\int_{0}^{1} e^{x} \sqrt{2 x+1}\left(1+x+x^{2}\right)^{100} d x \leq \sqrt{\frac{\left(e^{2}-1\right)\left(3^{201}-1\right)}{402}} You may not use any integral computation tools such as Wolfram Alpha for this question. HINT: Think about inner products.