Advertisements
Advertisements
प्रश्न
Find: `int (dx)/(x^2 - 6x + 13)`
Advertisements
उत्तर
Given integral is I = `int (dx)/(x^2 - 6x + 13)`
= `int (dx)/((x - 3)^2 + 13 - 9)`
= `int (dx)/((x - 3)^2 + 4)`
= `int (dx)/((x - 3)^2 + 2^2)`
= `1/2 tan^-1 ((x - 3)/2) + C` ...`["Using" int 1/(x^2 + a^2) dx = 1/a tan^-1 x/a + C]`
APPEARS IN
संबंधित प्रश्न
Evaluate: `int(5x-2)/(1+2x+3x^2)dx`
find : `int(3x+1)sqrt(4-3x-2x^2)dx`
Integrate the function `(3x^2)/(x^6 + 1)`
Integrate the function `1/sqrt((2-x)^2 + 1)`
Integrate the function `(sec^2 x)/sqrt(tan^2 x + 4)`
Integrate the function `1/(9x^2 + 6x + 5)`
Integrate the function `1/sqrt(8+3x - x^2)`
Integrate the function `(6x + 7)/sqrt((x - 5)(x - 4))`
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
\[\int\frac{1 + x + x^2}{x^2 \left( 1 + x \right)} \text{ dx}\]
`int (a^x - b^x)^2/(a^xb^x)dx` equals ______.
What is a standard integral?
Evaluate \[\int \frac{dx}{a^2-x^2}\].
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 \[\frac{1}{x^2-a^2}\]?
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 \[x^2-6x+13\]?
For \[x+2=A(4x+6)+B\], what are the values of \[A\] and \[B\]?
Which statement is correct when integrating an expression that is not immediately a standard integral?
