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
Evaluate : ` int x^2/((x^2+4)(x^2+9))dx`
find : `int(3x+1)sqrt(4-3x-2x^2)dx`
Evaluate:
`int((x+3)e^x)/((x+5)^3)dx`
Integrate the function `(3x^2)/(x^6 + 1)`
Integrate the function `(3x)/(1+ 2x^4)`
Integrate the function `x^2/sqrt(x^6 + a^6)`
Integrate the function `1/sqrt(x^2 +2x + 2)`
Integrate the function `1/sqrt(7 - 6x - x^2)`
Integrate the function `1/sqrt(8+3x - x^2)`
Integrate the function `1/sqrt((x - a)(x - b))`
Integrate the function `(x + 2)/sqrt(x^2 -1)`
Integrate the function `(5x - 2)/(1 + 2x + 3x^2)`
Integrate the function `(x + 2)/sqrt(4x - x^2)`
Integrate the function `(5x + 3)/sqrt(x^2 + 4x + 10)`
`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(1-4x - x^2)`
Integrate the function:
`sqrt(1+ x^2/9)`
`int sqrt(x^2 - 8x + 7) dx` is equal to ______.
Evaluate : `int_2^3 3^x dx`
\[\int\frac{8x + 13}{\sqrt{4x + 7}} \text{ dx }\]
\[\int\frac{1 + x + x^2}{x^2 \left( 1 + x \right)} \text{ dx}\]
Find: `int (dx)/(x^2 - 6x + 13)`
