, then f(x) is equal to ______.
Find: `int e^(x^2) (x^5 + 2x^3)dx`.
Evaluate :
`int(4x - 6)/(x^2 - 3x + 5)^(3/2) dx`
`inte^(xloga).e^x dx` is ______
The integrating factor of `ylogy.dx/dy+x-logy=0` is ______.
`int(f'(x))/sqrt(f(x)) dx = 2sqrt(f(x))+c`
Evaluate the following.
`int (x^3)/(sqrt(1 + x^4))dx`
Solve the following
`int_0^1 e^(x^2) x^3 dx`
Evaluate:
`int (sin(x - a))/(sin(x + a))dx`
Evaluate `int (1 + x + x^2/(2!))dx`
Evaluate the following.
`int x sqrt(1 + x^2) dx`
Evaluate the following.
`intx^2e^(4x)dx`
Evaluate `int(1 + x + x^2/(2!))dx`.
Evaluate.
`int(5x^2 - 6x + 3)/(2x - 3) dx`
