Advertisements
Advertisements
Question
Integrate the function:
`sqrt(x^2 + 4x +1)`
Advertisements
Solution
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
RELATED QUESTIONS
Evaluate: `int(5x-2)/(1+2x+3x^2)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 `x^2/sqrt(x^6 + a^6)`
Integrate the function `(sec^2 x)/sqrt(tan^2 x + 4)`
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 `(x + 2)/sqrt(4x - x^2)`
Integrate the function:
`sqrt(4 - x^2)`
Integrate the function:
`sqrt(1- 4x^2)`
Integrate the function:
`sqrt(x^2 + 4x + 6)`
\[\int\frac{8x + 13}{\sqrt{4x + 7}} \text{ dx }\]
\[\int\frac{1 + x + x^2}{x^2 \left( 1 + x \right)} \text{ dx}\]
Find : \[\int\left( 2x + 5 \right)\sqrt{10 - 4x - 3 x^2}dx\] .
If θ f(x) = `int_0^x t sin t dt` then `f^1(x)` is
Find `int (dx)/sqrt(4x - x^2)`
`int (a^x - b^x)^2/(a^xb^x)dx` equals ______.
Evaluate \[\int \frac{dx}{a^2-x^2}\].
Evaluate \[\int \frac{dx}{\sqrt{x^2-a^2}}\].
Evaluate \[\int \frac{dx}{\sqrt{a^2-x^2}}\].
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?
What is the completed-square form of \[x^2-6x+13\]?
Evaluate \[\int\frac{dx}{x^2-6x+13}\].
For \[x+2=A(4x+6)+B\], what are the values of \[A\] and \[B\]?
Evaluate \[\int\frac{x+2}{2x^2+6x+5}\,dx\].
Which statement is correct when integrating an expression that is not immediately a standard integral?
