Advertisements
Advertisements
Question
`int (f^'(x))/(f(x))dx` = ______ + c.
Advertisements
Solution
`int (f^'(x))/(f(x))dx` = log f(x) + c.
APPEARS IN
RELATED QUESTIONS
Evaluate : `int (sinx)/sqrt(36-cos^2x)dx`
Evaluate :`intxlogxdx`
Integrate the functions:
`1/(x + x log x)`
Integrate the functions:
sin x ⋅ sin (cos x)
Integrate the functions:
sin (ax + b) cos (ax + b)
Integrate the functions:
`xsqrt(1+ 2x^2)`
Integrate the functions:
`e^(tan^(-1)x)/(1+x^2)`
Integrate the functions:
`sqrt(sin 2x) cos 2x`
Write a value of\[\int\text{ tan x }\sec^3 x\ dx\]
Write a value of
Write a value of\[\int e^{ax} \sin\ bx\ dx\]
The value of \[\int\frac{\cos \sqrt{x}}{\sqrt{x}} dx\] is
Integrate the following functions w.r.t. x : `(1)/(4x + 5x^-11)`
Integrate the following functions w.r.t. x : `(2x + 1)sqrt(x + 2)`
Integrate the following functions w.r.t. x:
`x^5sqrt(a^2 + x^2)`
Integrate the following functions w.r.t. x : `(cos3x - cos4x)/(sin3x + sin4x)`
Integrate the following functions w.r.t. x : `(1)/(2 + 3tanx)`
Integrate the following functions w.r.t. x : `(3e^(2x) + 5)/(4e^(2x) - 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 - 2cos 2x).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: ∫ |x| dx if x < 0
`int ("e"^(3x))/("e"^(3x) + 1) "d"x`
`int sqrt(x) sec(x)^(3/2) tan(x)^(3/2)"d"x`
`int ((x + 1)(x + log x))^4/(3x) "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 ______.
If f ′(x) = 4x3 − 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x)
Evaluate the following.
`int1/(x^2+4x-5)dx`
Evaluate the following.
`intx^3/sqrt(1+x^4)dx`
Evaluate `int (5x^2 - 6x + 3)/(2x - 3) dx`
