Advertisements
Advertisements
प्रश्न
`int sqrt(x^2 + 2x + 5)` dx = ______________
विकल्प
`(x + 1) sqrt(x^2 + 2x + 5) + log [(x + 1) + sqrt(x^2 + 2x + 5)] + "c"`
`(x + 2) sqrt(x^2 + 2x + 5) + log [(x + 2) + sqrt(x^2 + 2x + 5)] + "c"`
`(("x" + 2)/2) sqrt(x^2 + 2x + 5) + 1/2 log [(x + 2) + sqrt(x^2 + 2x + 5)] + "c"`
`(("x" + 1)/2) sqrt(x^2 + 2x + 5) + 2 log [(x + 1) + sqrt(x^2 + 2x + 5)] + "c"`
Advertisements
उत्तर
`(("x" + 1)/2) sqrt(x^2 + 2x + 5) + 2 log [(x + 1) + sqrt(x^2 + 2x + 5)] + "c"`
APPEARS IN
संबंधित प्रश्न
Prove that `int_a^bf(x)dx=f(a+b-x)dx.` Hence evaluate : `int_a^bf(x)/(f(x)+f(a-b-x))dx`
Evaluate :
`∫(x+2)/sqrt(x^2+5x+6)dx`
Integrate the functions:
sin x ⋅ sin (cos x)
Integrate the functions:
`1/(x-sqrtx)`
Integrate the functions:
`x/(sqrt(x+ 4))`, x > 0
Integrate the functions:
`x/(9 - 4x^2)`
Write a value of
Write a value of
Write a value of\[\int\frac{1}{1 + e^x} \text{ dx }\]
Write a value of\[\int a^x e^x \text{ dx }\]
Write a value of
Write a value of\[\int\frac{1}{x \left( \log x \right)^n} \text { dx }\].
Evaluate: \[\int\frac{x^3 - 1}{x^2} \text{ dx}\]
Evaluate the following integrals:
`int (cos2x)/sin^2x dx`
Evaluate the following integrals : `int sqrt(1 + sin 2x) dx`
Evaluate the following integrals:
`int (sin4x)/(cos2x).dx`
Integrate the following functions w.r.t. x : `(logx)^n/x`
Integrate the following functions w.r.t. x : `sqrt(tanx)/(sinx.cosx)`
Integrate the following functions w.r.t. x : `(1)/(x(x^3 - 1)`
Evaluate the following : `int (1)/sqrt(x^2 + 8x - 20).dx`
Evaluate the following : `int (1)/(4 + 3cos^2x).dx`
Evaluate the following:
`int sinx/(sin 3x) dx`
Integrate the following functions w.r.t. x : `int (1)/(2 + cosx - sinx).dx`
Choose the correct options from the given alternatives :
`int dx/(cosxsqrt(sin^2x - cos^2x))*dx` =
`int logx/(log ex)^2*dx` = ______.
Evaluate `int (-2)/(sqrt("5x" - 4) - sqrt("5x" - 2))`dx
Evaluate `int (1 + x + x^2/(2!))`dx
Evaluate the following.
`int 1/(4"x"^2 - 1)` dx
Evaluate: If f '(x) = `sqrt"x"` and f(1) = 2, then find the value of f(x).
Evaluate: ∫ |x| dx if x < 0
Evaluate: `int (2"e"^"x" - 3)/(4"e"^"x" + 1)` dx
Evaluate: `int "x" * "e"^"2x"` dx
`int (log x)/(log ex)^2` dx = _________
`int sqrt(1 + sin2x) dx`
`int cos^7 x "d"x`
`int ((x + 1)(x + log x))^4/(3x) "dx" =`______.
General solution of `(x + y)^2 ("d"y)/("d"x) = "a"^2, "a" ≠ 0` is ______. (c is arbitrary constant)
`int (f^'(x))/(f(x))dx` = ______ + c.
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 ______.
`int x/sqrt(1 - 2x^4) dx` = ______.
(where c is a constant of integration)
Find `int (x + 2)/sqrt(x^2 - 4x - 5) dx`.
If f′(x) = 4x3 − 3x2 + 2x + k, f(0) = -1 and f(1) = 4, find f(x)
Evaluate `int 1/("x"("x" - 1)) "dx"`
Evaluate `int1/(x(x - 1))dx`
Evaluate:
`int 1/(1 + cosα . cosx)dx`
Evaluate `int1/(x(x-1))dx`
If f'(x) = 4x3 - 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
