Advertisements
Advertisements
प्रश्न
Integrate the function in x2 log x.
Advertisements
उत्तर
Let `I = int x^2 log x dx`
`= log (x) (x^3/3) - int [d/dx (log x) (x^3/3)] dx`
`= log x. x^3/3 - int 1/x. x^3/3 dx`
`= x^3/3 log x - 1/3 int x^2 dx`
`= x^3/3 log x - 1/3. x^3/3 + C`
`= x^3/3 log x - x^3/9 + C`
APPEARS IN
संबंधित प्रश्न
If u and v are two functions of x then prove that
`intuvdx=uintvdx-int[du/dxintvdx]dx`
Hence evaluate, `int xe^xdx`
Integrate the function in x sec2 x.
Evaluate the following : `int x^2.log x.dx`
Evaluate the following: `int x.sin^-1 x.dx`
Evaluate the following : `int log(logx)/x.dx`
Evaluate the following : `int(sin(logx)^2)/x.log.x.dx`
Evaluate the following: `int logx/x.dx`
Integrate the following functions w.r.t. x : `sqrt((x - 3)(7 - x)`
Integrate the following functions w.r.t. x : `sqrt(4^x(4^x + 4))`
Integrate the following functions w.r.t. x : `sec^2x.sqrt(tan^2x + tan x - 7)`
Integrate the following functions w.r.t. x : `((1 + sin x)/(1 + cos x)).e^x`
Integrate the following functions w.r.t. x : `[x/(x + 1)^2].e^x`
Integrate the following functions w.r.t.x:
`e^(5x).[(5x.logx + 1)/x]`
Integrate the following functions w.r.t. x : `e^(sin^-1x)*[(x + sqrt(1 - x^2))/sqrt(1 - x^2)]`
Choose the correct options from the given alternatives :
`int [sin (log x) + cos (log x)]*dx` =
Integrate the following with respect to the respective variable : cos 3x cos 2x cos x
Integrate the following w.r.t. x: `(1 + log x)^2/x`
Integrate the following w.r.t.x : log (log x)+(log x)–2
Evaluate the following.
`int [1/(log "x") - 1/(log "x")^2]` dx
Choose the correct alternative from the following.
`int (("e"^"2x" + "e"^"-2x")/"e"^"x") "dx"` =
`int 1/(4x + 5x^(-11)) "d"x`
`int 1/sqrt(2x^2 - 5) "d"x`
Choose the correct alternative:
`int ("d"x)/((x - 8)(x + 7))` =
`int(x + 1/x)^3 dx` = ______.
`int (x^2 + x - 6)/((x - 2)(x - 1)) "d"x` = x + ______ + c
`int logx/(1 + logx)^2 "d"x`
`int [(log x - 1)/(1 + (log x)^2)]^2`dx = ?
`int log x * [log ("e"x)]^-2` dx = ?
The value of `int "e"^(5x) (1/x - 1/(5x^2)) "d"x` is ______.
`int tan^-1 sqrt(x) "d"x` is equal to ______.
The value of `int_0^(pi/2) log ((4 + 3 sin x)/(4 + 3 cos x)) dx` is
Find: `int e^x.sin2xdx`
`int e^x [(2 + sin 2x)/(1 + cos 2x)]dx` = ______.
Find `int (sin^-1x)/(1 - x^2)^(3//2) dx`.
Solution of the equation `xdy/dx=y log y` is ______
Evaluate `int(3x-2)/((x+1)^2(x+3)) dx`
Evaluate `int(1 + x + (x^2)/(2!))dx`
Solve the following
`int_0^1 e^(x^2) x^3 dx`
The value of `int e^x((1 + sinx)/(1 + cosx))dx` is ______.
Evaluate the following.
`intx^3e^(x^2) dx`
