Advertisements
Advertisements
प्रश्न
`int sqrt(1 + "x"^2) "dx"` =
विकल्प
`"x"/2 sqrt(1 + "x"^2) + 1/2 log ("x" + sqrt(1 + "x"^2))`+ c
`2/3 (1 + "x"^2)^(3/2) + "c"`
`1/3 (1 + "x"^2)` + c
`("(x)")/sqrt(1 + "x"^2)` + c
Advertisements
उत्तर
`"x"/2 sqrt(1 + "x"^2) + 1/2 log ("x" + sqrt(1 + "x"^2))`+ c
Explanation:
∵ `int sqrt(a^2 + "x"^2) "dx"` = `x/2 sqrt(a^2 + x^2) + a^2/2 log | x + sqrt(a^2 + x^2)| + c`
∴ I = `x/2 sqrt(1 + x^2) + 1/2 log |x + sqrt(1 + x^2) + c`
APPEARS IN
संबंधित प्रश्न
Find `int((3sintheta-2)costheta)/(5-cos^2theta-4sin theta)d theta`.
Integrate the functions:
`(sin^(-1) x)/(sqrt(1-x^2))`
Integrate the functions:
`cos sqrt(x)/sqrtx`
Integrate the functions:
`1/(1 + cot x)`
Integrate the functions:
`(1+ log x)^2/x`
Integrate the functions:
`((x+1)(x + logx)^2)/x`
Write a value of\[\int\text{ tan x }\sec^3 x\ dx\]
Show that : `int _0^(pi/4) "log" (1+"tan""x")"dx" = pi /8 "log"2`
Evaluate the following integrals:
`int x/(x + 2).dx`
Integrate the following functions w.r.t. x : `(e^(2x) + 1)/(e^(2x) - 1)`
Integrate the following functions w.r.t. x : `(1)/(4x + 5x^-11)`
Integrate the following function w.r.t. x:
x9.sec2(x10)
Evaluate the following : `int (1)/(7 + 2x^2).dx`
Integrate the following functions w.r.t. x : `int (1)/(cosx - sinx).dx`
Evaluate the following integrals : `int (3x + 4)/sqrt(2x^2 + 2x + 1).dx`
Choose the correct options from the given alternatives :
`int f x^x (1 + log x)*dx`
Evaluate `int 1/(x (x - 1))` dx
Evaluate the following.
`int 1/(sqrt("x"^2 + 4"x"+ 29))` dx
`int 1/(xsin^2(logx)) "d"x`
If f(x) = 3x + 6, g(x) = 4x + k and fog (x) = gof (x) then k = ______.
`int "e"^(sin^-1 x) ((x + sqrt(1 - x^2))/(sqrt1 - x^2)) "dx" = ?`
General solution of `(x + y)^2 ("d"y)/("d"x) = "a"^2, "a" ≠ 0` is ______. (c is arbitrary constant)
`int ("e"^x(x + 1))/(sin^2(x"e"^x)) "d"x` = ______.
Evaluate `int (1+x+x^2/(2!))dx`
Evaluate the following.
`int "x"^3/sqrt(1 + "x"^4)` dx
Evaluate the following.
`int 1/ (x^2 + 4x - 5) dx`
Evaluate `int(5x^2-6x+3)/(2x-3)dx`
Evaluate the following.
`intx^3/sqrt(1 + x^4)dx`
Evaluate `int (5x^2 - 6x + 3)/(2x - 3) dx`
`int (x + 1)/(x(1 + xe^x)) dx` is equal to
