Applications of Integration - Integration as an Inverse Process of Differentiation

Applications of Integration - Integration as an Inverse Process of Differentiation

Differentiate \(y = 5xe^{2x+1}\) with respect to \(x\) and hence, find \(\displaystyle\displaystyle \displaystyle\int xe^{2x+1} \, \mathrm{d}x.\)

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Answer:\(\displaystyle\int x\mathrm e^{2x+1}\,\mathrm dx=\frac12x\mathrm e^{2x+1}-\frac14\mathrm e^{2x+1}+C\)

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