Evaluate the integral integral 625 x3 e5x dx Solution 625x3

Solution

625x^3 * e^(5x) dx
= 5 * (5x)^3 * e^(5x) dx

Let u = 5x ==> dx = (1/5) du

Continue from above
= u^3 * e^u du
= u^3 e^u - 3 u^2 e^u du
= u^3 e^u - 3 [ u^2 e^u - 2 u e^u du ]
= u^3 e^u - 3 u^2 e^u + 6 u e^u du
= u^3 e^u - 3 u^2 e^u + 6 [ u e^u - e^u du ]
= u^3 e^u - 3 u^2 e^u + 6 [ u e^u - e^u ] + C
= u^3 e^u - 3 u^2 e^u + 6 u e^u - 6 e^u + C
= e^u * (u^3 - 3u^2 + 6u - 6) + C
= e^(5x) * (125x^3 - 75x^2 + 30x - 6) + C