Advertisements
Advertisements
प्रश्न
Evaluate the following.
`int 1/(sqrt"x" + "x")` dx
Advertisements
उत्तर
Let I = `int 1/(sqrt"x" + "x")` dx
= `int 1/(sqrt"x" (1 + sqrt"x"))`dx
Put `1 + sqrt"x" = "t"`
∴ `1/(2sqrt"x") "dx" = "dt"`
∴ `1/sqrt"x"`dx = 2 dt
∴ I = `int (2 * "dt")/"t"`
`= 2 int 1/"t" * "dt"`
= 2 log | t | + c
∴ I = 2 log `|1 + sqrt"x"|` + c
APPEARS IN
संबंधित प्रश्न
Find: `int(x+3)sqrt(3-4x-x^2dx)`
Integrate the functions:
`1/(x(log x)^m), x > 0, m ne 1`
Integrate the functions:
`((x+1)(x + logx)^2)/x`
Integrate the functions:
`(x^3 sin(tan^(-1) x^4))/(1 + x^8)`
Integrate the following w.r.t. x:
`2x^3 - 5x + 3/x + 4/x^5`
Evaluate the following integrals : `int tanx/(sec x + tan x)dx`
Evaluate the following integrals : `int(5x + 2)/(3x - 4).dx`
Integrate the following function w.r.t. x:
x9.sec2(x10)
Evaluate the following : `int (1)/(4 + 3cos^2x).dx`
Integrate the following functions w.r.t. x : `int (1)/(3 + 2sinx).dx`
Evaluate `int 1/(x (x - 1))` dx
Evaluate the following.
`int (2"e"^"x" + 5)/(2"e"^"x" + 1)`dx
Evaluate the following.
`int 1/(sqrt("x"^2 -8"x" - 20))` dx
Evaluate:
`int (5x^2 - 6x + 3)/(2x − 3)` dx
Evaluate: ∫ |x| dx if x < 0
`int (2 + cot x - "cosec"^2x) "e"^x "d"x`
`int (7x + 9)^13 "d"x` ______ + c
`int "dx"/((sin x + cos x)(2 cos x + sin x))` = ?
`int dx/(1 + e^-x)` = ______
If I = `int (sin2x)/(3x + 4cosx)^3 "d"x`, then I is equal to ______.
General solution of `(x + y)^2 ("d"y)/("d"x) = "a"^2, "a" ≠ 0` is ______. (c is arbitrary constant)
`int ("d"x)/(sinx cosx + 2cos^2x)` = ______.
If `int sinx/(sin^3x + cos^3x)dx = α log_e |1 + tan x| + β log_e |1 - tan x + tan^2x| + γ tan^-1 ((2tanx - 1)/sqrt(3)) + C`, when C is constant of integration, then the value of 18(α + β + γ2) is ______.
The value of `int (sinx + cosx)/sqrt(1 - sin2x) dx` is equal to ______.
Evaluate `int(1 + x + x^2/(2!) )dx`
`int "cosec"^4x dx` = ______.
Evaluate the following.
`int1/(x^2 + 4x-5)dx`
If f'(x) = 4x3 - 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
