Advertisements
Advertisements
प्रश्न
`int (x^2 + x - 6)/((x - 2)(x - 1)) "d"x` = x + ______ + c
उत्तर
`int (x^2 + x - 6)/((x - 2)(x - 1)) "d"x` = x + 4 log|x-1| + c
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 cos-1 x.
Integrate the function in tan-1 x.
`int e^x sec x (1 + tan x) dx` equals:
Find :
`∫(log x)^2 dx`
Integrate the following functions w.r.t.x:
`e^-x cos2x`
Integrate the following functions w.r.t. x : `log(1 + x)^((1 + x)`
Choose the correct options from the given alternatives :
`int sin (log x)*dx` =
Integrate the following with respect to the respective variable : `(3 - 2sinx)/(cos^2x)`
Integrate the following w.r.t.x : `sqrt(x)sec(x^(3/2))*tan(x^(3/2))`
Integrate the following w.r.t.x : `log (1 + cosx) - xtan(x/2)`
Integrate the following w.r.t.x : log (x2 + 1)
Solve the following differential equation.
(x2 − yx2 ) dy + (y2 + xy2) dx = 0
Evaluate the following.
`int "e"^"x" [(log "x")^2 + (2 log "x")/"x"]` dx
`int ("x" + 1/"x")^3 "dx"` = ______
Choose the correct alternative from the following.
`int (("e"^"2x" + "e"^"-2x")/"e"^"x") "dx"` =
Evaluate: ∫ (log x)2 dx
`int 1/sqrt(2x^2 - 5) "d"x`
Evaluate `int 1/(x log x) "d"x`
Evaluate `int (2x + 1)/((x + 1)(x - 2)) "d"x`
State whether the following statement is true or false.
If `int (4e^x - 25)/(2e^x - 5)` dx = Ax – 3 log |2ex – 5| + c, where c is the constant of integration, then A = 5.
`int1/sqrt(x^2 - a^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
`int (sin^-1 sqrt(x) + cos^-1 sqrt(x))dx` = ______.
If f′(x) = 4x3 − 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
Evaluate the following.
`int x sqrt(1 + x^2) dx`
Evaluate:
`inte^x "cosec" x(1 - cot x)dx`