Advertisements
Advertisements
प्रश्न
Evaluate:
`int((x+3)e^x)/((x+5)^3)dx`
Advertisements
उत्तर
`int((x+3)e^x)/((x+5)^3)dx`
`=int((x+5-2)e^x)/((x+5)^3)dx`
`=int((x+5)/(x+5)^3-2/(x+5)^3)e^xdx`
`=int[1/(x+5)^2-2/(x+5)^3]e^xdx`
This is of the form
`int e^x[f(x)+f'(x)]dx=e^xf(x)+C`
`=>int[1/(x+5)^2-2/(x+5)^3]e^xdx`
`=e^x/(x+5)^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`
find : `int(3x+1)sqrt(4-3x-2x^2)dx`
Integrate the function `(3x)/(1+ 2x^4)`
Integrate the function `x^2/(1 - x^6)`
Integrate the function `1/(9x^2 + 6x + 5)`
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 + 3)/(x^2 - 2x - 5)`
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(1+ 3x - x^2)`
Integrate the function:
`sqrt(1+ x^2/9)`
`int sqrt(1+ x^2) dx` is equal to ______.
`int sqrt(x^2 - 8x + 7) dx` is equal to ______.
Integration of \[\frac{1}{1 + \left( \log_e x \right)^2}\] with respect to loge x is
\[\int\frac{8x + 13}{\sqrt{4x + 7}} \text{ dx }\]
Find:
`int_(-pi/4)^0 (1+tan"x")/(1-tan"x") "dx"`
`int (a^x - b^x)^2/(a^xb^x)dx` equals ______.
