Advertisements
Advertisements
प्रश्न
Integrate the function:
`1/(sqrt(x+a) + sqrt(x+b))`
Advertisements
उत्तर
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
संबंधित प्रश्न
Write the antiderivative of `(3sqrtx+1/sqrtx).`
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.
(axe + b)2
Find the following integrals:
`int(1 - x) sqrtx dx`
Find the following integrals:
`intsqrtx( 3x^2 + 2x + 3) dx`
Find the following integrals:
`int(2x - 3cos x + e^x) dx`
Find the following integrals:
`int(2x^2 - 3sinx + 5sqrtx) dx`
Integrate the function:
`1/(x^2(x^4 + 1)^(3/4))`
Integrate the function:
`1/(x^(1/2) + x^(1/3)) ["Hint:" 1/(x^(1/2) + x^(1/3)) = 1/(x^(1/3)(1+x^(1/6))), "put x" = t^6]`
Integrate the function:
`(5x)/((x+1)(x^2 +9))`
Integrate the function:
`e^x/((1+e^x)(2+e^x))`
Integrate the functions `(sin^(-1) sqrtx - cos^(-1) sqrtx)/ (sin^(-1) sqrtx + cos^(-1) sqrtx) , x in [0,1]`
Integrate the function:
`(x^2 + x + 1)/((x + 1)^2 (x + 2))`
Integrate the function:
`tan^(-1) sqrt((1-x)/(1+x))`
Integrate the function:
`(sqrt(x^2 +1) [log(x^2 + 1) - 2log x])/x^4`
Evaluate `int tan^(-1) sqrtx dx`
Find : \[\int\frac{\left( x^2 + 1 \right)\left( x^2 + 4 \right)}{\left( x^2 + 3 \right)\left( x^2 - 5 \right)}dx\] .
If `d/(dx) f(x) = 4x^3 - 3/x^4`, such that `f(2) = 0`, then `f(x)` is
`int (dx)/(sin^2x cos^2x) dx` equals
`int (sin^2x - cos^2x)/(sin^2x cos^2x) dx` is equal to
`int (dx)/sqrt(9x - 4x^2)` equal
`int (dx)/(x(x^2 + 1))` equals
What is anti derivative of `e^(2x)`
`d/(dx)x^(logx)` = ______.
`int (dx)/sqrt(5x - 6 - x^2)` equals ______.
In \[\int f(x)\,dx\], what is \(f(x)\) called?
For \(n\ne -1\), which is the correct integral of \(x^n\)?
Evaluate \[\int \sec^2 x\,dx\]
Evaluate \[\int \text{cosec}^2 x\,dx\]
Evaluate \[\int \sec x\tan x\,dx\]
Which expression is also an antiderivative of \[\frac{1}{\sqrt{1-x^2}}\]?
Evaluate \[\int \frac{dx}{1+x^2}\]
