Advertisements
Advertisements
प्रश्न
Integrate the function:
`sqrt(x^2 + 4x +1)`
Advertisements
उत्तर
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
संबंधित प्रश्न
Evaluate: `int(5x-2)/(1+2x+3x^2)dx`
Evaluate : ` int x^2/((x^2+4)(x^2+9))dx`
find : `int(3x+1)sqrt(4-3x-2x^2)dx`
Integrate the function `1/sqrt(1+4x^2)`
Integrate the function `x^2/(1 - x^6)`
Integrate the function `(x - 1)/sqrt(x^2 - 1)`
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 `(x + 2)/sqrt(x^2 -1)`
Integrate the function `(5x - 2)/(1 + 2x + 3x^2)`
Integrate the function `(6x + 7)/sqrt((x - 5)(x - 4))`
Integrate the function `(x + 2)/sqrt(4x - x^2)`
Integrate the function `(x+2)/sqrt(x^2 + 2x + 3)`
Integrate the function:
`sqrt(4 - x^2)`
Integrate the function:
`sqrt(1+ 3x - x^2)`
`int sqrt(1+ x^2) dx` is equal to ______.
`int sqrt(x^2 - 8x + 7) dx` is equal to ______.
\[\int\frac{1 + x + x^2}{x^2 \left( 1 + x \right)} \text{ dx}\]
Find : \[\int\left( 2x + 5 \right)\sqrt{10 - 4x - 3 x^2}dx\] .
Find:
`int_(-pi/4)^0 (1+tan"x")/(1-tan"x") "dx"`
Find `int (dx)/sqrt(4x - x^2)`
Find: `int (dx)/(x^2 - 6x + 13)`
