Advertisements
Advertisements
प्रश्न
Choose the correct alternative:
`int ("d"x)/((x - 8)(x + 7))` =
पर्याय
`1/15 log((x + 2)/(x - 1)) + "c"`
`1/15 log((x + 8)/(x + 7)) + "c"`
`1/15 log((x - 8)/(x + 7)) + "c"`
(x – 8)(x – 7) + c
Advertisements
उत्तर
`1/15 log((x - 8)/(x + 7)) + "c"`
APPEARS IN
संबंधित प्रश्न
Integrate the function in x log 2x.
Integrate the function in x2 log x.
Integrate the function in `(x cos^(-1) x)/sqrt(1-x^2)`.
Integrate the following functions w.r.t. x : cosec (log x)[1 – cot (log x)]
Integrate the following with respect to the respective variable : `(3 - 2sinx)/(cos^2x)`
Integrate the following w.r.t.x : cot–1 (1 – x + x2)
Integrate the following w.r.t.x : `sqrt(x)sec(x^(3/2))*tan(x^(3/2))`
Evaluate the following.
∫ x log x dx
Evaluate the following.
`int "e"^"x" "x"/("x + 1")^2` dx
`int ["cosec"(logx)][1 - cot(logx)] "d"x`
`int (cos2x)/(sin^2x cos^2x) "d"x`
`int(x + 1/x)^3 dx` = ______.
`int "e"^x x/(x + 1)^2 "d"x`
`int logx/(1 + logx)^2 "d"x`
`int "dx"/(sin(x - "a")sin(x - "b"))` is equal to ______.
Solve: `int sqrt(4x^2 + 5)dx`
Find `int (sin^-1x)/(1 - x^2)^(3//2) dx`.
Evaluate the following.
`int x^3 e^(x^2) 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
The integrating factor of `ylogy.dx/dy+x-logy=0` is ______.
Evaluate `int(1 + x + (x^2)/(2!))dx`
Evaluate:
`int e^(logcosx)dx`
Evaluate `int tan^-1x dx`
Evaluate:
`int1/(x^2 + 25)dx`
If ∫(cot x – cosec2 x)ex dx = ex f(x) + c then f(x) will be ______.
Evaluate the following.
`intx^2e^(4x)dx`
Evaluate the following.
`intx^3 e^(x^2)dx`
Evaluate.
`int(5x^2 - 6x + 3)/(2x - 3) dx`
