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Question
Find: `int e^(x^2) (x^5 + 2x^3)dx`.
Solution
I = `int e^(x^2) (x^5 + 2x^3)dx`
I = `int x^5 e^(x^2) dx + 2int x^3 e^(x^2) dx`
Applying integration by part in `int x^3e^(x^2) dx`
I = `int x^5 e^(x^2) dx + (2x^4)/4 e^(x^2) - 2int e^(x^2) 2x . x^4/4 dx`
= `int x^5e^(x^2) dx + (2x^4e^(x^2))/4 - 2int (x^5e^(x^2))/2dx`
= `(x^4e^(x^2))/2 + C`.
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