Advertisements
Advertisements
Question
Integrate the following functions w.r.t. x : `(1)/(x.logx.log(logx)`.
Advertisements
Solution
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
RELATED QUESTIONS
Integrate the functions:
sin (ax + b) cos (ax + b)
Integrate the functions:
`x/(sqrt(x+ 4))`, x > 0
Integrate the functions:
`x^2/(2+ 3x^3)^3`
Integrate the functions:
`x/(9 - 4x^2)`
Integrate the functions:
`sin x/(1+ cos x)`
Integrate the functions:
`1/(1 - tan x)`
Integrate the functions:
`(1+ log x)^2/x`
`(10x^9 + 10^x log_e 10)/(x^10 + 10^x) dx` equals:
Write a value of
Write a value of\[\int \cos^4 x \text{ sin x dx }\]
Write a value of\[\int\left( e^{x \log_e \text{ a}} + e^{a \log_e x} \right) dx\] .
Write a value of\[\int\frac{\sin 2x}{a^2 \sin^2 x + b^2 \cos^2 x} \text{ dx }\]
Write a value of\[\int e^{ax} \sin\ bx\ dx\]
Integrate the following w.r.t. x : x3 + x2 – x + 1
Integrate the following w.r.t. x : `int x^2(1 - 2/x)^2 dx`
Integrate the following functions w.r.t. x : `e^(3x)/(e^(3x) + 1)`
Integrate the following functions w.r.t. x : `(x^2 + 2)/((x^2 + 1)).a^(x + tan^-1x)`
Integrate the following functions w.r.t. x:
`(1)/(sinx.cosx + 2cos^2x)`
Integrate the following functions w.r.t. x : `(4e^x - 25)/(2e^x - 5)`
Integrate the following functions w.r.t. x:
`(sinx cos^3x)/(1 + cos^2x)`
Integrate the following functions w.r.t. x : `int (1)/(3 + 2sinx).dx`
Evaluate the following : `int (logx)2.dx`
Choose the correct options from the given alternatives :
`int (e^x(x - 1))/x^2*dx` =
Integrate the following w.r.t.x: `(3x + 1)/sqrt(-2x^2 + x + 3)`
Evaluate `int 1/("x" ("x" - 1))` dx
Evaluate the following.
`int 1/(sqrt(3"x"^2 + 8))` dx
Evaluate `int "x - 1"/sqrt("x + 4")` dx
`int 1/sqrt((x - 3)(x + 2))` dx = ______.
`int e^x/x [x (log x)^2 + 2 log x]` dx = ______________
`int ("e"^x(x - 1))/(x^2) "d"x` = ______
`int ("e"^(3x))/("e"^(3x) + 1) "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:
`int3^(2x + 3) "d"x = (3^(2x + 3))/2 + "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 (1 + x)/(x + "e"^(-x)) "d"x`
If f(x) = 3x + 6, g(x) = 4x + k and fog (x) = gof (x) then k = ______.
`int (x^2 + 1)/(x^4 - x^2 + 1)`dx = ?
If f'(x) = `x + 1/x`, then f(x) is ______.
The value of `sqrt(2) int (sinx dx)/(sin(x - π/4))` is ______.
Find `int (x + 2)/sqrt(x^2 - 4x - 5) dx`.
if `f(x) = 4x^3 - 3x^2 + 2x +k, f (0) = - 1 and f (1) = 4, "find " f(x)`
Evaluate `int (1)/(x(x - 1))dx`
`int x^2/sqrt(1 - x^6)dx` = ______.
Evaluate `int1/(x(x-1))dx`
Evaluate `int(1+x+x^2/(2!))dx`
Evaluate `int(5x^2-6x+3)/(2x-3)dx`
Evaluate the following:
`int x^3/(sqrt(1 + x^4)) dx`
Evaluate `int (5x^2 - 6x + 3)/(2x - 3) dx`
If f'(x) = 4x3 - 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
