Advertisements
Advertisements
प्रश्न
`int ("d"x)/(x - x^2)` = ______
विकल्प
log x – log(1 – x) + c
log(1 – x2) + c
– log x + log(1 – x) + c
log(x – x2) + c
Advertisements
उत्तर
`int ("d"x)/(x - x^2)` = log x – log(1 – x) + c
APPEARS IN
संबंधित प्रश्न
Integrate the function in x cos-1 x.
Integrate the function in `(xe^x)/(1+x)^2`.
Evaluate the following : `int x^2.log x.dx`
Evaluate the following : `int x^2tan^-1x.dx`
Evaluate the following : `int x^2*cos^-1 x*dx`
Evaluate the following : `int log(logx)/x.dx`
Integrate the following functions w.r.t. x : `sqrt(4^x(4^x + 4))`
Integrate the following functions w.r.t. x : `(x + 1) sqrt(2x^2 + 3)`
Integrate the following functions w.r.t. x : `sqrt(2x^2 + 3x + 4)`
Integrate the following functions w.r.t. x : `((1 + sin x)/(1 + cos x)).e^x`
Choose the correct options from the given alternatives :
`int (log (3x))/(xlog (9x))*dx` =
Integrate the following w.r.t.x : `(1)/(x^3 sqrt(x^2 - 1)`
Evaluate the following.
`int x^2 e^4x`dx
Evaluate the following.
`int [1/(log "x") - 1/(log "x")^2]` dx
`int (sin(x - "a"))/(cos (x + "b")) "d"x`
Evaluate `int 1/(4x^2 - 1) "d"x`
`int_0^"a" sqrt("x"/("a" - "x")) "dx"` = ____________.
`int "e"^x [x (log x)^2 + 2 log x] "dx"` = ______.
Evaluate the following:
`int ((cos 5x + cos 4x))/(1 - 2 cos 3x) "d"x`
Find: `int (2x)/((x^2 + 1)(x^2 + 2)) dx`
Find the general solution of the differential equation: `e^((dy)/(dx)) = x^2`.
If `int(2e^(5x) + e^(4x) - 4e^(3x) + 4e^(2x) + 2e^x)/((e^(2x) + 4)(e^(2x) - 1)^2)dx = tan^-1(e^x/a) - 1/(b(e^(2x) - 1)) + C`, where C is constant of integration, then value of a + b is equal to ______.
Evaluate `int(3x-2)/((x+1)^2(x+3)) dx`
Solve the differential equation (x2 + y2) dx - 2xy dy = 0 by completing the following activity.
Solution: (x2 + y2) dx - 2xy dy = 0
∴ `dy/dx=(x^2+y^2)/(2xy)` ...(1)
Puty = vx
∴ `dy/dx=square`
∴ equation (1) becomes
`x(dv)/dx = square`
∴ `square dv = dx/x`
On integrating, we get
`int(2v)/(1-v^2) dv =intdx/x`
∴ `-log|1-v^2|=log|x|+c_1`
∴ `log|x| + log|1-v^2|=logc ...["where" - c_1 = log c]`
∴ x(1 - v2) = c
By putting the value of v, the general solution of the D.E. is `square`= cx
`inte^(xloga).e^x dx` is ______
The integrating factor of `ylogy.dx/dy+x-logy=0` is ______.
`int(xe^x)/((1+x)^2) dx` = ______
Evaluate:
`intcos^-1(sqrt(x))dx`
Evaluate the following.
`intx^2e^(4x)dx`
