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Explanation: To integrate x to a power times e to a power, we expect to differentiate the x and integrate the e to a power. ∫x2ex2dx. In order to integrate ex2dx we need an x so that we can use substitution. ∫x2ex2dx = ∫xex2 xdx . Let u = x and dv = ex2 xdx. The du = 1dx and v = 1 2ex2. ∫x2ex2dx = 1 2 xex2 − 1 2∫ex2dx. Now we need.
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