Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Mathematics
Mathematics
Problem
Determine an antiderivative of
1
4
x
2
−
4
x
+
5
\displaystyle\frac{1}{4x^{2}-4x+5}
4
x
2
−
4
x
+
5
1
. a)
1
2
ln
∣
4
x
2
−
4
x
+
5
∣
+
C
\dfrac{1}{2}\ln\left|4x^{2}-4x+5\right|+C
2
1
ln
4
x
2
−
4
x
+
5
+
C
b)
1
4
arctan
(
x
−
1
2
)
+
C
\dfrac{1}{4}\arctan\left(x-\dfrac{1}{2}\right)+C
4
1
arctan
(
x
−
2
1
)
+
C
c)
arctan
(
x
−
1
2
)
+
C
\arctan\left(x-\dfrac{1}{2}\right)+C
arctan
(
x
−
2
1
)
+
C
d)
1
2
arctan
(
2
x
−
1
)
+
C
\dfrac{1}{2}\arctan\left(2x-1\right)+C
2
1
arctan
(
2
x
−
1
)
+
C
Browse the problem library