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Mathematics
Problem
Evaluate the integral
∫
d
x
a
2
−
x
2
\displaystyle \int \frac{dx}{\sqrt{a^{2}-x^{2}}}
∫
a
2
−
x
2
d
x
for
∣
x
∣
<
∣
a
∣
|x|<|a|
∣
x
∣
<
∣
a
∣
and
a
>
0
a>0
a
>
0
. a)
cos
−
1
(
x
a
)
+
C
\cos^{-1}\!\left(\dfrac{x}{a}\right)+C
cos
−
1
(
a
x
)
+
C
b)
ln
∣
x
+
a
2
−
x
2
∣
+
C
\ln\left|x+\sqrt{a^{2}-x^{2}}\right|+C
ln
x
+
a
2
−
x
2
+
C
c)
sin
−
1
(
x
a
)
+
C
\sin^{-1}\!\left(\dfrac{x}{a}\right)+C
sin
−
1
(
a
x
)
+
C
d)
1
a
tan
−
1
(
x
a
)
+
C
\dfrac{1}{a}\tan^{-1}\!\left(\dfrac{x}{a}\right)+C
a
1
tan
−
1
(
a
x
)
+
C
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