A calculus problem by Rohith M.Athreya

Calculus Level 3

There is a common integration trick when evaluating indefinite integrals, namely, ex(f(x)+f(x))dx=exf(x)+C \displaystyle \int e^{x} \left( f(x)+f^{'}(x) \right) \, dx = e^{x}f(x)+C .

Hence, or otherwise, calculate

01ex(256x15x17x16)dx.\large \int _{0}^{1} e^{x}\left(256x^{15}-x^{17}-x^{16}\right) \, dx .

Clarification: CC denotes the arbitrary constant of integration.

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