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`
find : `int(3x+1)sqrt(4-3x-2x^2)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 `1/sqrt(9 - 25x^2)`
Integrate the function `1/sqrt((x -1)(x - 2))`
Integrate the function `1/sqrt(8+3x - x^2)`
Integrate the function `(4x+ 1)/sqrt(2x^2 + x - 3)`
Integrate the function `(5x - 2)/(1 + 2x + 3x^2)`
Integrate the function `(x + 3)/(x^2 - 2x - 5)`
Integrate the function `(5x + 3)/sqrt(x^2 + 4x + 10)`
Integrate the function:
`sqrt(1- 4x^2)`
Integrate the function:
`sqrt(1-4x - x^2)`
Integrate the function:
`sqrt(x^2 + 4x - 5)`
Integrate the function:
`sqrt(x^2 + 3x)`
Find `int dx/(5 - 8x - x^2)`
Evaluate : `int_2^3 3^x dx`
\[\int\frac{8x + 13}{\sqrt{4x + 7}} \text{ dx }\]
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)/(x^2 - 6x + 13)`
Evaluate \[\int \frac{dx}{x^2+a^2}\].
Evaluate \[\int \frac{dx}{\sqrt{x^2-a^2}}\].
Evaluate \[\int \frac{dx}{\sqrt{x^2+a^2}}\].
Which factorization is used before applying partial fractions to \[\frac{1}{x^2-a^2}\]?
Which trigonometric substitution is suitable for \[a^2-x^2\] and \[\sqrt{a^2-x^2}\]?
Which trigonometric substitution is suitable for \[x^2-a^2\] and \[\sqrt{x^2-a^2}\]?
What is the completed-square form of \[x^2-6x+13\]?
What is the completed-square form of \[3x^2+13x-10\]?
For \[x+2=A(4x+6)+B\], what are the values of \[A\] and \[B\]?
Which is the correct split for \[\int\frac{x+2}{2x^2+6x+5}\,dx\]?
