Advertisements
Advertisements
प्रश्न
Evaluate:
`int log x dx`
Advertisements
उत्तर
Let `I = int log x dx`
= `int log x * 1 dx`
`I = log x int 1 dx - int [int 1 dx * d/dx (log x)] dx`
= `(log x) (x) - int [x * 1/x] dx`
= `x log x - int 1 dx`
∴ I = x log x − x + c
APPEARS IN
संबंधित प्रश्न
If `y=log[x+sqrt(x^2+a^2)]` show that `(x^2+a^2)(d^2y)/(dx^2)+xdy/dx=0`
Differentiate the function with respect to x.
(x + 3)2 . (x + 4)3 . (x + 5)4
Differentiate the function with respect to x.
xsin x + (sin x)cos x
Find `bb(dy/dx)` for the given function:
(cos x)y = (cos y)x
Differentiate the function with respect to x:
xx + xa + ax + aa, for some fixed a > 0 and x > 0
if `x^m y^n = (x + y)^(m + n)`, prove that `(d^2y)/(dx^2)= 0`
Evaluate
`int 1/(16 - 9x^2) dx`
Differentiate
log (1 + x2) w.r.t. tan-1 (x)
Find `"dy"/"dx"` , if `"y" = "x"^("e"^"x")`
If `"x"^(5/3) . "y"^(2/3) = ("x + y")^(7/3)` , the show that `"dy"/"dx" = "y"/"x"`
Solve the following differential equation: (3xy + y2) dx + (x2 + xy) dy = 0
If `(sin "x")^"y" = "x" + "y", "find" (d"y")/(d"x")`
If y = (log x)x + xlog x, find `"dy"/"dx".`
If `log_5((x^4 + y^4)/(x^4 - y^4)) = 2, "show that""dy"/"dx" = (12x^3)/(13y^3)`.
`"If" y = sqrt(logx + sqrt(log x + sqrt(log x + ... ∞))), "then show that" dy/dx = (1)/(x(2y - 1).`
If y = `x^(x^(x^(.^(.^.∞))`, then show that `"dy"/"dx" = y^2/(x(1 - logy).`.
If ey = yx, then show that `"dy"/"dx" = (logy)^2/(log y - 1)`.
If x = esin3t, y = ecos3t, then show that `dy/dx = -(ylogx)/(xlogy)`.
If x = a cos3t, y = a sin3t, show that `"dy"/"dx" = -(y/x)^(1/3)`.
If x = `(2bt)/(1 + t^2), y = a((1 - t^2)/(1 + t^2)), "show that" "dx"/"dy" = -(b^2y)/(a^2x)`.
If y = `log(x + sqrt(x^2 + a^2))^m`, show that `(x^2 + a^2)(d^2y)/(dx^2) + x "d"/"dx"` = 0.
If y = log (log 2x), show that xy2 + y1 (1 + xy1) = 0.
Find the nth derivative of the following: log (ax + b)
Find the nth derivative of the following : log (2x + 3)
If y = A cos (log x) + B sin (log x), show that x2y2 + xy1 + y = 0.
If f(x) = logx (log x) then f'(e) is ______
If y = log [cos(x5)] then find `("d"y)/("d"x)`
If y = 5x. x5. xx. 55 , find `("d"y)/("d"x)`
If x7 . y5 = (x + y)12, show that `("d"y)/("d"x) = y/x`
If y = `(sin x)^sin x` , then `"dy"/"dx"` = ?
Derivative of loge2 (logx) with respect to x is _______.
`d/dx(x^{sinx})` = ______
If y = `("e"^"2x" sin x)/(x cos x), "then" "dy"/"dx" = ?`
`2^(cos^(2_x)`
`8^x/x^8`
`log (x + sqrt(x^2 + "a"))`
If y `= "e"^(3"x" + 7), "then the value" |("dy")/("dx")|_("x" = 0)` is ____________.
Given f(x) = `log((1 + x)/(1 - x))` and g(x) = `(3x + x^3)/(1 + 3x^2)`, then fog(x) equals
If y = `x^(x^2)`, then `dy/dx` is equal to ______.
If `log_10 ((x^2 - y^2)/(x^2 + y^2))` = 2, then `dy/dx` is equal to ______.
The derivative of x2x w.r.t. x is ______.
If y = `log(x + sqrt(x^2 + 4))`, show that `dy/dx = 1/sqrt(x^2 + 4)`
The derivative of log x with respect to `1/x` is ______.
