Advertisements
Advertisements
प्रश्न
Choose the correct options from the given alternatives :
`int f x^x (1 + log x)*dx`
विकल्प
`(1)/(2)(1 + log x)^2 + c`
x2x + c
xx log x + c
xx + c
Advertisements
उत्तर
xx + c
[ Hint : `d/dx(x^x)` = xx (1 + log x)].
APPEARS IN
संबंधित प्रश्न
Evaluate : `int (sinx)/sqrt(36-cos^2x)dx`
Evaluate :`intxlogxdx`
Find `int((3sintheta-2)costheta)/(5-cos^2theta-4sin theta)d theta`.
Integrate the functions:
sin x ⋅ sin (cos x)
Integrate the functions:
`xsqrt(1+ 2x^2)`
Integrate the functions:
`cos x /(sqrt(1+sinx))`
Evaluate: `int (2y^2)/(y^2 + 4)dx`
Evaluate: `int_0^3 f(x)dx` where f(x) = `{(cos 2x, 0<= x <= pi/2),(3, pi/2 <= x <= 3) :}`
Write a value of\[\int\frac{1}{1 + e^x} \text{ dx }\]
Write a value of\[\int\frac{\sin 2x}{a^2 \sin^2 x + b^2 \cos^2 x} \text{ dx }\]
Write a value of\[\int e^{ax} \left\{ a f\left( x \right) + f'\left( x \right) \right\} dx\] .
Prove that: `int "dx"/(sqrt("x"^2 +"a"^2)) = log |"x" +sqrt("x"^2 +"a"^2) | + "c"`
Integrate the following w.r.t. x : x3 + x2 – x + 1
Evaluate the following integrals : `int(5x + 2)/(3x - 4).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 : `(sin6x)/(sin 10x sin 4x)`
Evaluate the following:
`int (1)/(25 - 9x^2)*dx`
Evaluate the following : `int (1)/sqrt(2x^2 - 5).dx`
Evaluate the following : `int sqrt((10 + x)/(10 - x)).dx`
Evaluate the following : `int (1)/(x^2 + 8x + 12).dx`
Evaluate the following : `int (1)/(4 + 3cos^2x).dx`
Evaluate the following integral:
`int (3cosx)/(4sin^2x + 4sinx - 1).dx`
Choose the correct options from the given alternatives :
`int (e^x(x - 1))/x^2*dx` =
Choose the correct options from the given alternatives :
`int (e^(2x) + e^-2x)/e^x*dx` =
Evaluate `int (-2)/(sqrt("5x" - 4) - sqrt("5x" - 2))`dx
Evaluate the following.
`int ((3"e")^"2t" + 5)/(4"e"^"2t" - 5)`dt
To find the value of `int ((1 + log x) )/x dx` the proper substitution is ______.
Evaluate: `int 1/(sqrt("x") + "x")` dx
Evaluate: `int "e"^sqrt"x"` dx
`int (log x)/(log ex)^2` dx = _________
`int ("e"^(3x))/("e"^(3x) + 1) "d"x`
State whether the following statement is True or False:
`int"e"^(4x - 7) "d"x = ("e"^(4x - 7))/(-7) + "c"`
`int (1 + x)/(x + "e"^(-x)) "d"x`
`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(3x + 1)/(2x^2 - 2x + 3)dx` equals ______.
`int 1/(sinx.cos^2x)dx` = ______.
Evaluate `int_-a^a f(x) dx`, where f(x) = `9^x/(1 + 9^x)`.
Evaluate `int1/(x(x - 1))dx`
Evaluate `int (1)/(x(x - 1))dx`
`int x^2/sqrt(1 - x^6)dx` = ______.
Evaluate:
`int(cos 2x)/sinx dx`
Evaluate:
`int(5x^2-6x+3)/(2x-3)dx`
Evaluate.
`int (5x^2 -6x + 3)/(2x -3)dx`
After choosing \[u=g(x)\], what is the next step?
