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
Integrate the functions:
`cos x /(sqrt(1+sinx))`
Write a value of\[\int a^x e^x \text{ dx }\]
Write a value of\[\int\left( e^{x \log_e \text{ a}} + e^{a \log_e x} \right) dx\] .
`int "dx"/(9"x"^2 + 1)= ______. `
Find : ` int (sin 2x ) /((sin^2 x + 1) ( sin^2 x + 3 ) ) dx`
Evaluate the following integrals : `int (cos2x)/(sin^2x.cos^2x)dx`
Integrate the following functions w.r.t. x : `e^x.log (sin e^x)/tan(e^x)`
Integrate the following functions w.r.t. x : sin5x.cos8x
Evaluate the following : `int (1)/(7 + 2x^2).dx`
Evaluate the following : `int (1)/(cos2x + 3sin^2x).dx`
Integrate the following functions w.r.t. x : `int (1)/(4 - 5cosx).dx`
Evaluate `int 1/("x" ("x" - 1))` dx
Evaluate the following.
`int (1 + "x")/("x" + "e"^"-x")` dx
Evaluate the following.
`int 1/(x(x^6 + 1))` dx
Evaluate the following.
`int 1/("x"^2 + 4"x" - 5)` dx
Choose the correct alternative from the following.
`int "dx"/(("x" - "x"^2))`=
If f '(x) = `1/"x" + "x"` and f(1) = `5/2`, then f(x) = log x + `"x"^2/2` + ______
Evaluate: `int 1/(2"x" + 3"x" log"x")` dx
Evaluate: `int log ("x"^2 + "x")` dx
`int 1/(cos x - sin x)` dx = _______________
`int sqrt(1 + sin2x) dx`
`int 1/(xsin^2(logx)) "d"x`
General solution of `(x + y)^2 ("d"y)/("d"x) = "a"^2, "a" ≠ 0` is ______. (c is arbitrary constant)
The integral `int ((1 - 1/sqrt(3))(cosx - sinx))/((1 + 2/sqrt(3) sin2x))dx` is equal to ______.
Write `int cotx dx`.
Evaluated the following
`int x^3/ sqrt (1 + x^4 )dx`
Evaluate `int1/(x(x-1))dx`
Evaluate `int 1/(x(x-1))dx`
Evaluate `int(1 + x + x^2 / (2!))dx`
