Advertisements
Advertisements
प्रश्न
`int x^x (1 + logx) "d"x`
Advertisements
उत्तर
Since `"d"/("d"x)(x^x)` = xx (1 + log x),
`int x^x (1 + log x) "d"x` = xx + c
APPEARS IN
संबंधित प्रश्न
Find the particular solution of the differential equation x2dy = (2xy + y2) dx, given that y = 1 when x = 1.
Integrate the functions:
sin (ax + b) cos (ax + b)
Integrate the functions:
`x/(9 - 4x^2)`
Integrate the functions:
`(e^(2x) - 1)/(e^(2x) + 1)`
Integrate the functions:
`(2cosx - 3sinx)/(6cos x + 4 sin x)`
Integrate the functions:
`1/(cos^2 x(1-tan x)^2`
Integrate the functions:
`cos x /(sqrt(1+sinx))`
`int (dx)/(sin^2 x cos^2 x)` equals:
Write a value of
Write a value of
Write a value of\[\int \cos^4 x \text{ sin x dx }\]
Write a value of\[\int\frac{1}{x \left( \log x \right)^n} \text { dx }\].
Write a value of\[\int e^{ax} \sin\ bx\ dx\]
\[\int\frac{\sin x + 2 \cos x}{2 \sin x + \cos x} \text{ dx }\]
`int "dx"/(9"x"^2 + 1)= ______. `
Evaluate the following integrals : tan2x dx
Evaluate the following integrals : `int sin x/cos^2x dx`
Evaluate the following integrals : `int(5x + 2)/(3x - 4).dx`
Integrate the following functions w.r.t. x : `(1)/(x(x^3 - 1)`
Integrate the following functions w.r.t. x : `sin(x - a)/cos(x + b)`
Integrate the following functions w.r.t. x : `(4e^x - 25)/(2e^x - 5)`
Evaluate the following : `int (1)/sqrt(3x^2 + 5x + 7).dx`
Evaluate the following : `int (1)/sqrt(x^2 + 8x - 20).dx`
Choose the correct option from the given alternatives :
`int (1 + x + sqrt(x + x^2))/(sqrt(x) + sqrt(1 + x))*dx` =
Choose the correct options from the given alternatives :
`int (cos2x - 1)/(cos2x + 1)*dx` =
Integrate the following with respect to the respective variable:
`x^7/(x + 1)`
Evaluate the following.
`int (20 - 12"e"^"x")/(3"e"^"x" - 4)`dx
Evaluate the following.
`int (2"e"^"x" + 5)/(2"e"^"x" + 1)`dx
Evaluate: `int 1/(sqrt("x") + "x")` dx
`int sqrt(x) sec(x)^(3/2) tan(x)^(3/2)"d"x`
`int (cos2x)/(sin^2x) "d"x`
`int cot^2x "d"x`
`int cos^7 x "d"x`
`int(log(logx))/x "d"x`
`int(1 - x)^(-2) dx` = ______.
To find the value of `int ((1 + logx))/x` dx the proper substitution is ______
State whether the following statement is True or False:
`int3^(2x + 3) "d"x = (3^(2x + 3))/2 + "c"`
`int "dx"/((sin x + cos x)(2 cos x + sin x))` = ?
`int ((x + 1)(x + log x))^4/(3x) "dx" =`______.
If I = `int (sin2x)/(3x + 4cosx)^3 "d"x`, then I is equal to ______.
If `int sinx/(sin^3x + cos^3x)dx = α log_e |1 + tan x| + β log_e |1 - tan x + tan^2x| + γ tan^-1 ((2tanx - 1)/sqrt(3)) + C`, when C is constant of integration, then the value of 18(α + β + γ2) is ______.
`int x/sqrt(1 - 2x^4) dx` = ______.
(where c is a constant of integration)
Evaluate the following.
`int 1/(x^2 + 4x - 5)dx`
Evaluate `int 1/(x(x-1))dx`
Evaluate `int(1+x+(x^2)/(2!))dx`
If f'(x) = 4x3 – 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
