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Without using a calculator, determine the exact value of $\int_{0}^{2} 4\,e^{-x}(e^{3x} + 1)\,dx$.
Mathematics 9709 · AS & A Level · Integration
Without using a calculator, determine the exact value of $\int_{0}^{2} 4\,e^{-x}(e^{3x} + 1)\,dx$.