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
Integrate the function in (sin-1x)2.
Integrate the function in x sec2 x.
Integrate the function in `sin^(-1) ((2x)/(1+x^2))`.
Evaluate the following:
`int sec^3x.dx`
Integrate the following functions w.r.t. x : `x^2 .sqrt(a^2 - x^6)`
Integrate the following functions w.r.t. x : `(x + 1) sqrt(2x^2 + 3)`
Integrate the following functions w.r.t. x : `[x/(x + 1)^2].e^x`
Choose the correct options from the given alternatives :
`int [sin (log x) + cos (log x)]*dx` =
Integrate the following w.r.t. x: `(1 + log x)^2/x`
Integrate the following w.r.t.x : `log (1 + cosx) - xtan(x/2)`
`int ("x" + 1/"x")^3 "dx"` = ______
Choose the correct alternative from the following.
`int (("x"^3 + 3"x"^2 + 3"x" + 1))/("x + 1")^5 "dx"` =
Evaluate: `int ("ae"^("x") + "be"^(-"x"))/("ae"^("x") - "be"^(−"x"))` dx
Evaluate: `int "dx"/sqrt(4"x"^2 - 5)`
Evaluate: `int e^x/sqrt(e^(2x) + 4e^x + 13)` dx
Evaluate: `int "e"^"x"/(4"e"^"2x" -1)` dx
`int (sinx)/(1 + sin x) "d"x`
`int (sin(x - "a"))/(cos (x + "b")) "d"x`
`int 1/sqrt(2x^2 - 5) "d"x`
`int ["cosec"(logx)][1 - cot(logx)] "d"x`
`int ("d"x)/(x - x^2)` = ______
∫ log x · (log x + 2) dx = ?
Find the general solution of the differential equation: `e^((dy)/(dx)) = x^2`.
If `π/2` < x < π, then `intxsqrt((1 + cos2x)/2)dx` = ______.
`int_0^1 x tan^-1 x dx` = ______.
`int((4e^x - 25)/(2e^x - 5))dx = Ax + B log(2e^x - 5) + c`, then ______.
If `int (f(x))/(log(sin x))dx` = log[log sin x] + c, then f(x) is equal to ______.
`int(1-x)^-2 dx` = ______
`int1/(x+sqrt(x)) dx` = ______
`int(f'(x))/sqrt(f(x)) dx = 2sqrt(f(x))+c`
Evaluate:
`intcos^-1(sqrt(x))dx`
Evaluate:
`int e^(ax)*cos(bx + c)dx`
If u and v are two differentiable functions of x, then prove that `intu*v*dx = u*intv dx - int(d/dx u)(intv dx)dx`. Hence evaluate: `intx cos x dx`
Evaluate:
`int1/(x^2 + 25)dx`
If ∫(cot x – cosec2 x)ex dx = ex f(x) + c then f(x) will be ______.
Evaluate the following.
`intx^3/sqrt(1+x^4)`dx
Evaluate `int(1 + x + x^2/(2!))dx`.
