Advertisements
Advertisements
प्रश्न
Choose the correct option from the given alternatives :
`int (1 + x + sqrt(x + x^2))/(sqrt(x) + sqrt(1 + x))*dx` =
पर्याय
`(1)/(2)sqrt(x + 1) + c`
`(2)/(3)(x + 1)^(3/2) + c`
`sqrt(x + 1) + c`
`2(x - 1)^(3/2) + c`
Advertisements
उत्तर
`(2)/(3)(x + 1)^(3/2) + c`
Explanation:
`I = int (1 + x + sqrt(x + x^2))/(sqrt(x) + sqrt(1 + x))*dx`
I = `int sqrt((1+x)^2+ sqrtx *sqrt(1+ x) )/ (sqrt(x) + sqrt(1+x))*dx`
I = `int( sqrt(1 + x) sqrt(1 + x) + sqrtx )/ (sqrt(x)+sqrt(1 + x))*dx`
I `= int(sqrt(1+x)) dx = 2/3 (x + 1)^(3/2) + c`
I = `(2)/(3)(x + 1)^(3/2) + c`
APPEARS IN
संबंधित प्रश्न
Integrate the functions:
sin (ax + b) cos (ax + b)
Integrate the functions:
`1/(x(log x)^m), x > 0, m ne 1`
Integrate the functions:
`1/(1 - tan x)`
Integrate the functions:
`(x^3 sin(tan^(-1) x^4))/(1 + x^8)`
`(10x^9 + 10^x log_e 10)/(x^10 + 10^x) dx` equals:
`int (dx)/(sin^2 x cos^2 x)` equals:
Write a value of
Evaluate: \[\int\frac{x^3 - 1}{x^2} \text{ dx}\]
`int "dx"/(9"x"^2 + 1)= ______. `
Evaluate the following integrals : `int (sin2x)/(cosx)dx`
Evaluate the following integrals : `int sqrt(1 + sin 2x) dx`
Evaluate the following integrals : `int (3)/(sqrt(7x - 2) - sqrt(7x - 5)).dx`
Integrate the following functions w.r.t. x : e3logx(x4 + 1)–1
Integrate the following functions w.r.t. x : `sin(x - a)/cos(x + b)`
Integrate the following functions w.r.t. x : sin5x.cos8x
Evaluate the following:
`int sinx/(sin 3x) dx`
Integrate the following functions w.r.t. x : `int (1)/(4 - 5cosx).dx`
Integrate the following functions w.r.t. x : `int (1)/(3 + 2sin x - cosx)dx`
Integrate the following functions w.r.t. x : `int (1)/(cosx - sqrt(3)sinx).dx`
Evaluate the following integrals:
`int (7x + 3)/sqrt(3 + 2x - x^2).dx`
Evaluate the following integrals : `int sqrt((e^(3x) - e^(2x))/(e^x + 1)).dx`
Evaluate `int (3"x"^3 - 2sqrt"x")/"x"` dx
Evaluate the following.
`int "x" sqrt(1 + "x"^2)` dx
Evaluate the following.
∫ (x + 1)(x + 2)7 (x + 3)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 log ("x"^2 + "x")` dx
`int (log x)/(log ex)^2` dx = _________
`int sqrt(x) sec(x)^(3/2) tan(x)^(3/2)"d"x`
`int (cos2x)/(sin^2x) "d"x`
General solution of `(x + y)^2 ("d"y)/("d"x) = "a"^2, "a" ≠ 0` is ______. (c is arbitrary constant)
`int ("d"x)/(x(x^4 + 1))` = ______.
If `int(cosx - sinx)/sqrt(8 - sin2x)dx = asin^-1((sinx + cosx)/b) + c`. where c is a constant of integration, then the ordered pair (a, b) is equal to ______.
Write `int cotx dx`.
Evaluate `int_(logsqrt(2))^(logsqrt(3)) 1/((e^x + e^-x)(e^x - e^-x)) dx`.
Evaluate `int(1 + x + x^2/(2!))dx`
Evaluate `int (1)/(x(x - 1))dx`
Evaluate the following
`int x^3/sqrt(1+x^4) dx`
Evaluate:
`int(sqrt(tanx) + sqrt(cotx))dx`
`int x^2/sqrt(1 - x^6)dx` = ______.
Evaluate `int(1+x+x^2/(2!))dx`
Evaluate the following.
`int "x"^3/sqrt(1 + "x"^4)` dx
Evaluate `int(1 + x + x^2 / (2!))dx`
Which standard substitution is used for \[\sqrt{\mathrm{a}^2-x^2}\], \[\frac{1}{\sqrt{\mathrm{a}^2-x^2}}\], or \[\mathrm{a}^2-x^2\]?
Which substitution is appropriate for \[\sqrt{\frac{x}{a-x}}\], \[\sqrt{\frac{a-x}{x}}\], \[\sqrt{x(a-x)}\], or \[\frac{1}{\sqrt{x(a-x)}}\]?
For \[\sqrt{\frac{x-\alpha}{\beta-x}}\] or \[\sqrt{(x-\alpha)(\beta-x)}\], where \[\beta>\alpha\], which substitution is used?
