Advertisements
Advertisements
Question
Choose the correct options from the given alternatives :
`int f x^x (1 + log x)*dx`
Options
`(1)/(2)(1 + log x)^2 + c`
x2x + c
xx log x + c
xx + c
Advertisements
Solution
xx + c
[ Hint : `d/dx(x^x)` = xx (1 + log x)].
APPEARS IN
RELATED QUESTIONS
Evaluate :
`int(sqrt(cotx)+sqrt(tanx))dx`
Find : `int((2x-5)e^(2x))/(2x-3)^3dx`
Find `intsqrtx/sqrt(a^3-x^3)dx`
Integrate the functions:
sin (ax + b) cos (ax + b)
Integrate the functions:
(4x + 2) `sqrt(x^2 + x +1)`
Integrate the functions:
`x^2/(2+ 3x^3)^3`
Integrate the functions:
`e^(2x+3)`
Integrate the functions:
`e^(tan^(-1)x)/(1+x^2)`
Write a value of\[\int\frac{\sin 2x}{a^2 \sin^2 x + b^2 \cos^2 x} \text{ dx }\]
Write a value of\[\int e^{ax} \sin\ bx\ dx\]
Write a value of\[\int\sqrt{9 + x^2} \text{ dx }\].
Show that : `int _0^(pi/4) "log" (1+"tan""x")"dx" = pi /8 "log"2`
Integrate the following w.r.t. x : `int x^2(1 - 2/x)^2 dx`
Evaluate the following integrals:
`int (cos2x)/sin^2x dx`
Evaluate the following integrals : `int (cos2x)/(sin^2x.cos^2x)dx`
Evaluate the following integrals: `int sin 4x cos 3x dx`
Integrate the following functions w.r.t. x : `(cos3x - cos4x)/(sin3x + sin4x)`
Integrate the following functions w.r.t. x : `(20 + 12e^x)/(3e^x + 4)`
Integrate the following functions w.r.t. x : `(sin6x)/(sin 10x sin 4x)`
Evaluate the following : `int (1)/(4x^2 - 3).dx`
Evaluate the following : `int (1)/(7 + 2x^2).dx`
Evaluate the following : `int sqrt((2 + x)/(2 - x)).dx`
Evaluate the following : `int (1)/(5 - 4x - 3x^2).dx`
Integrate the following functions w.r.t. x : `int (1)/(3 + 2sin x - cosx)dx`
Integrate the following functions w.r.t. x : `int (1)/(3 - 2cos 2x).dx`
Evaluate `int (1 + x + x^2/(2!))`dx
Evaluate the following.
`int 1/(x(x^6 + 1))` dx
Evaluate the following.
`int x/(4x^4 - 20x^2 - 3) dx`
Evaluate the following.
`int 1/(7 + 6"x" - "x"^2)` dx
`int 1/sqrt((x - 3)(x + 2))` dx = ______.
`int (cos2x)/(sin^2x) "d"x`
`int cot^2x "d"x`
`int cos^7 x "d"x`
Evaluate `int(3x^2 - 5)^2 "d"x`
If f(x) = 3x + 6, g(x) = 4x + k and fog (x) = gof (x) then k = ______.
`int dx/(1 + e^-x)` = ______
`int1/(4 + 3cos^2x)dx` = ______
If I = `int (sin2x)/(3x + 4cosx)^3 "d"x`, then I is equal to ______.
`int sec^6 x tan x "d"x` = ______.
The value of `sqrt(2) int (sinx dx)/(sin(x - π/4))` is ______.
Evaluate the following.
`int(1)/(x^2 + 4x - 5)dx`
Evaluate the following.
`int1/(x^2+4x-5) dx`
Evaluate:
`int(cos 2x)/sinx dx`
Evaluate the following.
`int x^3/sqrt(1+x^4) dx`
Evaluate `int(1 + x + x^2 / (2!))dx`
Evaluate the following.
`int1/(x^2+4x-5)dx`
