First slide

Methods of integration

Question

$\int e^{x} (\frac{x^{4} + x^{2} + 1}{x^{2} + x + 1}) d x =$

Moderate

Solution

$\begin{array}{l} \int e^{x} (\frac{(x^{2} + x + 1) (x^{2} - x + 1)}{x^{2} + x + 1}) d x integration by parts \\ = e^{x} (x^{2} - 3 x + 4) + c \end{array}$

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