Advertisements
Advertisements
Question
`int 1/sqrt(x^2 - 9) dx` = ______.
Options
`1/3 log |x + sqrt(x^2 - 9)| + c`
`log |x + sqrt(x^2 - 9)| + c`
`3log |x + sqrt(x^2 - 9)| + c`
`log |x - sqrt(x^2 - 9)| + c`
Advertisements
Solution
`int 1/sqrt(x^2 - 9) dx` = `bb(log |x + sqrt(x^2 - 9)| + c)`.
Explanation:
`int 1/sqrt(x^2 - 9) dx = int 1/sqrt(x^2 - 3^2) dx`
= `log |x + sqrt(x^2 - 3^2)| + c`
= `log |x + sqrt(x^2 - 9)| + c`
APPEARS IN
RELATED QUESTIONS
Prove that: `int sqrt(a^2 - x^2) * dx = x/2 * sqrt(a^2 - x^2) + a^2/2 * sin^-1(x/a) + c`
Integrate the function in `x^2e^x`.
Integrate the function in x (log x)2.
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 e2x sin x.
Evaluate the following:
`int sec^3x.dx`
Integrate the following functions w.r.t. x : `(x + 1) sqrt(2x^2 + 3)`
Integrate the following with respect to the respective variable : `(3 - 2sinx)/(cos^2x)`
Integrate the following w.r.t.x : `log (1 + cosx) - xtan(x/2)`
Integrate the following w.r.t.x : e2x sin x cos x
Evaluate the following.
`int "x"^2 *"e"^"3x"`dx
Evaluate the following.
`int "e"^"x" "x - 1"/("x + 1")^3` dx
Evaluate the following.
`int "e"^"x" [(log "x")^2 + (2 log "x")/"x"]` dx
Choose the correct alternative from the following.
`int (("e"^"2x" + "e"^"-2x")/"e"^"x") "dx"` =
State whether the following statement is True or False:
If `int((x - 1)"d"x)/((x + 1)(x - 2))` = A log|x + 1| + B log|x – 2|, then A + B = 1
`int [(log x - 1)/(1 + (log x)^2)]^2`dx = ?
The value of `int "e"^(5x) (1/x - 1/(5x^2)) "d"x` is ______.
Evaluate the following:
`int_0^pi x log sin x "d"x`
`int "dx"/(sin(x - "a")sin(x - "b"))` is equal to ______.
Find `int (sin^-1x)/(1 - x^2)^(3//2) dx`.
Find: `int e^(x^2) (x^5 + 2x^3)dx`.
Evaluate :
`int(4x - 6)/(x^2 - 3x + 5)^(3/2) dx`
Evaluate the following.
`int x^3 e^(x^2) dx`
Evaluate:
`int(1+logx)/(x(3+logx)(2+3logx)) dx`
Evaluate:
`inte^x sinx 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`
