Advertisements
Advertisements
प्रश्न
Integrate the functions:
`(sin^(-1) x)/(sqrt(1-x^2))`
Advertisements
उत्तर
Let `I = int (sin^-1 x)/sqrt(1 - x^2)` dx
Put sin-1 x = t
`1/sqrt(1 - x^2)` dx = dt
Hence, `I = int t dt`
`=1/2t^2 + C`
`=1/2 (sin^-1 x)^2 + C`
APPEARS IN
संबंधित प्रश्न
Find: `int(x+3)sqrt(3-4x-x^2dx)`
Integrate the functions:
`xsqrt(1+ 2x^2)`
Integrate the functions:
`(2cosx - 3sinx)/(6cos x + 4 sin x)`
Integrate the functions:
`1/(cos^2 x(1-tan x)^2`
Write a value of
Show that : `int _0^(pi/4) "log" (1+"tan""x")"dx" = pi /8 "log"2`
Integrate the following functions w.r.t. x : `(logx)^n/x`
Integrate the following functions w.r.t. x : `sqrt(tanx)/(sinx.cosx)`
Integrate the following functions w.r.t. x : `((x - 1)^2)/(x^2 + 1)^2`
Integrate the following functions w.r.t. x : `sin(x - a)/cos(x + b)`
Integrate the following functions w.r.t. x : tan 3x tan 2x tan x
Integrate the following functions w.r.t. x : sin5x.cos8x
Evaluate the following : `int (1)/(7 + 2x^2).dx`
Evaluate the following : `int sqrt((9 + x)/(9 - x)).dx`
Evaluate the following : `int (1)/(5 - 4x - 3x^2).dx`
Evaluate the following : `int (1)/sqrt(x^2 + 8x - 20).dx`
Evaluate the following integrals : `int (3x + 4)/sqrt(2x^2 + 2x + 1).dx`
`int logx/(log ex)^2*dx` = ______.
Choose the correct options from the given alternatives :
`int (e^(2x) + e^-2x)/e^x*dx` =
Evaluate the following.
`int "x"^3/sqrt(1 + "x"^4)` dx
Evaluate the following.
`int 1/("x" log "x")`dx
Evaluate the following.
`int (2"e"^"x" + 5)/(2"e"^"x" + 1)`dx
Evaluate the following.
`int 1/("x"^2 + 4"x" - 5)` dx
Evaluate the following.
`int 1/("a"^2 - "b"^2 "x"^2)` dx
Evaluate `int 1/((2"x" + 3))` dx
Evaluate: `int "e"^sqrt"x"` dx
`int 1/(cos x - sin x)` dx = _______________
`int 2/(sqrtx - sqrt(x + 3))` dx = ________________
`int sqrt(("e"^(3x) - "e"^(2x))/("e"^x + 1)) "d"x`
`int (sin (5x)/2)/(sin x/2)dx` is equal to ______. (where C is a constant of integration).
The integral `int ((1 - 1/sqrt(3))(cosx - sinx))/((1 + 2/sqrt(3) sin2x))dx` is equal to ______.
`int (logx)^2/x dx` = ______.
Evaluate the following.
`int x sqrt(1 + x^2) dx`
`int (cos4x)/(sin2x + cos2x)dx` = ______.
Evaluate `int (1 + "x" + "x"^2/(2!))`dx
If f'(x) = 4x3 - 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
Evaluate `int1/(x(x - 1))dx`
Evaluate the following.
`int1/(x^2 + 4x - 5)dx`
