Advertisements
Advertisements
प्रश्न
Integrate the function `1/sqrt(1+4x^2)`
Advertisements
उत्तर
Let `I = int 1/sqrt(1 + 4x^2) dx`
`= 1/2 int dx/sqrt(1/4 + x)`
`= 1/2 int dx/sqrt((1/2)^2 + x^2)`
`= 1/2 log abs (x sqrt(1/4 +x^2)) C_1`
.....`[because int dx/sqrt(x^2 + a^2) = log abs (x + sqrt(x^2 + a^2)) + C]`
`= 1/2 log abs ((2x + sqrt(1 + 4x^2))/2) + C_1`
`= 1/2 log abs (2x + sqrt(1 + 4x^2)) - 1/2 log 2 + C_1`
`= 1/2 log |2x + sqrt 1 + 4x^2| + C` .... [`C = -1/2 log 2 + C_1`]
APPEARS IN
संबंधित प्रश्न
find : `int(3x+1)sqrt(4-3x-2x^2)dx`
Evaluate:
`int((x+3)e^x)/((x+5)^3)dx`
Integrate the function `(3x)/(1+ 2x^4)`
Integrate the function `x^2/(1 - x^6)`
Integrate the function `(x - 1)/sqrt(x^2 - 1)`
Integrate the function `1/sqrt((x - a)(x - b))`
Integrate the function `(4x+ 1)/sqrt(2x^2 + x - 3)`
Integrate the function `(x + 3)/(x^2 - 2x - 5)`
`int dx/sqrt(9x - 4x^2)` equals:
Integrate the function:
`sqrt(4 - x^2)`
Integrate the function:
`sqrt(x^2 + 3x)`
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`
Find: `int (dx)/(x^2 - 6x + 13)`
`int (a^x - b^x)^2/(a^xb^x)dx` equals ______.
Evaluate \[\int \frac{dx}{a^2-x^2}\].
Evaluate \[\int \frac{dx}{\sqrt{x^2-a^2}}\].
Which expression is the general transformation obtained by completing the square?
What is the completed-square form of \[x^2-6x+13\]?
Evaluate \[\int\frac{dx}{3x^2+13x-10}\].
Which is the correct split for \[\int\frac{x+2}{2x^2+6x+5}\,dx\]?
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?
