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
`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 sin−1 x.
Integrate the function in `e^x (1/x - 1/x^2)`.
Evaluate the following: `int x.sin^-1 x.dx`
Evaluate the following : `int x^2*cos^-1 x*dx`
Evaluate the following: `int logx/x.dx`
Integrate the following functions w.r.t. x : `x^2 .sqrt(a^2 - x^6)`
Integrate the following functions w.r.t. x : `sqrt((x - 3)(7 - x)`
Integrate the following functions w.r.t. x : `[x/(x + 1)^2].e^x`
Integrate the following functions w.r.t. x : `log(1 + x)^((1 + x)`
Integrate the following functions w.r.t. x : cosec (log x)[1 – cot (log x)]
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)
Evaluate the following.
∫ x log x dx
Evaluate the following.
`int e^x (1/x - 1/x^2)`dx
Choose the correct alternative from the following.
`int (("e"^"2x" + "e"^"-2x")/"e"^"x") "dx"` =
Evaluate: `int "dx"/(3 - 2"x" - "x"^2)`
Evaluate: `int "e"^"x"/(4"e"^"2x" -1)` dx
`int [(log x - 1)/(1 + (log x)^2)]^2`dx = ?
`int_0^"a" sqrt("x"/("a" - "x")) "dx"` = ____________.
`int 1/sqrt(x^2 - 9) dx` = ______.
Find: `int (2x)/((x^2 + 1)(x^2 + 2)) dx`
The integral `int x cos^-1 ((1 - x^2)/(1 + x^2))dx (x > 0)` is equal to ______.
If `int (f(x))/(log(sin x))dx` = log[log sin x] + c, then f(x) is equal to ______.
Find: `int e^(x^2) (x^5 + 2x^3)dx`.
`intsqrt(1+x) dx` = ______
Evaluate `int(1 + x + (x^2)/(2!))dx`
Evaluate:
`int e^(logcosx)dx`
Evaluate the following.
`intx^3/sqrt(1+x^4)`dx
Evaluate:
`inte^x "cosec" x(1 - cot x)dx`
