Advertisements
Advertisements
प्रश्न
Integrate the following functions w.r.t. x : `(1)/(x.logx.log(logx)`.
Advertisements
उत्तर
Let I = `int (1)/(x.logx.log(logx)).dx`
= `int(1)/log(logx).(1)/(x.logx).dx`
Put log(log x) = t
∴ `(1)/logx.(1)/x.dx` = dt
∴ `(1)/(x.logx).dx` = dt
∴ I = `int (1)/t dt = log|t| + c`
= log|log (logx)| + c.
APPEARS IN
संबंधित प्रश्न
Find `int((3sintheta-2)costheta)/(5-cos^2theta-4sin theta)d theta`.
Integrate the functions:
`1/(x-sqrtx)`
Integrate the functions:
`e^(2x+3)`
Integrate the functions:
`1/(cos^2 x(1-tan x)^2`
`(10x^9 + 10^x log_e 10)/(x^10 + 10^x) dx` equals:
Evaluate : `∫1/(3+2sinx+cosx)dx`
Evaluate: `int_0^3 f(x)dx` where f(x) = `{(cos 2x, 0<= x <= pi/2),(3, pi/2 <= x <= 3) :}`
Write a value of\[\int e^{ax} \left\{ a f\left( x \right) + f'\left( x \right) \right\} dx\] .
Write a value of\[\int\sqrt{9 + x^2} \text{ dx }\].
`int "dx"/(9"x"^2 + 1)= ______. `
Integrate the following functions w.r.t. x : `e^x.log (sin e^x)/tan(e^x)`
Integrate the following functions w.r.t. x : `cosx/sin(x - a)`
Integrate the following functions w.r.t. x:
`(1)/(sinx.cosx + 2cos^2x)`
Integrate the following functions w.r.t. x : `(20 + 12e^x)/(3e^x + 4)`
Integrate the following functions w.r.t. x : tan 3x tan 2x tan x
Integrate the following functions w.r.t. x:
`(sinx cos^3x)/(1 + cos^2x)`
`int logx/(log ex)^2*dx` = ______.
Evaluate the following.
`int "x" sqrt(1 + "x"^2)` dx
Evaluate the following.
`int "x"^3/sqrt(1 + "x"^4)` dx
Evaluate the following.
`int (1 + "x")/("x" + "e"^"-x")` dx
Evaluate the following.
`int 1/(x(x^6 + 1))` dx
Choose the correct alternative from the following.
`int "dx"/(("x" - "x"^2))`=
Fill in the Blank.
`int (5("x"^6 + 1))/("x"^2 + 1)` dx = x4 + ______ x3 + 5x + c
Evaluate `int 1/((2"x" + 3))` dx
Evaluate: `int 1/(2"x" + 3"x" log"x")` dx
`int 1/sqrt((x - 3)(x + 2))` dx = ______.
`int ("e"^(3x))/("e"^(3x) + 1) "d"x`
`int sqrt(("e"^(3x) - "e"^(2x))/("e"^x + 1)) "d"x`
`int (7x + 9)^13 "d"x` ______ + c
`int ("e"^x(x + 1))/(sin^2(x"e"^x)) "d"x` = ______.
If f'(x) = `x + 1/x`, then f(x) is ______.
The value of `sqrt(2) int (sinx dx)/(sin(x - π/4))` is ______.
`int x/sqrt(1 - 2x^4) dx` = ______.
(where c is a constant of integration)
Write `int cotx dx`.
Evaluate `int(1 + x + x^2/(2!))dx`
Evaluate the following.
`int 1/(x^2 + 4x - 5)dx`
Evaluate `int (1)/(x(x - 1))dx`
Evaluate.
`int (5x^2 - 6x + 3)/(2x - 3) dx`
Evaluate:
`int sin^2(x/2)dx`
`int x^2/sqrt(1 - x^6)dx` = ______.
Evaluate the following.
`int 1/ (x^2 + 4x - 5) dx`
Evaluate `int(5x^2-6x+3)/(2x-3)dx`
Evaluate the following.
`int1/(x^2+4x-5)dx`
Evaluate the following.
`int1/(x^2 + 4x - 5)dx`
If f'(x) = 4x3 - 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
Evaluate the following.
`intx^3/sqrt(1 + x^4) dx`
