Advertisements
Advertisements
प्रश्न
Integrate the functions:
`1/(x(log x)^m), x > 0, m ne 1`
Advertisements
उत्तर
Let `I = int 1/(x (log x)^m) dx`
Put log x = t
`1/x dx = dt`
`therefore I = int dt/t^m`
`= int t^(-m) dt = (t^(-m + 1)/(- m + 1)) + C`
`= (log x)^(- m + 1)/(1 - m) + C`
APPEARS IN
संबंधित प्रश्न
Integrate the functions:
`x^2/(2+ 3x^3)^3`
Integrate the functions:
`(2cosx - 3sinx)/(6cos x + 4 sin x)`
Integrate the functions:
`1/(1 - tan x)`
Evaluate `int (x-1)/(sqrt(x^2 - x)) dx`
Write a value of
Write a value of
Write a value of\[\int\frac{\left( \tan^{- 1} x \right)^3}{1 + x^2} dx\]
Write a value of\[\int\frac{\sec^2 x}{\left( 5 + \tan x \right)^4} dx\]
Write a value of\[\int\frac{\sin x + \cos x}{\sqrt{1 + \sin 2x}} dx\]
Write a value of
`int "dx"/(9"x"^2 + 1)= ______. `
Evaluate the following integrals:
`int x/(x + 2).dx`
Evaluate the following integrals: `int (2x - 7)/sqrt(4x - 1).dx`
Integrate the following function w.r.t. x:
`(10x^9 +10^x.log10)/(10^x + x^10)`
Integrate the following functions w.r.t. x : `x^2/sqrt(9 - x^6)`
Integrate the following functions w.r.t. x : `(cos3x - cos4x)/(sin3x + sin4x)`
Integrate the following functions w.r.t. x:
`(1)/(sinx.cosx + 2cos^2x)`
Evaluate the following : `int (1)/sqrt(3x^2 - 8).dx`
Evaluate the following : `int sqrt((2 + x)/(2 - x)).dx`
Integrate the following functions w.r.t. x : `int (1)/(cosx - sqrt(3)sinx).dx`
`int logx/(log ex)^2*dx` = ______.
Evaluate `int (3"x"^2 - 5)^2` dx
Evaluate the following.
`int (20 - 12"e"^"x")/(3"e"^"x" - 4)`dx
Evaluate `int 1/((2"x" + 3))` dx
Evaluate: `int sqrt(x^2 - 8x + 7)` dx
`int x/(x + 2) "d"x`
State whether the following statement is True or False:
If `int x "f"(x) "d"x = ("f"(x))/2`, then f(x) = `"e"^(x^2)`
`int "dx"/((sin x + cos x)(2 cos x + sin x))` = ?
`int[ tan (log x) + sec^2 (log x)] dx= ` ______
The integral `int ((1 - 1/sqrt(3))(cosx - sinx))/((1 + 2/sqrt(3) sin2x))dx` is equal to ______.
`int (logx)^2/x dx` = ______.
Evaluated the following
`int x^3/ sqrt (1 + x^4 )dx`
If f′(x) = 4x3 − 3x2 + 2x + k, f(0) = -1 and f(1) = 4, find f(x)
Evaluate `int (1)/(x(x - 1))dx`
Evaluate the following
`int x^3/sqrt(1+x^4) dx`
Evaluate:
`int(sqrt(tanx) + sqrt(cotx))dx`
`int "cosec"^4x dx` = ______.
Evaluate `int 1/(x(x-1))dx`
