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
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
Evaluate : `int(x-3)sqrt(x^2+3x-18) dx`
Write a value of\[\int \cos^4 x \text{ sin x dx }\]
Prove that: `int "dx"/(sqrt("x"^2 +"a"^2)) = log |"x" +sqrt("x"^2 +"a"^2) | + "c"`
Integrate the following w.r.t. x:
`3 sec^2x - 4/x + 1/(xsqrt(x)) - 7`
Evaluate the following integrals : `int sin 4x cos 3x dx`
Integrate the following functions w.r.t. x : `((x - 1)^2)/(x^2 + 1)^2`
Integrate the following functions w.r.t.x:
`(5 - 3x)(2 - 3x)^(-1/2)`
Evaluate the following integrals : `int (3x + 4)/(x^2 + 6x + 5).dx`
Evaluate the following integrals : `int (3cosx)/(4sin^2x + 4sinx - 1).dx`
Evaluate the following.
`int "x"^3/(16"x"^8 - 25)` dx
`int 2/(sqrtx - sqrt(x + 3))` dx = ________________
General solution of `(x + y)^2 ("d"y)/("d"x) = "a"^2, "a" ≠ 0` is ______. (c is arbitrary constant)
`int secx/(secx - tanx)dx` equals ______.
Evaluate the following.
`int(20 - 12"e"^"x")/(3"e"^"x" - 4) "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.
`int(1)/(x^2 + 4x - 5)dx`
Evaluate `int (1 + "x" + "x"^2/(2!))`dx
Evaluate `int(5x^2-6x+3)/(2x-3) dx`
