Advertisements
Advertisements
Question
Integrate the function:
`sqrt(x^2 + 3x)`
Solution
Let `I = int sqrt(x^2 + 3x)` dx
`= int sqrt((x^2 + 3x + 9/4) - 9/4)` dx
`= int sqrt((x + 3/2)^2 - (3/2)^2)` dx
`= ((x + 3/2))/2 sqrt((x + 3/2)^2 - 9/4) - 9/8 log abs ((x + 3/2) + sqrt((x + 3/2)^2 - 9/4)) + C` `....[∵ int sqrt (x^2 - a^2) dx = x/2 sqrt (x^2 - a^2) - a^2/2 log |x + sqrt (x^2 - a^2)| + C]`
`= (2x + 3)/4 sqrt (x^2 + 3x) - 9/8 log abs (x + 3/2 + sqrt(x^2 + 3x)) + C`
APPEARS IN
RELATED QUESTIONS
Evaluate: `int(5x-2)/(1+2x+3x^2)dx`
Evaluate : ` int x^2/((x^2+4)(x^2+9))dx`
Find:
`int(x^3-1)/(x^3+x)dx`
Integrate the function `(3x^2)/(x^6 + 1)`
Integrate the function `1/sqrt(1+4x^2)`
Integrate the function `(3x)/(1+ 2x^4)`
Integrate the function `x^2/(1 - x^6)`
Integrate the function `x^2/sqrt(x^6 + a^6)`
Integrate the function `(sec^2 x)/sqrt(tan^2 x + 4)`
Integrate the function `1/sqrt(7 - 6x - x^2)`
Integrate the function `1/sqrt((x -1)(x - 2))`
Integrate the function `1/sqrt(8+3x - x^2)`
Integrate the function `1/sqrt((x - a)(x - b))`
Integrate the function `(6x + 7)/sqrt((x - 5)(x - 4))`
Integrate the function:
`sqrt(4 - x^2)`
Integrate the function:
`sqrt(1- 4x^2)`
Integrate the function:
`sqrt(x^2 + 4x + 6)`
Integrate the function:
`sqrt(x^2 + 4x +1)`
Integrate the function:
`sqrt(1+ 3x - x^2)`
Evaluate : `int_2^3 3^x dx`
Integration of \[\frac{1}{1 + \left( \log_e x \right)^2}\] with respect to loge x is
Find:
`int_(-pi/4)^0 (1+tan"x")/(1-tan"x") "dx"`
If θ f(x) = `int_0^x t sin t dt` then `f^1(x)` is
