Advertisements
Advertisements
Question
Integrate the functions:
`1/(x(log x)^m), x > 0, m ne 1`
Advertisements
Solution
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
RELATED QUESTIONS
Integrate the functions:
`sqrt(sin 2x) cos 2x`
`(10x^9 + 10^x log_e 10)/(x^10 + 10^x) dx` equals:
Write a value of
Write a value of
Evaluate: \[\int\frac{x^3 - 1}{x^2} \text{ dx}\]
Evaluate : `int ("e"^"x" (1 + "x"))/("cos"^2("x""e"^"x"))"dx"`
Find : ` int (sin 2x ) /((sin^2 x + 1) ( sin^2 x + 3 ) ) dx`
Evaluate the following integrals : `int sinx/(1 + sinx)dx`
Evaluate the following integrals: `int(x - 2)/sqrt(x + 5).dx`
Integrate the following functions w.r.t. x : `((sin^-1 x)^(3/2))/(sqrt(1 - x^2)`
Integrate the following functions w.r.t. x : e3logx(x4 + 1)–1
Integrate the following functions w.r.t. x : tan 3x tan 2x tan x
Evaluate the following : `int (1)/sqrt(11 - 4x^2).dx`
Integrate the following with respect to the respective variable:
`x^7/(x + 1)`
Evaluate `int 1/(x (x - 1))` dx
Evaluate the following.
`int 1/(4"x"^2 - 1)` dx
Evaluate the following.
`int "x"^3/(16"x"^8 - 25)` dx
Evaluate: `int "e"^sqrt"x"` dx
`int (sin4x)/(cos 2x) "d"x`
`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)`
State whether the following statement is True or False:
`int"e"^(4x - 7) "d"x = ("e"^(4x - 7))/(-7) + "c"`
State whether the following statement is True or False:
`int sqrt(1 + x^2) *x "d"x = 1/3(1 + x^2)^(3/2) + "c"`
`int(5x + 2)/(3x - 4) dx` = ______
If `tan^-1x = 2tan^-1((1 - x)/(1 + x))`, then the value of x is ______
`int(7x - 2)^2dx = (7x -2)^3/21 + c`
Evaluate `int(1+ x + x^2/(2!)) dx`
Evaluate:
`int sqrt((a - x)/x) dx`
If f ′(x) = 4x3 − 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x)
Evaluate.
`int (5x^2-6x+3)/(2x-3)dx`
`int x^2/sqrt(1 - x^6)dx` = ______.
Evaluate the following
`int x^3 e^(x^2) ` dx
Evaluate `int1/(x(x-1))dx`
Evaluate the following.
`int 1/ (x^2 + 4x - 5) dx`
Evaluate the following.
`intx^3/sqrt(1+x^4)dx`
Evaluate the following.
`int1/(x^2 + 4x - 5)dx`
`int (x + 1)/(x(1 + xe^x)) dx` is equal to
