Advertisements
Advertisements
प्रश्न
Find :
`∫(log x)^2 dx`
Advertisements
उत्तर
`∫(log x)^2 dx`
let `u = (logx)^2 , "v" = 1`
`∫u."v" dx = u∫"v"dx - ∫[(du)/dx∫"v"dx]dx`
`therefore ∫ (log x)^2 . 1dx = (log x)^2 ∫1dx - ∫[2log x xx 1/x xx xdx]`
= `x(log|x|^2) - 2∫log x dx`
`x(log x)^2 - 2(x log|x| - x) + C`
= `x(log|x|)^2 - 2x log|x| + 2x + C` .
APPEARS IN
संबंधित प्रश्न
`int1/xlogxdx=...............`
(A)log(log x)+ c
(B) 1/2 (logx )2+c
(C) 2log x + c
(D) log x + c
If u and v are two functions of x then prove that
`intuvdx=uintvdx-int[du/dxintvdx]dx`
Hence evaluate, `int xe^xdx`
Integrate the function in x sin−1 x.
Integrate the function in x (log x)2.
Evaluate the following:
`int sec^3x.dx`
Evaluate the following : `int (t.sin^-1 t)/sqrt(1 - t^2).dt`
Evaluate the following:
`int x.sin 2x. cos 5x.dx`
Integrate the following functions w.r.t. x : `e^(2x).sin3x`
Integrate the following functions w.r.t. x : `x^2 .sqrt(a^2 - x^6)`
Integrate the following functions w.r.t. x : `xsqrt(5 - 4x - x^2)`
Integrate the following functions w.r.t. x : `((1 + sin x)/(1 + cos x)).e^x`
Integrate the following functions w.r.t. x : `e^(sin^-1x)*[(x + sqrt(1 - x^2))/sqrt(1 - x^2)]`
Choose the correct options from the given alternatives :
`int (log (3x))/(xlog (9x))*dx` =
Choose the correct options from the given alternatives :
`int (1)/(cosx - cos^2x)*dx` =
Integrate the following w.r.t.x : `sqrt(x)sec(x^(3/2))*tan(x^(3/2))`
Integrate the following w.r.t.x : log (x2 + 1)
Evaluate the following.
`int "x"^3 "e"^("x"^2)`dx
`int (sinx)/(1 + sin x) "d"x`
`int 1/(x^2 - "a"^2) "d"x` = ______ + c
Evaluate `int 1/(x(x - 1)) "d"x`
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`
The integral `int x cos^-1 ((1 - x^2)/(1 + x^2))dx (x > 0)` is equal to ______.
Find `int e^x ((1 - sinx)/(1 - cosx))dx`.
Evaluate :
`int(4x - 6)/(x^2 - 3x + 5)^(3/2) dx`
`int(1-x)^-2 dx` = ______
`int1/sqrt(x^2 - a^2) dx` = ______
The integrating factor of `ylogy.dx/dy+x-logy=0` is ______.
Evaluate:
`int((1 + sinx)/(1 + cosx))e^x dx`
Evaluate:
`int e^(ax)*cos(bx + c)dx`
Evaluate:
`int1/(x^2 + 25)dx`
