Advertisements
Advertisements
प्रश्न
Integrate the function `1/sqrt(x^2 +2x + 2)`
Advertisements
उत्तर
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
संबंधित प्रश्न
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(9 - 25x^2)`
Integrate the function `(3x)/(1+ 2x^4)`
Integrate the function `1/(9x^2 + 6x + 5)`
Integrate the function `1/sqrt(7 - 6x - x^2)`
Integrate the function `1/sqrt(8+3x - x^2)`
Integrate the function `(4x+ 1)/sqrt(2x^2 + x - 3)`
Integrate the function `(x + 2)/sqrt(x^2 -1)`
Integrate the function `(6x + 7)/sqrt((x - 5)(x - 4))`
Integrate the function `(5x + 3)/sqrt(x^2 + 4x + 10)`
`int dx/sqrt(9x - 4x^2)` equals:
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(1-4x - 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 ______.
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)/sqrt(4x - x^2)`
