Advertisements
Advertisements
Question
Integrate the function `1/sqrt(x^2 +2x + 2)`
Advertisements
Solution
Let `I = int 1/ sqrt (x^2 + 2x + 2) dx`
`= dx/ sqrt ((x + 1)^2 + 1)`
∴ `I = log |(x + 1) + sqrt ((x + 1)^2 + 1)| + C` ` ....[∵ int dx/sqrt (a^2 + x^2) = log |x + sqrt (x^2 + a^2)| + C]`
`= log |(x + 1) + sqrt (x^2 + 2x + 2)| +C`
APPEARS IN
RELATED QUESTIONS
Evaluate : ` int x^2/((x^2+4)(x^2+9))dx`
find : `int(3x+1)sqrt(4-3x-2x^2)dx`
Find:
`int(x^3-1)/(x^3+x)dx`
Evaluate:
`int((x+3)e^x)/((x+5)^3)dx`
Integrate the function `(3x^2)/(x^6 + 1)`
Integrate the function `1/sqrt(1+4x^2)`
Integrate the function `1/sqrt((2-x)^2 + 1)`
Integrate the function `1/sqrt(9 - 25x^2)`
Integrate the function `x^2/(1 - x^6)`
Integrate the function `x^2/sqrt(x^6 + a^6)`
Integrate the function `1/sqrt((x -1)(x - 2))`
Integrate the function `1/sqrt(8+3x - x^2)`
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:
`int dx/sqrt(9x - 4x^2)` equals:
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(x^2 + 4x - 5)`
Integrate the function:
`sqrt(x^2 + 3x)`
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 ______.
Find `int dx/(5 - 8x - x^2)`
\[\int\frac{8x + 13}{\sqrt{4x + 7}} \text{ dx }\]
`int (a^x - b^x)^2/(a^xb^x)dx` equals ______.
