Advertisements
Advertisements
Question
`int1/xlogxdx=...............`
(A)log(log x)+ c
(B) 1/2 (logx )2+c
(C) 2log x + c
(D) log x + c
Solution
(B) ` 1/2 (logx )^2+c`
APPEARS IN
RELATED QUESTIONS
Integrate the function in x cos-1 x.
Integrate the function in `(x cos^(-1) x)/sqrt(1-x^2)`.
Integrate the function in x sec2 x.
Evaluate the following : `int x^2 sin 3x dx`
Evaluate the following : `int x tan^-1 x .dx`
Evaluate the following:
`int sec^3x.dx`
Evaluate the following : `int e^(2x).cos 3x.dx`
Evaluate the following : `int cos sqrt(x).dx`
Evaluate the following : `int logx/x.dx`
Evaluate the following:
`int x.sin 2x. cos 5x.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(4^x(4^x + 4))`
Integrate the following functions w.r.t. x : `sqrt(2x^2 + 3x + 4)`
Integrate the following functions w.r.t. x : `e^x/x [x (logx)^2 + 2 (logx)]`
Integrate the following functions w.r.t. x : `e^(sin^-1x)*[(x + sqrt(1 - x^2))/sqrt(1 - x^2)]`
Integrate the following functions w.r.t. x : cosec (log x)[1 – cot (log x)]
Choose the correct options from the given alternatives :
`int (x- sinx)/(1 - cosx)*dx` =
If f(x) = `sin^-1x/sqrt(1 - x^2), "g"(x) = e^(sin^-1x)`, then `int f(x)*"g"(x)*dx` = ______.
Choose the correct options from the given alternatives :
`int cos -(3)/(7)x*sin -(11)/(7)x*dx` =
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 : `t^3/(t + 1)^2`
Integrate the following with respect to the respective variable : `(sin^6θ + cos^6θ)/(sin^2θ*cos^2θ)`
Integrate the following w.r.t.x : `sqrt(x)sec(x^(3/2))*tan(x^(3/2))`
Integrate the following w.r.t.x : `(1)/(x^3 sqrt(x^2 - 1)`
Evaluate the following.
∫ x log x dx
Evaluate the following.
`int "x"^2 "e"^"4x"`dx
Evaluate the following.
`int "x"^3 "e"^("x"^2)`dx
Choose the correct alternative from the following.
`int (("x"^3 + 3"x"^2 + 3"x" + 1))/("x + 1")^5 "dx"` =
Evaluate: `int "dx"/sqrt(4"x"^2 - 5)`
Evaluate: `int "dx"/(3 - 2"x" - "x"^2)`
Evaluate: `int "dx"/(5 - 16"x"^2)`
Evaluate: ∫ (log x)2 dx
`int 1/(4x + 5x^(-11)) "d"x`
`int (sin(x - "a"))/(cos (x + "b")) "d"x`
`int 1/sqrt(2x^2 - 5) "d"x`
`int sin4x cos3x "d"x`
`int ("e"^xlog(sin"e"^x))/(tan"e"^x) "d"x`
`int (x^2 + x - 6)/((x - 2)(x - 1)) "d"x` = x + ______ + c
Evaluate `int 1/(x(x - 1)) "d"x`
`int "e"^x x/(x + 1)^2 "d"x`
∫ log x · (log x + 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 "e"^x [x (log x)^2 + 2 log x] "dx"` = ______.
Evaluate the following:
`int (sin^-1 x)/((1 - x)^(3/2)) "d"x`
`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
State whether the following statement is true or false.
If `int (4e^x - 25)/(2e^x - 5)` dx = Ax – 3 log |2ex – 5| + c, where c is the constant of integration, then A = 5.
`int x/((x + 2)(x + 3)) dx` = ______ + `int 3/(x + 3) dx`
Find: `int (2x)/((x^2 + 1)(x^2 + 2)) dx`
Find the general solution of the differential equation: `e^((dy)/(dx)) = x^2`.
If `int(2e^(5x) + e^(4x) - 4e^(3x) + 4e^(2x) + 2e^x)/((e^(2x) + 4)(e^(2x) - 1)^2)dx = tan^-1(e^x/a) - 1/(b(e^(2x) - 1)) + C`, where C is constant of integration, then value of a + b is equal to ______.
`int e^x [(2 + sin 2x)/(1 + cos 2x)]dx` = ______.
Solution of the equation `xdy/dx=y log y` is ______
Evaluate the following.
`int x^3 e^(x^2) dx`
Evaluate `int(3x-2)/((x+1)^2(x+3)) dx`
`inte^(xloga).e^x dx` is ______
The integrating factor of `ylogy.dx/dy+x-logy=0` is ______.
`int logx dx = x(1+logx)+c`
`int(f'(x))/sqrt(f(x)) dx = 2sqrt(f(x))+c`
Evaluate:
`intcos^-1(sqrt(x))dx`
Evaluate:
`inte^x sinx dx`
Evaluate:
`int e^(logcosx)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`
If ∫(cot x – cosec2 x)ex dx = ex f(x) + c then f(x) will be ______.
The value of `inta^x.e^x dx` equals
Evaluate:
`inte^x "cosec" x(1 - cot x)dx`
Evaluate the following.
`intx^3 e^(x^2)dx`
Evaluate `int(1 + x + x^2/(2!))dx`.