Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Mathematics
Mathematics
Problem
For a nonzero constant
a
a
a
, evaluate
∫
x
2
+
a
2
x
2
+
2
a
x
+
a
2
+
1
d
x
\displaystyle \int \frac{x^{2}+a^{2}}{x^{2}+2ax+a^{2}+1}\,dx
∫
x
2
+
2
a
x
+
a
2
+
1
x
2
+
a
2
d
x
in terms of
a
a
a
. a)
x
−
a
ln
(
(
x
+
a
)
2
+
1
)
+
(
2
a
2
−
1
)
arctan
(
x
+
a
)
+
C
x-a\ln\!\big((x+a)^{2}+1\big)+(2a^{2}-1)\arctan(x+a)+C
x
−
a
ln
(
(
x
+
a
)
2
+
1
)
+
(
2
a
2
−
1
)
arctan
(
x
+
a
)
+
C
b)
x
+
a
ln
(
(
x
+
a
)
2
+
1
)
+
(
2
a
2
−
1
)
arctan
(
x
+
a
)
+
C
x+a\ln\!\big((x+a)^{2}+1\big)+(2a^{2}-1)\arctan(x+a)+C
x
+
a
ln
(
(
x
+
a
)
2
+
1
)
+
(
2
a
2
−
1
)
arctan
(
x
+
a
)
+
C
c)
x
−
a
ln
(
(
x
+
a
)
2
+
1
)
+
(
2
a
2
+
1
)
arctan
(
x
+
a
)
+
C
x-a\ln\!\big((x+a)^{2}+1\big)+(2a^{2}+1)\arctan(x+a)+C
x
−
a
ln
(
(
x
+
a
)
2
+
1
)
+
(
2
a
2
+
1
)
arctan
(
x
+
a
)
+
C
d)
x
−
a
2
ln
(
(
x
+
a
)
2
+
1
)
+
(
2
a
2
−
1
)
arctan
(
x
+
a
)
+
C
x-\tfrac{a}{2}\ln\!\big((x+a)^{2}+1\big)+(2a^{2}-1)\arctan(x+a)+C
x
−
2
a
ln
(
(
x
+
a
)
2
+
1
)
+
(
2
a
2
−
1
)
arctan
(
x
+
a
)
+
C
Browse the problem library