Advertisements
Advertisements
प्रश्न
Integrate the function `1/(9x^2 + 6x + 5)`
Advertisements
उत्तर १
`1/(9x^2 + 6x + 5)`
I = `int1/(9x^2 + 6x + 5)dx = int 1/((3x + 1)^2 + 2^2)`
let (3x + 1) = t ⇒ 3dx = dt
I = `int 1/((3x + 1)^2 + 2^2)dx`
= `1/3 int 1/(t^2 + 2^2)dt`
= `1/3[1/2tan^-1 (t/2)] + C`
= `1/6 tan^-1 (t/2) + C`
Substituting the value of t
= `1/6 tan^-1((3x + 1)/2) + C`
उत्तर २
Let `I = int dx/ (9x^2 + 6x + 5)`
`= 1/9 int dx/ (x^2 + 2/3x + 5/9)`
`= 1/9 int dx/ ((x^2 + 2/3x + 1/9) + (5/9 - 1/9))`
`= 1/9 int dx/ ((x + 1/3)^2 + (2/3)^2)`
`= 1/9 xx 1/ (2/3) tan^-1 ((x + 1/3)/ (2/3)) + C` `....[∵ int dx/ (x^2 + a^2) = 1/a tan^-1 x/a + C]`
`= 1/6 tan^-1 ((3x + 1)/2) + 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`
Integrate the function `1/sqrt(1+4x^2)`
Integrate the function `1/sqrt(9 - 25x^2)`
Integrate the function `x^2/(1 - x^6)`
Integrate the function `(sec^2 x)/sqrt(tan^2 x + 4)`
Integrate the function `1/sqrt(7 - 6x - 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)`
Integrate the function `(5x - 2)/(1 + 2x + 3x^2)`
Integrate the function `(6x + 7)/sqrt((x - 5)(x - 4))`
Integrate the function `(5x + 3)/sqrt(x^2 + 4x + 10)`
`int dx/(x^2 + 2x + 2)` equals:
Integrate the function:
`sqrt(4 - x^2)`
Integrate the function:
`sqrt(x^2 + 4x + 6)`
Integrate the function:
`sqrt(x^2 + 4x - 5)`
Integrate the function:
`sqrt(x^2 + 3x)`
Integrate the function:
`sqrt(1+ x^2/9)`
`int sqrt(1+ x^2) dx` is equal to ______.
If θ f(x) = `int_0^x t sin t dt` then `f^1(x)` is
`int (a^x - b^x)^2/(a^xb^x)dx` equals ______.
Which trigonometric substitution is suitable for \[x^2+a^2\] and \[\sqrt{x^2+a^2}\]?
Which trigonometric substitution is suitable for \[x^2-a^2\] and \[\sqrt{x^2-a^2}\]?
Evaluate \[\int\frac{dx}{x^2-6x+13}\].
What is the completed-square form of \[3x^2+13x-10\]?
Which is the correct split for \[\int\frac{x+2}{2x^2+6x+5}\,dx\]?
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?
