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Mathematics
Mathematics
Problem
Find an antiderivative of
3
x
2
x
2
+
1
e
x
2
+
1
\displaystyle \frac{3x}{2\sqrt{x^{2}+1}}\,e^{\sqrt{x^{2}+1}}
2
x
2
+
1
3
x
e
x
2
+
1
. a)
e
x
2
+
1
+
C
e^{\sqrt{x^{2}+1}} + C
e
x
2
+
1
+
C
b)
3
e
x
2
+
1
+
C
3\,e^{\sqrt{x^{2}+1}} + C
3
e
x
2
+
1
+
C
c)
3
2
e
x
2
+
1
+
C
\dfrac{3}{2}\,e^{\sqrt{x^{2}+1}} + C
2
3
e
x
2
+
1
+
C
d)
3
2
x
2
+
1
e
x
2
+
1
+
C
\dfrac{3}{2}\,\sqrt{x^{2}+1}\,e^{\sqrt{x^{2}+1}} + C
2
3
x
2
+
1
e
x
2
+
1
+
C
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