Advertisements
Advertisements
प्रश्न
Evaluate: `int "dx"/sqrt(4"x"^2 - 5)`
Advertisements
उत्तर
Let I = `int "dx"/sqrt(4"x"^2 - 5)`
`= int 1/(sqrt (4("x"^2 - 5/4)))`dx
`= 1/2 int 1/(sqrt("x"^2 - ((sqrt5)/2)^2))` dx
`= 1/2 log |"x" + sqrt("x"^2 - (sqrt5/2)^2)|` + c
∴ I = `1/2 log |"x" + sqrt("x"^2 - 5/4)|` + c
APPEARS IN
संबंधित प्रश्न
Integrate the function in x2 log x.
Integrate the function in x sec2 x.
Integrate the function in x (log x)2.
Integrate the function in `e^x (1/x - 1/x^2)`.
Integrate the function in e2x sin x.
Evaluate the following:
`int x^2 sin 3x dx`
Evaluate the following : `int x.sin^2x.dx`
Integrate the following functions w.r.t. x : `sqrt((x - 3)(7 - x)`
Integrate the following functions w.r.t. x : `sqrt(2x^2 + 3x + 4)`
Choose the correct options from the given alternatives :
`int tan(sin^-1 x)*dx` =
Integrate the following w.r.t.x : `(1)/(x^3 sqrt(x^2 - 1)`
Evaluate the following.
`int "e"^"x" "x"/("x + 1")^2` dx
`int ("x" + 1/"x")^3 "dx"` = ______
Evaluate: `int e^x/sqrt(e^(2x) + 4e^x + 13)` dx
Evaluate: `int "dx"/("x"[(log "x")^2 + 4 log "x" - 1])`
`int (cos2x)/(sin^2x cos^2x) "d"x`
`int(x + 1/x)^3 dx` = ______.
Evaluate `int 1/(x(x - 1)) "d"x`
Evaluate `int (2x + 1)/((x + 1)(x - 2)) "d"x`
`int cot "x".log [log (sin "x")] "dx"` = ____________.
Find `int_0^1 x(tan^-1x) "d"x`
Evaluate the following:
`int (sin^-1 x)/((1 - x)^(3/2)) "d"x`
Evaluate the following:
`int_0^1 x log(1 + 2x) "d"x`
Find `int (sin^-1x)/(1 - x^2)^(3//2) dx`.
Evaluate:
`int(1+logx)/(x(3+logx)(2+3logx)) dx`
The integrating factor of `ylogy.dx/dy+x-logy=0` is ______.
`int logx dx = x(1+logx)+c`
Evaluate the following.
`int (x^3)/(sqrt(1 + x^4))dx`
