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Mathematics
Mathematics
Problem
The value of
∫
−
1
/
3
1
/
3
cos
−
1
(
2
x
1
+
x
2
)
+
tan
−
1
(
2
x
1
−
x
2
)
1
+
e
x
d
x
\int_{-1/\sqrt{3}}^{1/\sqrt{3}} \frac{\cos^{-1}\left(\frac{2x}{1+x^2}\right) + \tan^{-1}\left(\frac{2x}{1-x^2}\right)}{1+e^x} dx
∫
−
1/
3
1/
3
1
+
e
x
c
o
s
−
1
(
1
+
x
2
2
x
)
+
t
a
n
−
1
(
1
−
x
2
2
x
)
d
x
is equal to a.
π
2
\frac{\pi}{2}
2
π
b.
π
3
\frac{\pi}{\sqrt{3}}
3
π
c.
π
2
3
\frac{\pi}{2\sqrt{3}}
2
3
π
d.
π
3
3
\frac{\pi}{3\sqrt{3}}
3
3
π
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