Advertisements
Advertisements
Question
`int logx/(log ex)^2*dx` = ______.
Options
`x/(1 + log x) + c`
x(1 + log x) + c
`1/(1 + log x) + c`
`1/(1 - log x) + c`
Advertisements
Solution
`int logx/(log ex)^2*dx` = `underlinebb(x/(1 + log x) + c)`.
APPEARS IN
RELATED QUESTIONS
Find: `int(x+3)sqrt(3-4x-x^2dx)`
Find `intsqrtx/sqrt(a^3-x^3)dx`
Evaluate :
`∫(x+2)/sqrt(x^2+5x+6)dx`
Integrate the functions:
`1/(x-sqrtx)`
Integrate the functions:
`e^(2x+3)`
Integrate the functions:
tan2(2x – 3)
Integrate the functions:
`(2cosx - 3sinx)/(6cos x + 4 sin x)`
Integrate the functions:
`(sin x)/(1+ cos x)^2`
Write a value of
Write a value of \[\int\frac{1 - \sin x}{\cos^2 x} \text{ dx }\]
Integrate the following w.r.t. x:
`2x^3 - 5x + 3/x + 4/x^5`
Evaluate the following integrals : `intsqrt(1 + sin 5x).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 : `(sin6x)/(sin 10x sin 4x)`
Evaluate the following:
`int sinx/(sin 3x) dx`
Evaluate the following integral:
`int (3cosx)/(4sin^2x + 4sinx - 1).dx`
Evaluate the following integrals : `int sqrt((e^(3x) - e^(2x))/(e^x + 1)).dx`
Evaluate `int (-2)/(sqrt("5x" - 4) - sqrt("5x" - 2))`dx
Evaluate the following.
`int (20 - 12"e"^"x")/(3"e"^"x" - 4)`dx
Evaluate the following.
`int 1/("a"^2 - "b"^2 "x"^2)` dx
Evaluate the following.
`int 1/(7 + 6"x" - "x"^2)` dx
Evaluate the following.
`int 1/(sqrt(3"x"^2 + 8))` dx
Choose the correct alternative from the following.
`int "x"^2 (3)^("x"^3) "dx"` =
State whether the following statement is True or False.
If `int x "e"^(2x)` dx is equal to `"e"^(2x)` f(x) + c, where c is constant of integration, then f(x) is `(2x - 1)/2`.
Evaluate `int "x - 1"/sqrt("x + 4")` dx
Evaluate: If f '(x) = `sqrt"x"` and f(1) = 2, then find the value of f(x).
If `tan^-1x = 2tan^-1((1 - x)/(1 + x))`, then the value of x is ______
`int ((x + 1)(x + log x))^4/(3x) "dx" =`______.
If I = `int (sin2x)/(3x + 4cosx)^3 "d"x`, then I is equal to ______.
`int(log(logx) + 1/(logx)^2)dx` = ______.
If `int sinx/(sin^3x + cos^3x)dx = α log_e |1 + tan x| + β log_e |1 - tan x + tan^2x| + γ tan^-1 ((2tanx - 1)/sqrt(3)) + C`, when C is constant of integration, then the value of 18(α + β + γ2) is ______.
The value of `sqrt(2) int (sinx dx)/(sin(x - π/4))` is ______.
`int (logx)^2/x dx` = ______.
Find `int (x + 2)/sqrt(x^2 - 4x - 5) dx`.
Evaluate `int(1 + x + x^2/(2!) )dx`
Prove that:
`int 1/sqrt(x^2 - a^2) dx = log |x + sqrt(x^2 - a^2)| + c`.
`int x^3 e^(x^2) dx`
Evaluate.
`int (5x^2 - 6x + 3)/(2x - 3) dx`
Evaluate `int(1+x+(x^2)/(2!))dx`
Evaluate `int (1 + "x" + "x"^2/(2!))`dx
Evaluate `int 1/(x(x-1))dx`
Evaluate `int(5x^2-6x+3)/(2x-3) dx`
Evaluate `int(5x^2-6x+3)/(2x-3)dx`
Evaluate the following.
`intx^3/sqrt(1 + x^4)dx`
Which substitution is appropriate for \[\sqrt{\frac{x}{a-x}}\], \[\sqrt{\frac{a-x}{x}}\], \[\sqrt{x(a-x)}\], or \[\frac{1}{\sqrt{x(a-x)}}\]?
For \[\sqrt{\frac{x-\alpha}{\beta-x}}\] or \[\sqrt{(x-\alpha)(\beta-x)}\], where \[\beta>\alpha\], which substitution is used?
