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
Prove that: `int sqrt(a^2 - x^2) * dx = x/2 * sqrt(a^2 - x^2) + a^2/2 * sin^-1(x/a) + c`
Evaluate `int_0^(pi)e^2x.sin(pi/4+x)dx`
Integrate the function in `x^2e^x`.
Integrate the function in x log x.
Integrate the function in x sin−1 x.
Integrate the function in tan-1 x.
Integrate the function in (x2 + 1) log x.
Integrate the function in `(xe^x)/(1+x)^2`.
Integrate the function in `e^x (1 + sin x)/(1+cos x)`.
Integrate the function in `((x- 3)e^x)/(x - 1)^3`.
Evaluate the following:
`int sec^3x.dx`
Evaluate the following : `int x^3.logx.dx`
Evaluate the following : `int (t.sin^-1 t)/sqrt(1 - t^2).dt`
Evaluate the following : `int cos sqrt(x).dx`
Integrate the following functions w.r.t. x : `sec^2x.sqrt(tan^2x + tan x - 7)`
Choose the correct options from the given alternatives :
`int tan(sin^-1 x)*dx` =
Choose the correct options from the given alternatives :
`int sin (log x)*dx` =
Choose the correct options from the given alternatives :
`int cos -(3)/(7)x*sin -(11)/(7)x*dx` =
Integrate the following with respect to the respective variable : `t^3/(t + 1)^2`
Integrate the following w.r.t. x: `(1 + log x)^2/x`
Integrate the following w.r.t.x : cot–1 (1 – x + x2)
Integrate the following w.r.t.x : e2x sin x cos x
Evaluate: `int ("ae"^("x") + "be"^(-"x"))/("ae"^("x") - "be"^(−"x"))` dx
Evaluate: `int "dx"/(5 - 16"x"^2)`
Evaluate:
∫ (log x)2 dx
Evaluate `int 1/(x log x) "d"x`
`int logx/(1 + logx)^2 "d"x`
`int cot "x".log [log (sin "x")] "dx"` = ____________.
The value of `int "e"^(5x) (1/x - 1/(5x^2)) "d"x` is ______.
`int "e"^x int [(2 - sin 2x)/(1 - cos 2x)]`dx = ______.
The value of `int_(- pi/2)^(pi/2) (x^3 + x cos x + tan^5x + 1) dx` 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)`
Solve: `int sqrt(4x^2 + 5)dx`
`int(logx)^2dx` equals ______.
If `int(x + (cos^-1 3x)^2)/sqrt(1 - 9x^2)dx = 1/α(sqrt(1 - 9x^2) + (cos^-1 3x)^β) + C`, where C is constant of integration , then (α + 3β) is equal to ______.
The integral `int x cos^-1 ((1 - x^2)/(1 + x^2))dx (x > 0)` is equal to ______.
`int e^x [(2 + sin 2x)/(1 + cos 2x)]dx` = ______.
Evaluate :
`int(4x - 6)/(x^2 - 3x + 5)^(3/2) dx`
`int1/sqrt(x^2 - a^2) dx` = ______
Evaluate `int(1 + x + (x^2)/(2!))dx`
Evaluate:
`intcos^-1(sqrt(x))dx`
Evaluate:
`int e^(ax)*cos(bx + c)dx`
Evaluate:
`int e^(logcosx)dx`
The value of `int (x sin^-1)/(sqrt(1 - x^2)) dx` is equal to:
