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
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`
Integrate the function `(3x^2)/(x^6 + 1)`
Integrate the function `1/sqrt(9 - 25x^2)`
Integrate the function `(3x)/(1+ 2x^4)`
Integrate the function `1/sqrt(7 - 6x - x^2)`
Integrate the function `1/sqrt((x -1)(x - 2))`
Integrate the function `1/sqrt((x - a)(x - b))`
Integrate the function `(4x+ 1)/sqrt(2x^2 + x - 3)`
Integrate the function `(x + 2)/sqrt(x^2 -1)`
`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(1-4x - x^2)`
Integrate the function:
`sqrt(1+ 3x - x^2)`
`int sqrt(x^2 - 8x + 7) dx` is equal to ______.
Find `int dx/(5 - 8x - x^2)`
`int (a^x - b^x)^2/(a^xb^x)dx` equals ______.
Evaluate \[\int \frac{dx}{\sqrt{a^2-x^2}}\].
Which factorization is used before applying partial fractions to \[\frac{1}{x^2-a^2}\]?
Which trigonometric substitution is suitable for \[x^2-a^2\] and \[\sqrt{x^2-a^2}\]?
Which method transforms \[\int\frac{dx}{ax^2+bx+c}\] or \[\int\frac{dx}{\sqrt{ax^2+bx+c}}\] into an expression compatible with standard formulae?
What is \[\frac{d}{dx}(ax^2+bx+c)\]?
What is the completed-square form of \[x^2-6x+13\]?
What is the completed-square form of \[3x^2+13x-10\]?
Which is the correct split for \[\int\frac{x+2}{2x^2+6x+5}\,dx\]?
