Question

integrel(x⁴epower x) find answer​

Answer 1

By product rule,

$\displaystyle\int x^4\ e^x\ dx=x^4\ e^x-\int 4x^3\ e^x\ dx\\\\\\\int x^4\ e^x\ dx=x^4\ e^x-4\left [x^3\ e^x-\int 3x^2\ e^x \dx\right]\\\\\\\int x^4\ e^x\ dx=x^4\ e^x-4x^3\ e^x+12\left [x^2\ e^x-\int 2x\ e^x\ dx\right]\\\\\\\int x^4\ e^x\ dx=x^4\ e^x-4x^3\ e^x+12x^2\ e^x-24\left [x\ e^x-\int e^x\ dx\right]\\\\\\\int x^4\ e^x\ dx=x^4\ e^x-4x^3\ e^x+12x^2\ e^x-24x\ e^x+24e^x+c\\\\\\\int x^4\ e^x\ dx=\underline {\underline{\left (x^4-4x^3+12x^2-24x+24\right)e^x+c}}$