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Mathematics
Problem
Which statement correctly describes the indefinite integral
∫
e
−
x
2
d
x
\displaystyle \int e^{-x^{2}}\,dx
∫
e
−
x
2
d
x
? a)
−
e
−
x
2
+
C
-e^{-x^{2}}+C
−
e
−
x
2
+
C
b)
π
2
erf
(
x
)
+
C
\dfrac{\sqrt{\pi}}{2}\,\operatorname{erf}(x)+C
2
π
erf
(
x
)
+
C
, where
erf
\operatorname{erf}
erf
is an elementary function c) It cannot be expressed in terms of elementary functions. d)
−
1
2
x
e
−
x
2
+
C
-\dfrac{1}{2x}\,e^{-x^{2}}+C
−
2
x
1
e
−
x
2
+
C
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