Advertisements
Advertisements
प्रश्न
Evaluate `int 1/(x(x - 1)) "d"x`
Advertisements
उत्तर
Let I = `int 1/(x(x - 1)) "d"x`
= `int(x - x + 1)/(x(x - 1)) "d"x`
= `int(x - (x - 1))/(x(x - 1)) "d"x`
= `int(1/(x - 1) - 1/x) "d"x`
= `int 1/(x - 1) "d"x - int 1/x "d"x`
= `log |x - 1| - log |x| + "c"`
∴ I = `log |(x - 1)/x| + "c"`
APPEARS IN
संबंधित प्रश्न
Integrate the function in x sin x.
Integrate the function in x2 log x.
Integrate the function in x tan-1 x.
Integrate the function in (sin-1x)2.
Integrate the following functions w.r.t. x : `e^(2x).sin3x`
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)`
Choose the correct options from the given alternatives :
`int (1)/(cosx - cos^2x)*dx` =
Integrate the following with respect to the respective variable : cos 3x cos 2x cos x
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.
∫ x log x dx
Evaluate: `int "dx"/sqrt(4"x"^2 - 5)`
`int "e"^x x/(x + 1)^2 "d"x`
`int 1/sqrt(x^2 - 8x - 20) "d"x`
`int "e"^x [x (log x)^2 + 2 log x] "dx"` = ______.
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`
`int x/((x + 2)(x + 3)) dx` = ______ + `int 3/(x + 3) dx`
Find `int (sin^-1x)/(1 - x^2)^(3//2) dx`.
Evaluate :
`int(4x - 6)/(x^2 - 3x + 5)^(3/2) dx`
`inte^(xloga).e^x dx` is ______
`int(xe^x)/((1+x)^2) dx` = ______
Evaluate:
`inte^x sinx dx`
Evaluate the following.
`intx^3/sqrt(1+x^4)`dx
Which expression is the integration-by-parts form for a product \(f(x)g(x)\)?
Which function is an example under priority \(I\) in the LIATE rule?
When applying integration by parts to \(\log x\) and inverse trig, what should they be multiplied by?
Repeated parts may be needed for which pair of integrals?
