Advertisements
Advertisements
प्रश्न
Evaluate: `int(5x-2)/(1+2x+3x^2)dx`
Advertisements
उत्तर
`int(5x-2)/(1+2x+3x^2)dx=5int(x-2/5)/(1+2x+3x^2)dx=5/6int(6x-12/5)/(1+2x+3x^2)dx`
`=5/6int(6x+2-12/5-2)/(1+2x+3x^2)dx=5/6int(6x+2-22/5)/(1+2x+3x^2)dx`
`=5/6int(6x+2)/(1+2x+3x^2)dx-5/6xx22/5int 1/3{(x+1/3)^2+2/9}dx`
`=5/6 log|1+2x+3x^2|-11/9int 1/3{(x+1/3)^2+2/9}dx`
`=5/6 log|1+2x+3x^2|-11/9xx3/sqrt2 tan^(-1)3/sqrt2(x+1/3)+C`
`=5/6 log|1+2x+3x^2|-11/(3sqrt2) tan^(-1)((3x+1)/sqrt2)+C`
APPEARS IN
संबंधित प्रश्न
find : `int(3x+1)sqrt(4-3x-2x^2)dx`
Integrate the function `x^2/(1 - x^6)`
Integrate the function `(x - 1)/sqrt(x^2 - 1)`
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/(9x^2 + 6x + 5)`
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 `(x + 2)/sqrt(4x - x^2)`
Integrate the function `(x+2)/sqrt(x^2 + 2x + 3)`
Integrate the function `(x + 3)/(x^2 - 2x - 5)`
`int dx/sqrt(9x - 4x^2)` equals:
Integrate the function:
`sqrt(x^2 + 4x + 6)`
Integrate the function:
`sqrt(x^2 + 4x +1)`
Integrate the function:
`sqrt(x^2 + 4x - 5)`
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
Evaluate \[\int \frac{dx}{a^2-x^2}\].
Evaluate \[\int \frac{dx}{\sqrt{a^2-x^2}}\].
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 \[\sqrt{x^2-a^2}\]?
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?
