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Question
\[\int \left( e^x + 1 \right)^2 e^x dx\]
Sum
Solution
\[\int \left( e^x + 1 \right)^2 e^x \text{dx} \]
\[ = \int\left( e^{2x} + 2 e^x + 1 \right) e^x dx\]
\[ = \int\left( e^{3x} + 2 e^{2x} + e^x \right) dx\]
\[ = \left[ \frac{e^{3x}}{3} + \frac{2 e^{2x}}{2} + e^x \right] + C\]
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