Advertisements
Advertisements
Question
Integrate the function:
`sqrt(x^2 + 4x +1)`
Advertisements
Solution
Let `I = int sqrt(x^2 + 4x + 1)` dx
`= int sqrt((x^2 + 4x + 4) - 3)` dx
`= int sqrt((x + 2)^2 - (sqrt3)^2)` dx
`= ((x + 2))/2 sqrt((x + 2)^2 - 3) - 3/2 log abs ((x + 2) + sqrt ((x + 2)^2 + 3)) + C` `...[∵ sqrt (x^2 - a^2) dx = x/2 sqrt (x^2 - a^2) - a^2/2 log |x + sqrt (x^2 - a^2)| + C]`
`= ((x + 2))/2 sqrt(x^2 + 4x + 1) - 3/2 log abs((x + 2) + sqrt(x^2 + 4x + 1)) + C`
APPEARS IN
RELATED QUESTIONS
Evaluate : ` int x^2/((x^2+4)(x^2+9))dx`
Find:
`int(x^3-1)/(x^3+x)dx`
Evaluate:
`int((x+3)e^x)/((x+5)^3)dx`
Integrate the function `1/sqrt(1+4x^2)`
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(x^2 +2x + 2)`
Integrate the function `1/(9x^2 + 6x + 5)`
Integrate the function `1/sqrt((x -1)(x - 2))`
Integrate the function `(4x+ 1)/sqrt(2x^2 + x - 3)`
Integrate the function `(5x - 2)/(1 + 2x + 3x^2)`
Integrate the function `(6x + 7)/sqrt((x - 5)(x - 4))`
Integrate the function `(5x + 3)/sqrt(x^2 + 4x + 10)`
`int dx/(x^2 + 2x + 2)` equals:
Integrate the function:
`sqrt(4 - x^2)`
Integrate the function:
`sqrt(x^2 + 4x - 5)`
Integrate the function:
`sqrt(1+ x^2/9)`
`int sqrt(1+ x^2) dx` is equal to ______.
`int sqrt(x^2 - 8x + 7) dx` is equal to ______.
Evaluate : `int_2^3 3^x dx`
Find `int (2x)/(x^2 + 1)(x^2 + 2)^2 dx`
Integration of \[\frac{1}{1 + \left( \log_e x \right)^2}\] with respect to loge x is
\[\int\frac{8x + 13}{\sqrt{4x + 7}} \text{ dx }\]
Find: `int (dx)/(x^2 - 6x + 13)`
`int (a^x - b^x)^2/(a^xb^x)dx` equals ______.
