Advertisements
Advertisements
प्रश्न
If f'(x) = `x + 1/x`, then f(x) is ______.
विकल्प
`x^2 + log |x| + C`
`x^2/2 + log |x| + C`
`x/2 + log |x| + C`
`x/2 - log |x| + C`
Advertisements
उत्तर
If f'(x) = `x + 1/x`, then f(x) is `underline(bb(x^2/2 + log |x| + C))`.
Explanation:
`x^2/2 + log |x| + C` .....`(∵ f(x) = int(x + 1/x)dx)`
APPEARS IN
संबंधित प्रश्न
Evaluate : `int(x-3)sqrt(x^2+3x-18) dx`
Integrate the functions:
sin x ⋅ sin (cos x)
Integrate the functions:
(4x + 2) `sqrt(x^2 + x +1)`
Integrate the functions:
`x/(9 - 4x^2)`
Integrate the functions:
`e^(tan^(-1)x)/(1+x^2)`
`(10x^9 + 10^x log_e 10)/(x^10 + 10^x) dx` equals:
Write a value of\[\int\frac{1}{1 + e^x} \text{ dx }\]
Integrate the following functions w.r.t. x : `(x^2 + 2)/((x^2 + 1)).a^(x + tan^-1x)`
Evaluate the following : `int (1)/sqrt(11 - 4x^2).dx`
Evaluate the following : `int (1)/(4 + 3cos^2x).dx`
Integrate the following functions w.r.t. x : `int (1)/(2sin 2x - 3)dx`
Choose the correct options from the given alternatives :
`int sqrt(cotx)/(sinx*cosx)*dx` =
If f'(x) = x2 + 5 and f(0) = −1, then find the value of f(x).
Evaluate the following.
`int ("e"^"x" + "e"^(- "x"))^2 ("e"^"x" - "e"^(-"x"))`dx
Evaluate the following.
`int 1/(sqrt"x" + "x")` dx
Evaluate the following.
`int 1/(x(x^6 + 1))` dx
Evaluate the following.
`int 1/(sqrt(3"x"^2 + 8))` dx
Choose the correct alternative from the following.
`int "dx"/(("x" - "x"^2))`=
`int (2(cos^2 x - sin^2 x))/(cos^2 x + sin^2 x)` dx = ______________
If `int 1/(x + x^5)` dx = f(x) + c, then `int x^4/(x + x^5)`dx = ______
`int sqrt(x) sec(x)^(3/2) tan(x)^(3/2)"d"x`
If I = `int (sin2x)/(3x + 4cosx)^3 "d"x`, then I is equal to ______.
`int[ tan (log x) + sec^2 (log x)] dx= ` ______
`int (f^'(x))/(f(x))dx` = ______ + c.
`int(7x - 2)^2dx = (7x -2)^3/21 + c`
The integral `int ((1 - 1/sqrt(3))(cosx - sinx))/((1 + 2/sqrt(3) sin2x))dx` is equal to ______.
The value of `int (sinx + cosx)/sqrt(1 - sin2x) dx` is equal to ______.
`int secx/(secx - tanx)dx` equals ______.
If f '(x) = 4x3 - 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
If f'(x) = 4x3 - 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
