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Mathematics
Problem
Evaluate
∫
x
5
e
x
2
d
x
\displaystyle \int x^{5}e^{x^{2}}\,dx
∫
x
5
e
x
2
d
x
. a)
1
2
e
x
2
(
x
4
+
2
x
2
+
2
)
+
C
\displaystyle \tfrac12\,e^{x^{2}}\bigl(x^{4}+2x^{2}+2\bigr)+C
2
1
e
x
2
(
x
4
+
2
x
2
+
2
)
+
C
b)
1
2
e
x
2
(
x
4
−
2
x
2
+
2
)
+
C
\displaystyle \tfrac12\,e^{x^{2}}\bigl(x^{4}-2x^{2}+2\bigr)+C
2
1
e
x
2
(
x
4
−
2
x
2
+
2
)
+
C
c)
1
2
e
x
2
(
x
4
−
2
x
2
)
+
C
\displaystyle \tfrac12\,e^{x^{2}}\bigl(x^{4}-2x^{2}\bigr)+C
2
1
e
x
2
(
x
4
−
2
x
2
)
+
C
d)
e
x
2
(
x
4
−
2
x
2
+
2
)
+
C
\displaystyle e^{x^{2}}\bigl(x^{4}-2x^{2}+2\bigr)+C
e
x
2
(
x
4
−
2
x
2
+
2
)
+
C
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