Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Mathematics
Mathematics
Problem
The integral
∫
x
d
x
2
−
x
2
+
2
−
x
2
\int \frac{x \, dx}{2 - x^2 + \sqrt{2 - x^2}}
∫
2
−
x
2
+
2
−
x
2
x
d
x
equals : (1)
−
x
ln
∣
1
−
2
−
x
2
∣
+
C
-x \ln|1 - \sqrt{2 - x^2}| + C
−
x
ln
∣1
−
2
−
x
2
∣
+
C
(2)
ln
∣
1
+
2
+
x
2
∣
+
C
\ln|1 + \sqrt{2 + x^2}| + C
ln
∣1
+
2
+
x
2
∣
+
C
(3)
x
ln
∣
1
−
2
+
x
2
∣
+
C
x \ln|1 - \sqrt{2 + x^2}| + C
x
ln
∣1
−
2
+
x
2
∣
+
C
(4)
−
ln
∣
1
+
2
−
x
2
∣
+
C
-\ln|1 + \sqrt{2 - x^2}| + C
−
ln
∣1
+
2
−
x
2
∣
+
C
Browse the problem library