Advertisements
Advertisements
Question
`int1/xlogxdx=...............`
(A)log(log x)+ c
(B) 1/2 (logx )2+c
(C) 2log x + c
(D) log x + c
Advertisements
Solution
(B) ` 1/2 (logx )^2+c`
APPEARS IN
RELATED QUESTIONS
If `int_(-pi/2)^(pi/2)sin^4x/(sin^4x+cos^4x)dx`, then the value of I is:
(A) 0
(B) π
(C) π/2
(D) π/4
Evaluate `int_0^(pi)e^2x.sin(pi/4+x)dx`
Integrate the function in x log x.
Integrate the function in (sin-1x)2.
Integrate the function in `(x cos^(-1) x)/sqrt(1-x^2)`.
Integrate the function in tan-1 x.
Integrate the function in (x2 + 1) log x.
Find :
`∫(log x)^2 dx`
Evaluate the following : `int x^3.tan^-1x.dx`
Evaluate the following : `int x.sin^2x.dx`
Evaluate the following : `int x^3.logx.dx`
Evaluate the following : `int cos sqrt(x).dx`
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 : `log(1 + x)^((1 + x)`
Choose the correct options from the given alternatives :
`int (1)/(x + x^5)*dx` = f(x) + c, then `int x^4/(x + x^5)*dx` =
Choose the correct options from the given alternatives :
`int (log (3x))/(xlog (9x))*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 (1)/(cosx - cos^2x)*dx` =
Integrate the following with respect to the respective variable : `t^3/(t + 1)^2`
Integrate the following w.r.t.x : `log (1 + cosx) - xtan(x/2)`
Integrate the following w.r.t.x : log (log x)+(log x)–2
Evaluate the following.
`int (log "x")/(1 + log "x")^2` dx
Choose the correct alternative from the following.
`int (1 - "x")^(-2) "dx"` =
Evaluate: `int "dx"/(5 - 16"x"^2)`
`int (cos2x)/(sin^2x cos^2x) "d"x`
`int log x * [log ("e"x)]^-2` dx = ?
The value of `int "e"^(5x) (1/x - 1/(5x^2)) "d"x` is ______.
If u and v ore differentiable functions of x. then prove that:
`int uv dx = u intv dx - int [(du)/(d) intv dx]dx`
Hence evaluate `intlog x dx`
Evaluate: `int_0^(pi/4) (dx)/(1 + tanx)`
`int((4e^x - 25)/(2e^x - 5))dx = Ax + B log(2e^x - 5) + c`, then ______.
`int(1-x)^-2 dx` = ______
`int1/(x+sqrt(x)) dx` = ______
Evaluate:
`int e^(logcosx)dx`
Evaluate `int tan^-1x dx`
If ∫(cot x – cosec2 x)ex dx = ex f(x) + c then f(x) will be ______.
Evaluate:
`int x^2 cos x dx`
