Advertisements
Advertisements
Question
Evaluate: `int "dx"/sqrt(4"x"^2 - 5)`
Advertisements
Solution
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
RELATED QUESTIONS
`int1/xlogxdx=...............`
(A)log(log x)+ c
(B) 1/2 (logx )2+c
(C) 2log x + c
(D) log x + c
Integrate the function in x log x.
Integrate the function in `e^x (1 + sin x)/(1+cos x)`.
Find :
`∫(log x)^2 dx`
Evaluate the following : `int x^2tan^-1x.dx`
Integrate the following functions w.r.t. x : `sec^2x.sqrt(tan^2x + tan x - 7)`
Integrate the following functions w.r.t. x : `[x/(x + 1)^2].e^x`
Integrate the following functions w.r.t. x : `e^x/x [x (logx)^2 + 2 (logx)]`
Integrate the following with respect to the respective variable : `t^3/(t + 1)^2`
Integrate the following w.r.t.x : cot–1 (1 – x + x2)
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)
Integrate the following w.r.t.x : sec4x cosec2x
Evaluate: `int "dx"/("9x"^2 - 25)`
Evaluate: `int e^x/sqrt(e^(2x) + 4e^x + 13)` dx
Evaluate: `int "dx"/(25"x" - "x"(log "x")^2)`
`int (sin(x - "a"))/(cos (x + "b")) "d"x`
`int ("d"x)/(x - x^2)` = ______
Evaluate `int 1/(x(x - 1)) "d"x`
Evaluate `int 1/(4x^2 - 1) "d"x`
`int [(log x - 1)/(1 + (log x)^2)]^2`dx = ?
`int "dx"/(sin(x - "a")sin(x - "b"))` is equal to ______.
`int x/((x + 2)(x + 3)) dx` = ______ + `int 3/(x + 3) dx`
Evaluate: `int_0^(pi/4) (dx)/(1 + tanx)`
`int_0^1 x tan^-1 x dx` = ______.
Evaluate:
`int (logx)^2 dx`
`int (sin^-1 sqrt(x) + cos^-1 sqrt(x))dx` = ______.
If u and v are two differentiable functions of x, then prove that `intu*v*dx = u*intv dx - int(d/dx u)(intv dx)dx`. Hence evaluate: `intx cos x dx`
Evaluate the following.
`intx^3/sqrt(1+x^4)`dx
