Advertisements
Advertisements
प्रश्न
The anti derivative of `(sqrtx + 1/ sqrtx)` equals:
पर्याय
`1/3 x^(1/3) + 2x^(1/2) + C`
`2/3 x^(2/3) + 1/2 x^2 + C`
`2/3 x^(3/2) + 2x^(1/2) + C`
`3/2 x^(3/2) + 1/2 x^(1/2) + C`
Advertisements
उत्तर
`2/3 x^(3/2) + 2x^(1/2) + C`
Explanation:
`(sqrtx + 1/sqrtx) = int (sqrtx + 1/sqrtx)`
`= int sqrtx dx + int 1/sqrtx`dx
`= int x^(1//2) dx + int x^(-1//2)`dx
`= (x^(1/2 + 1))/(1/2 + 1) + (x^(-1/2 + 1))/(- 1/2 + 1)` + C
`= (x^(3//2))/(3//2) + x^(1//2)/(1//2)` + C
`= 2/3 x^(3//2) + 2x^(1//2)` + C
APPEARS IN
संबंधित प्रश्न
Evaluate : `∫(sin^6x+cos^6x)/(sin^2x.cos^2x)dx`
If `f(x) =∫_0^xt sin t dt` , then write the value of f ' (x).
Find an anti derivative (or integral) of the following function by the method of inspection.
sin 2x
Find an anti derivative (or integral) of the following function by the method of inspection.
Cos 3x
Find an antiderivative (or integral) of the following function by the method of inspection.
sin 2x – 4 e3x
Find the following integrals:
`int (4e^(3x) + 1)`
Find the following integrals:
`intx^2 (1 - 1/x^2)dx`
Find the following integrals:
`int(1 - x) sqrtx dx`
Find the following integrals:
`intsec x (sec x + tan x) dx`
If `d/dx f(x) = 4x^3 - 3/x^4` such that f(2) = 0, then f(x) is ______.
Integrate the function:
`1/(x - x^3)`
Integrate the function:
`1/(x^2(x^4 + 1)^(3/4))`
Integrate the function:
`(5x)/((x+1)(x^2 +9))`
Integrate the function:
`(sin^8 x - cos^8 x)/(1-2sin^2 x cos^2 x)`
Integrate the function:
`1/(cos (x+a) cos(x+b))`
Integrate the function:
`cos^3 xe^(log sinx)`
Integrate the function:
`e^(3log x) (x^4 + 1)^(-1)`
Integrate the function:
f' (ax + b) [f (ax + b)]n
Integrate the function:
`1/sqrt(sin^3 x sin(x + alpha))`
Integrate the function:
`(x^2 + x + 1)/((x + 1)^2 (x + 2))`
Integrate the function:
`tan^(-1) sqrt((1-x)/(1+x))`
Evaluate `int(x^3+5x^2 + 4x + 1)/x^2 dx`
Evaluate `int tan^(-1) sqrtx dx`
Find : \[\int\frac{\left( x^2 + 1 \right)\left( x^2 + 4 \right)}{\left( x^2 + 3 \right)\left( x^2 - 5 \right)}dx\] .
The anti derivative of `(sqrt(x) + 1/sqrt(x))` is equals:
If `d/(dx) f(x) = 4x^3 - 3/x^4`, such that `f(2) = 0`, then `f(x)` is
`sqrt((10x^9 + 10^x log e^10)/(x^10 + 10^x)) dx` equals
`int (dx)/sqrt(9x - 4x^2)` equal
`int (dx)/sqrt(9x - 4x^2)` equals
`int (dx)/(x(x^2 + 1))` equals
`int x^2 e^(x^3) dx` equals
`int sqrt(1 + x^2) dx` is equal to
What is anti derivative of `e^(2x)`
If y = `x^((sinx)^(x^((sinx)^(x^(...∞)`, then `(dy)/(dx)` at x = `π/2` is equal to ______.
