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 x^2/((x^2+4)(x^2+9))dx`
Find:
`int(x^3-1)/(x^3+x)dx`
Integrate the function `1/sqrt(1+4x^2)`
Integrate the function `1/sqrt((2-x)^2 + 1)`
Integrate the function `(3x)/(1+ 2x^4)`
Integrate the function `1/sqrt((x - a)(x - b))`
Integrate the function `(x+2)/sqrt(x^2 + 2x + 3)`
Integrate the function `(x + 3)/(x^2 - 2x - 5)`
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(1+ 3x - x^2)`
Integrate the function:
`sqrt(1+ x^2/9)`
`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 : \[\int\left( 2x + 5 \right)\sqrt{10 - 4x - 3 x^2}dx\] .
Find `int (dx)/sqrt(4x - x^2)`
What is a standard integral?
Evaluate \[\int \frac{dx}{x^2+a^2}\].
Evaluate \[\int \frac{dx}{\sqrt{x^2-a^2}}\].
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?
Which expression is the general transformation obtained by completing the square?
For \[\int\frac{px+q}{ax^2+bx+c}\,dx\], how is \[px+q\] written in relation to the derivative of the denominator?
What is the completed-square form of \[x^2-6x+13\]?
Evaluate \[\int\frac{dx}{x^2-6x+13}\].
Evaluate \[\int\frac{dx}{3x^2+13x-10}\].
Evaluate \[\int\frac{x+2}{2x^2+6x+5}\,dx\].
