Advertisements
Advertisements
प्रश्न
If f'(x) = `x + 1/x`, then f(x) is ______.
पर्याय
`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 (sinx)/sqrt(36-cos^2x)dx`
Show that: `int1/(x^2sqrt(a^2+x^2))dx=-1/a^2(sqrt(a^2+x^2)/x)+c`
Find: `int(x+3)sqrt(3-4x-x^2dx)`
Find `int((3sintheta-2)costheta)/(5-cos^2theta-4sin theta)d theta`.
Integrate the functions:
`x/(9 - 4x^2)`
Integrate the functions:
sec2(7 – 4x)
Integrate the functions:
`sqrt(sin 2x) cos 2x`
Integrate the functions:
`cos x /(sqrt(1+sinx))`
Evaluate the following integrals : `int (3)/(sqrt(7x - 2) - sqrt(7x - 5)).dx`
Integrate the following functions w.r.t. x : `(x^n - 1)/sqrt(1 + 4x^n)`
Evaluate the following:
`int (1)/(25 - 9x^2)*dx`
State whether the following statement is True or False.
The proper substitution for `int x(x^x)^x (2log x + 1) "d"x` is `(x^x)^x` = t
`int sqrt(1 + sin2x) dx`
`int (cos2x)/(sin^2x) "d"x`
`int x/(x + 2) "d"x`
State whether the following statement is True or False:
`int"e"^(4x - 7) "d"x = ("e"^(4x - 7))/(-7) + "c"`
`int "dx"/((sin x + cos x)(2 cos x + sin 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(log(logx) + 1/(logx)^2)dx` = ______.
The integral `int ((1 - 1/sqrt(3))(cosx - sinx))/((1 + 2/sqrt(3) sin2x))dx` is equal to ______.
`int (x + sinx)/(1 + cosx)dx` is equal to ______.
Evaluate the following.
`int x^3/(sqrt(1+x^4))dx`
Evaluate.
`int(5"x"^2 - 6"x" + 3)/(2"x" - 3) "dx"`
Evaluate the following.
`int (x^3)/(sqrt(1 + x^4)) dx`
Evaluate:
`int(5x^2-6x+3)/(2x-3)dx`
Evaluate the following.
`intx^3/sqrt(1+x^4)dx`
Evaluate the following.
`int1/(x^2 + 4x-5)dx`
