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Question
\[\int2 x^3 e^{x^2} dx\]
Sum
Solution
\[\int2 x^3 \cdot e^{x^2} dx\]
\[ = \int x^2 \cdot \left( e^{x^2} \right) \cdot \text{ 2x dx }\]
` \text{ Let } x^2" = t `
\[ \Rightarrow \text{ 2x dx } = dt\]
\[ = \int t_I \cdot {e_{II}}^t dt\]
\[ = t \cdot e^t - \int1 \cdot e^t dt\]
\[ = \text{ t e}^t - e^t + C\]
\[ = \text{ x}^2 \text{ e}^{x^2} - e^{x^2} + C\]
\[ = e^{x^2} \left( x^2 - 1 \right) + C\]
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