Advertisements
Advertisements
प्रश्न
Integrate the function in x log x.
Advertisements
उत्तर
Let `I = int x log x dx`
`= log x int x dx - int [d/dx (log x) int x dx] dx`
`= log x (x^2/2) - int (1/x * x^2/2) dx`
`= x^2/2 log x - 1/2 int x dx + C`
`= x^2/2 log x -1/2 xx x^2/2 + C`
`= x^2/2 log x - 1/4 x^2 + C`
APPEARS IN
संबंधित प्रश्न
Prove that:
`int sqrt(x^2 - a^2)dx = x/2sqrt(x^2 - a^2) - a^2/2log|x + sqrt(x^2 - a^2)| + c`
Evaluate `int_0^(pi)e^2x.sin(pi/4+x)dx`
Integrate the function in x log 2x.
Integrate the function in tan-1 x.
Evaluate the following:
`int x^2 sin 3x dx`
Evaluate the following : `int x^2tan^-1x.dx`
Evaluate the following : `int x^3.tan^-1x.dx`
Evaluate the following : `int cos sqrt(x).dx`
Evaluate the following : `int cos(root(3)(x)).dx`
Integrate the following functions w.r.t. x : `x^2 .sqrt(a^2 - x^6)`
Integrate the following functions w.r.t. x: `sqrt(x^2 + 2x + 5)`.
Integrate the following functions w.r.t. x : `[x/(x + 1)^2].e^x`
Choose the correct options from the given alternatives :
`int (1)/(cosx - cos^2x)*dx` =
Choose the correct options from the given alternatives :
`int sin (log x)*dx` =
Solve the following differential equation.
(x2 − yx2 ) dy + (y2 + xy2) dx = 0
Evaluate the following.
`int "e"^"x" "x"/("x + 1")^2` dx
Evaluate: `int "dx"/("x"[(log "x")^2 + 4 log "x" - 1])`
Evaluate:
∫ (log x)2 dx
`int 1/(4x + 5x^(-11)) "d"x`
`int 1/sqrt(2x^2 - 5) "d"x`
Evaluate `int 1/(x(x - 1)) "d"x`
`int log x * [log ("e"x)]^-2` dx = ?
Evaluate the following:
`int ((cos 5x + cos 4x))/(1 - 2 cos 3x) "d"x`
`int 1/sqrt(x^2 - 9) dx` = ______.
Find: `int (2x)/((x^2 + 1)(x^2 + 2)) dx`
`int 1/sqrt(x^2 - a^2)dx` = ______.
`int(logx)^2dx` equals ______.
Find `int e^(cot^-1x) ((1 - x + x^2)/(1 + x^2))dx`.
`int1/sqrt(x^2 - a^2) dx` = ______
Evaluate the following.
`int x^3 e^(x^2) dx`
Evaluate the following.
`int (x^3)/(sqrt(1 + x^4))dx`
Evaluate:
`int (logx)^2 dx`
Evaluate `int tan^-1x dx`
If f′(x) = 4x3 − 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
If ∫(cot x – cosec2 x)ex dx = ex f(x) + c then f(x) will be ______.
Evaluate the following.
`int x^3 e^(x^2) dx`
Evaluate the following.
`intx^3/sqrt(1+x^4)`dx
Evaluate.
`int(5x^2 - 6x + 3)/(2x - 3) dx`
