Advertisements
Advertisements
प्रश्न
Evaluate the following: `int logx/x.dx`
Advertisements
उत्तर
Let I = `int logx/x.dx`
Put log x = t
∴ `(1)/x.dx` = dt
∴ I = `int t.dt`
= `t^2/(2) + c`
= `(logx)^2/(2) + c`
APPEARS IN
संबंधित प्रश्न
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
Integrate the function in `x^2e^x`.
Integrate the function in x2 log x.
Integrate the function in x tan-1 x.
Evaluate the following : `int x^2.log x.dx`
Evaluate the following : `int x^2tan^-1x.dx`
Evaluate the following : `int e^(2x).cos 3x.dx`
Evaluate the following : `int log(logx)/x.dx`
Evaluate the following : `int cos(root(3)(x)).dx`
Integrate the following functions w.r.t. x:
sin (log x)
Integrate the following functions w.r.t. x : `sqrt(4^x(4^x + 4))`
Integrate the following functions w.r.t. x: `sqrt(x^2 + 2x + 5)`.
Integrate the following functions w.r.t. x : `e^x .(1/x - 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 (sin^m x)/(cos^(m+2)x)*dx` =
`int ("x" + 1/"x")^3 "dx"` = ______
Choose the correct alternative from the following.
`int (1 - "x")^(-2) "dx"` =
Evaluate: `int "dx"/sqrt(4"x"^2 - 5)`
Evaluate: `int "dx"/(25"x" - "x"(log "x")^2)`
`int 1/x "d"x` = ______ + c
Evaluate `int (2x + 1)/((x + 1)(x - 2)) "d"x`
`int "e"^x x/(x + 1)^2 "d"x`
∫ log x · (log x + 2) dx = ?
`int "e"^x [x (log x)^2 + 2 log x] "dx"` = ______.
Find `int_0^1 x(tan^-1x) "d"x`
`int tan^-1 sqrt(x) "d"x` is equal to ______.
Find: `int e^x.sin2xdx`
Find the general solution of the differential equation: `e^((dy)/(dx)) = x^2`.
The integral `int x cos^-1 ((1 - x^2)/(1 + x^2))dx (x > 0)` is equal to ______.
If `int (f(x))/(log(sin x))dx` = log[log sin x] + c, then f(x) is equal to ______.
Find: `int e^(x^2) (x^5 + 2x^3)dx`.
`int(3x^2)/sqrt(1+x^3) dx = sqrt(1+x^3)+c`
`int1/(x+sqrt(x)) dx` = ______
`inte^(xloga).e^x dx` is ______
`int(xe^x)/((1+x)^2) dx` = ______
Evaluate the following.
`int (x^3)/(sqrt(1 + x^4))dx`
Evaluate:
`int (logx)^2 dx`
Evaluate the following.
`intx^3 e^(x^2) dx`
Evaluate the following:
`intx^3e^(x^2)dx`
Evaluate the following.
`intx^3 e^(x^2) dx`
Evaluate the following.
`intx^3/sqrt(1+x^4) dx`
Evaluate `int (1 + x + x^2/(2!))dx`
If ∫(cot x – cosec2 x)ex dx = ex f(x) + c then f(x) will be ______.
Evaluate `int(1 + x + x^2/(2!))dx`.
Evaluate the following.
`intx^3/(sqrt(1 + x^4))dx`
Evaluate.
`int(5x^2 - 6x + 3)/(2x - 3) dx`
Which pair is listed as Exponential in the LIATE rule?
Using \[t=1-x^2,\] what is \[\int \frac{x\,dx}{\sqrt{1-x^2}}?\]
Evaluate \[\int \frac{x\sin^{-1}x}{\sqrt{1-x^2}}\,dx.\]
Repeated parts may be needed for which pair of integrals?
