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A student completes the square in x² - 2x + 5 and then… | StemPy Lab
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A student completes the square in x² - 2x + 5 and then uses a standard form. Which is the antiderivative of 1/(x² - 2x + 5)?
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Functions and Calculus › Integrals
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StemPy Lab
A student completes the square in
x
2
−
2
x
+
5
x^2 - 2x + 5
x
2
−
2
x
+
5
and then uses a standard form. Which is the antiderivative of
1
x
2
−
2
x
+
5
\dfrac{1}{x^2 - 2x + 5}
x
2
−
2
x
+
5
1
?
1
5
tan
−
1
x
5
+
C
\dfrac{1}{5}\tan^{-1}\dfrac{x}{5} + C
5
1
tan
−
1
5
x
+
C
1
2
tan
−
1
x
−
1
2
+
C
\dfrac{1}{2}\tan^{-1}\dfrac{x - 1}{2} + C
2
1
tan
−
1
2
x
−
1
+
C
1
4
tan
−
1
x
−
1
4
+
C
\dfrac{1}{4}\tan^{-1}\dfrac{x - 1}{4} + C
4
1
tan
−
1
4
x
−
1
+
C
1
2
ln
∣
x
−
1
x
+
1
∣
+
C
\dfrac{1}{2}\ln\left|\dfrac{x - 1}{x + 1}\right| + C
2
1
ln
x
+
1
x
−
1
+
C
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Functions and Calculus › Integrals
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