If the integral of the product of x squared and e raised to the 5 times x power, dx equals the product of 125 times e raised to the 5 times x power and the quantity A times x squared plus B times x...

Question

If  , then the value of A + B + E is...

A	-17
B	13
C	17
D	37

Answer 1

Integration by parts (multiple times), choosing u = x² and dv = e^5xdx for the first iteration yields

e^5x[1/5·x² - 2/25·x + 2/125] + C. Giving the terms in the quadratic the common denominator of 125 before factoring it out gives A = 25 , B = - 10 , E = 2 and answer choice C (17) is correct.