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:
`xsqrt(x + 2)`
Integrate the functions:
`(x^3 - 1)^(1/3) x^5`
Integrate the functions:
`x/(e^(x^2))`
Integrate the functions:
`e^(tan^(-1)x)/(1+x^2)`
Integrate the functions:
tan2(2x – 3)
Integrate the functions:
`(sin^(-1) x)/(sqrt(1-x^2))`
Integrate the functions:
`sin x/(1+ cos x)`
Evaluate : `∫1/(3+2sinx+cosx)dx`
Write a value of
Write a value of
Write a value of\[\int\frac{1}{1 + e^x} \text{ dx }\]
Write a value of
The value of \[\int\frac{\cos \sqrt{x}}{\sqrt{x}} dx\] is
`int "dx"/(9"x"^2 + 1)= ______. `
Show that : `int _0^(pi/4) "log" (1+"tan""x")"dx" = pi /8 "log"2`
Evaluate the following integrals : `int sin x/cos^2x dx`
Integrate the following functions w.r.t. x : `(1)/(4x + 5x^-11)`
Integrate the following functions w.r.t. x : `(4e^x - 25)/(2e^x - 5)`
Integrate the following functions w.r.t. x : `(3e^(2x) + 5)/(4e^(2x) - 5)`
Evaluate the following : `int (1)/sqrt(8 - 3x + 2x^2).dx`
Integrate the following functions w.r.t. x : `int (1)/(3 + 2 sin2x + 4cos 2x).dx`
Evaluate the following integrals : `int (3x + 4)/(x^2 + 6x + 5).dx`
Evaluate the following integrals : `int sqrt((e^(3x) - e^(2x))/(e^x + 1)).dx`
`int logx/(log ex)^2*dx` = ______.
Integrate the following w.r.t.x: `(3x + 1)/sqrt(-2x^2 + x + 3)`
Evaluate `int 1/(x (x - 1))` dx
If f'(x) = x2 + 5 and f(0) = −1, then find the value of f(x).
Evaluate the following.
∫ (x + 1)(x + 2)7 (x + 3)dx
Evaluate the following.
`int 1/(4"x"^2 - 1)` dx
`int sqrt(x^2 + 2x + 5)` dx = ______________
`int 2/(sqrtx - sqrt(x + 3))` dx = ________________
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(sin2x)/(5sin^2x+3cos^2x) dx=` ______.
`int 1/(a^2 - x^2) dx = 1/(2a) xx` ______.
Write `int cotx dx`.
Find : `int sqrt(x/(1 - x^3))dx; x ∈ (0, 1)`.
Evaluate the following.
`int 1/(x^2 + 4x - 5) dx`
`int dx/((x+2)(x^2 + 1))` ...(given)
`1/(x^2 +1) dx = tan ^-1 + c`
If f ′(x) = 4x3 − 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x)
Evaluate the following.
`int(1)/(x^2 + 4x - 5)dx`
If f'(x) = 4x3- 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
`int 1/(sin^2x cos^2x)dx` = ______.
Evaluate:
`int sin^3x cos^3x dx`
Evaluate `int (1 + x + x^2/(2!)) dx`
Evaluate `int (1 + "x" + "x"^2/(2!))`dx
Evaluate the following.
`int "x"^3/sqrt(1 + "x"^4)` dx
Evaluate `int 1/(x(x-1))dx`
