Advertisements
Advertisements
Question
If f'(x) = `x + 1/x`, then f(x) is ______.
Options
`x^2 + log |x| + C`
`x^2/2 + log |x| + C`
`x/2 + log |x| + C`
`x/2 - log |x| + C`
Advertisements
Solution
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
RELATED QUESTIONS
Evaluate : `int (sinx)/sqrt(36-cos^2x)dx`
Find : `int((2x-5)e^(2x))/(2x-3)^3dx`
Integrate the functions:
`cos sqrt(x)/sqrtx`
The value of \[\int\frac{1}{x + x \log x} dx\] is
Integrate the following w.r.t. x:
`2x^3 - 5x + 3/x + 4/x^5`
Evaluate the following integrals : `int sin x/cos^2x dx`
Evaluate the following integrals : `int (cos2x)/(sin^2x.cos^2x)dx`
Integrate the following functions w.r.t. x : `x^2/sqrt(9 - x^6)`
Integrate the following functions w.r.t. x : `cosx/sin(x - a)`
Integrate the following functions w.r.t. x : `(4e^x - 25)/(2e^x - 5)`
Integrate the following functions w.r.t. x : tan 3x tan 2x tan x
Evaluate the following : `int (1)/(7 + 2x^2).dx`
Evaluate the following : `int (1)/sqrt(2x^2 - 5).dx`
Evaluate the following integral:
`int (3cosx)/(4sin^2x + 4sinx - 1).dx`
Integrate the following w.r.t.x: `(3x + 1)/sqrt(-2x^2 + x + 3)`
If f'(x) = 4x3 − 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
`int "e"^x[((x + 3))/((x + 4)^2)] "d"x`
General solution of `(x + y)^2 ("d"y)/("d"x) = "a"^2, "a" ≠ 0` is ______. (c is arbitrary constant)
`int x/sqrt(1 - 2x^4) dx` = ______.
(where c is a constant of integration)
`int(1 - x)^(-2)` dx = `(1 - x)^(-1) + c`
Evaluate the following.
`int x^3 e^(x^2) dx`
Evaluate the following.
`int x^3/sqrt(1+x^4) dx`
Evaluate.
`int (5x^2 -6x + 3)/(2x -3)dx`
Evaluate `int1/(x(x-1))dx`
Evaluate `int 1/(x(x-1))dx`
Evaluate `int (1 + x + x^2/(2!)) dx`
Evaluate the following.
`int1/(x^2 + 4x-5)dx`
Evaluate the following.
`intx^3/sqrt(1 + x^4) dx`
