Advertisements
Advertisements
Question
Integrate the function:
`1/(sqrt(x+a) + sqrt(x+b))`
Solution
Let I = `int 1/(sqrt(x + a) + sqrt(x + b))`
On multiplying the numerator and denominator by `sqrt(x + a) + sqrt(x + b)`
`= int 1/(sqrt(x + a) + sqrt(x + b)) xx (sqrt(x + a) - sqrt(x + b))/(sqrt(x + a) - sqrt(x + b))`
`= int (sqrt(x + a) - sqrt(x + b))/(sqrt(x + a) - sqrt(x + b))`
`= int (sqrt(x + a) - sqrt(x + b))/(a - b)` dx
`= 1/(a - b) int (x + a)^(1/2) dx - 1/(a - b) int (x + b)^(1/2)` dx
`= 1/(a - b) [2/3 (x + a)^(3/2) - 2/3 (x + b)^(3/2)] + C`
`= 2/(3(a - b))[(x + a)^(3/2) - (x + b)^(3/2)] + C`
APPEARS IN
RELATED QUESTIONS
Evaluate : `∫(sin^6x+cos^6x)/(sin^2x.cos^2x)dx`
Find :`int(x^2+x+1)/((x^2+1)(x+2))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.
Cos 3x
Find an anti derivative (or integral) of the following function by the method of inspection.
e2x
Find the following integrals:
`int (4e^(3x) + 1)`
Find the following integrals:
`intx^2 (1 - 1/x^2)dx`
Find the following integrals:
`int(sqrtx - 1/sqrtx)^2 dx`
Find the following integrals:
`int (x^3 + 5x^2 -4)/x^2 dx`
Find the following integrals:
`int (x^3 - x^2 + x - 1)/(x - 1) dx`
The anti derivative of `(sqrtx + 1/ sqrtx)` equals:
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:
`(5x)/((x+1)(x^2 +9))`
Integrate the function:
`sinx/(sin (x - a))`
Integrate the function:
`1/(cos (x+a) cos(x+b))`
Integrate the function:
`x^3/(sqrt(1-x^8)`
Integrate the function:
`e^(3log x) (x^4 + 1)^(-1)`
Integrate the function:
`(2+ sin 2x)/(1+ cos 2x) e^x`
Integrate the function:
`(sqrt(x^2 +1) [log(x^2 + 1) - 2log x])/x^4`
Evaluate `int(x^3+5x^2 + 4x + 1)/x^2 dx`
Find : \[\int\frac{\left( x^2 + 1 \right)\left( x^2 + 4 \right)}{\left( x^2 + 3 \right)\left( x^2 - 5 \right)}dx\] .
Evaluate: `int (1 - cos x)/(cos x(1 + cos x)) 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 (sin^2x - cos^2x)/(sin^2x cos^2x) dx` is equal to
`int (dx)/(x(x^2 + 1))` equals
`f x^2 e^(x^3) dx` equals
`int sqrt(x^2 - 8x + 7) dx` is equal to:-
`d/(dx)x^(logx)` = ______.
If y = `x^((sinx)^(x^((sinx)^(x^(...∞)`, then `(dy)/(dx)` at x = `π/2` is equal to ______.
Anti-derivative of `(tanx - 1)/(tanx + 1)` with respect to x is ______.
