Advertisements
Advertisements
प्रश्न
`int 1/sqrt(x^2 - a^2)dx` = ______.
Advertisements
उत्तर
`int 1/sqrt(x^2 - a^2)dx` = `bb(underline(log|x + sqrt(x^2 - a^2)| + c)`.
APPEARS IN
संबंधित प्रश्न
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 (x2 + 1) log x.
Evaluate the following: `int x.sin^-1 x.dx`
Integrate the following functions w.r.t. x : `(x + 1) sqrt(2x^2 + 3)`
Integrate the following functions w.r.t. x : `e^x/x [x (logx)^2 + 2 (logx)]`
Choose the correct options from the given alternatives :
`int (log (3x))/(xlog (9x))*dx` =
Choose the correct options from the given alternatives :
`int [sin (log x) + cos (log x)]*dx` =
Integrate the following w.r.t.x : `log (1 + cosx) - xtan(x/2)`
Evaluate: `int ("ae"^("x") + "be"^(-"x"))/("ae"^("x") - "be"^(−"x"))` dx
Evaluate: `int "dx"/(3 - 2"x" - "x"^2)`
Evaluate: `int "dx"/(25"x" - "x"(log "x")^2)`
Evaluate: `int "e"^"x"/(4"e"^"2x" -1)` dx
`int"e"^(4x - 3) "d"x` = ______ + c
Evaluate `int (2x + 1)/((x + 1)(x - 2)) "d"x`
`int cot "x".log [log (sin "x")] "dx"` = ____________.
Evaluate the following:
`int_0^1 x log(1 + 2x) "d"x`
The value of `int_0^(pi/2) log ((4 + 3 sin x)/(4 + 3 cos x)) dx` is
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 1/sqrt(x^2 - 9) dx` = ______.
If `int (f(x))/(log(sin x))dx` = log[log sin x] + c, then f(x) is equal to ______.
Evaluate the following.
`int x^3 e^(x^2) dx`
`int(xe^x)/((1+x)^2) dx` = ______
Evaluate:
`int((1 + sinx)/(1 + cosx))e^x dx`
Evaluate:
`inte^x sinx dx`
Evaluate:
`int e^(logcosx)dx`
Evaluate:
`int1/(x^2 + 25)dx`
Evaluate the following:
`intx^3e^(x^2)dx`
Evaluate the following.
`intx^3 e^(x^2)dx`
Evaluate `int(1 + x + x^2/(2!))dx`.
