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Find the integral value
Answer
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$\dfrac {e ^ {(x ^ {2})}} {2} + C$
using substitution
$\color{#FF6800}{\int xe ^ {(x ^ {2})}dx}$
$ $ Substitute $ t = e ^ {(x ^ {2})} $ to simplify integral calculation $ $
$\color{#FF6800}{\int \dfrac {1} {2}dt}$
$\color{#FF6800}{\int \dfrac {1} {2}dt}$
$ $ Using $ \int adx = a \times x $ , calculate the integral $ $
$\color{#FF6800}{\dfrac {1} {2}t}$
$\dfrac {1} {2}\color{#FF6800}{t}$
$ $ Change the substituted $ t = e ^ {(x ^ {2})} $ again $ $
$\dfrac {1} {2}\color{#FF6800}{e ^ {(x ^ {2})}}$
$\color{#FF6800}{\dfrac {1} {2}e ^ {(x ^ {2})}}$
$ $ Calculate the following $ $
$\color{#FF6800}{\dfrac {e ^ {(x ^ {2})}} {2}}$
$\color{#FF6800}{\dfrac {e ^ {(x ^ {2})}} {2}}$
$ $ Add integral constant $ C \in ℝ $ $ $
$\color{#FF6800}{\dfrac {e ^ {(x ^ {2})}} {2} + C}$
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