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Mathematics
Mathematics
Problem
Find the exact value of
∫
0
π
x
1
+
x
2
d
x
\displaystyle \int_{0}^{\pi} \frac{x}{\sqrt{1+x^{2}}}\,dx
∫
0
π
1
+
x
2
x
d
x
. a)
1
+
π
2
\sqrt{1+\pi^{2}}
1
+
π
2
b)
1
2
(
1
+
π
2
−
1
)
\dfrac{1}{2}\bigl(\sqrt{1+\pi^{2}}-1\bigr)
2
1
(
1
+
π
2
−
1
)
c)
1
+
π
2
−
1
\sqrt{1+\pi^{2}}-1
1
+
π
2
−
1
d)
ln
(
π
+
1
+
π
2
)
\ln\!\bigl(\pi+\sqrt{1+\pi^{2}}\bigr)
ln
(
π
+
1
+
π
2
)
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