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
Show that: `int1/(x^2sqrt(a^2+x^2))dx=-1/a^2(sqrt(a^2+x^2)/x)+c`
Prove that `int_a^bf(x)dx=f(a+b-x)dx.` Hence evaluate : `int_a^bf(x)/(f(x)+f(a-b-x))dx`
Integrate the functions:
`x/(e^(x^2))`
Integrate the functions:
`sqrt(sin 2x) cos 2x`
Write a value of
Write a value of\[\int e^x \left( \frac{1}{x} - \frac{1}{x^2} \right) dx\] .
Evaluate : `int ("e"^"x" (1 + "x"))/("cos"^2("x""e"^"x"))"dx"`
Integrate the following w.r.t. x : `(3x^3 - 2x + 5)/(xsqrt(x)`
Evaluate the following integrals : `int tanx/(sec x + tan x)dx`
Evaluate the following integrals : `intsqrt(1 + sin 5x).dx`
Evaluate the following integrals:
`int(2)/(sqrt(x) - sqrt(x + 3)).dx`
Evaluate the following integrals : `int (3)/(sqrt(7x - 2) - sqrt(7x - 5)).dx`
Integrate the following function w.r.t. x:
x9.sec2(x10)
Integrate the following functions w.r.t. x : `((x - 1)^2)/(x^2 + 1)^2`
Integrate the following functions w.r.t. x : `(1)/(x(x^3 - 1)`
Evaluate the following : `int (1)/sqrt(3x^2 - 8).dx`
Evaluate the following : `int (1)/sqrt(11 - 4x^2).dx`
Evaluate the following : `int sqrt((9 + x)/(9 - x)).dx`
Evaluate the following : `int (1)/(x^2 + 8x + 12).dx`
Evaluate the following.
`int x/(4x^4 - 20x^2 - 3) dx`
Evaluate: `int 1/(sqrt("x") + "x")` dx
`int 1/(xsin^2(logx)) "d"x`
`int cos^7 x "d"x`
If f(x) = 3x + 6, g(x) = 4x + k and fog (x) = gof (x) then k = ______.
If I = `int (sin2x)/(3x + 4cosx)^3 "d"x`, then I is equal to ______.
`int(3x + 1)/(2x^2 - 2x + 3)dx` equals ______.
Evaluate `int(1+x+(x^2)/(2!))dx`
Evaluate `int (1 + "x" + "x"^2/(2!))`dx
