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`
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 :
`∫(x+2)/sqrt(x^2+5x+6)dx`
Write a value of\[\int\frac{\sin 2x}{a^2 \sin^2 x + b^2 \cos^2 x} \text{ dx }\]
Write a value of\[\int\sqrt{4 - x^2} \text{ dx }\]
The value of \[\int\frac{1}{x + x \log x} dx\] is
Show that : `int _0^(pi/4) "log" (1+"tan""x")"dx" = pi /8 "log"2`
Evaluate the following integrals : `int tanx/(sec x + tan x)dx`
Evaluate the following integrals: `int (2x - 7)/sqrt(4x - 1).dx`
Integrate the following functions w.r.t. x : `e^x.log (sin e^x)/tan(e^x)`
Integrate the following functions w.r.t. x : `(1)/(sinx.cosx + 2cos^2x)`
Integrate the following functions w.r.t. x : `(3e^(2x) + 5)/(4e^(2x) - 5)`
Integrate the following functions w.r.t. x : `int (1)/(2 + cosx - sinx).dx`
Integrate the following functions w.r.t. x : `int (1)/(cosx - sinx).dx`
Evaluate the following.
`int ((3"e")^"2t" + 5)/(4"e"^"2t" - 5)`dt
Evaluate the following.
`int 1/("a"^2 - "b"^2 "x"^2)` dx
Evaluate: `int (2"e"^"x" - 3)/(4"e"^"x" + 1)` dx
`int 1/sqrt((x - 3)(x + 2))` dx = ______.
`int sqrt(x^2 + 2x + 5)` dx = ______________
`int x/(x + 2) "d"x`
State whether the following statement is True or False:
If `int x "f"(x) "d"x = ("f"(x))/2`, then f(x) = `"e"^(x^2)`
Evaluate `int"e"^x (1/x - 1/x^2) "d"x`
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 ______.
`int (logx)^2/x dx` = ______.
Evaluate `int_-a^a f(x) dx`, where f(x) = `9^x/(1 + 9^x)`.
Evaluate `int(1+ x + x^2/(2!)) dx`
Evaluate the following.
`int x^3 e^(x^2) dx`
Evaluate `int (1 + x + x^2/(2!)) dx`
Evaluate the following.
`intx^3/sqrt(1+x^4)dx`
Evaluate the following.
`intx^3/sqrt(1+x^4)dx`