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The fraction (2x² + 3)/(x² - 1) has top and bottom of… | StemPy Lab
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The fraction (2x² + 3)/(x² - 1) has top and bottom of the same degree. After dividing, the integral is found by partial fractions. What is the antiderivative on x > 1, apart from the constant?
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Functions and Calculus › Integrals
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The fraction
2
x
2
+
3
x
2
−
1
\dfrac{2x^2 + 3}{x^2 - 1}
x
2
−
1
2
x
2
+
3
has top and bottom of the same degree. After dividing, the integral is found by partial fractions. What is the antiderivative on
x
>
1
x > 1
x
>
1
, apart from the constant?
2
x
+
5
ln
x
−
1
x
+
1
2x + 5\ln\dfrac{x - 1}{x + 1}
2
x
+
5
ln
x
+
1
x
−
1
5
2
ln
x
−
1
x
+
1
\dfrac{5}{2}\ln\dfrac{x - 1}{x + 1}
2
5
ln
x
+
1
x
−
1
2
x
+
1
2
ln
x
−
1
x
+
1
2x + \dfrac{1}{2}\ln\dfrac{x - 1}{x + 1}
2
x
+
2
1
ln
x
+
1
x
−
1
2
x
+
5
2
ln
x
−
1
x
+
1
2x + \dfrac{5}{2}\ln\dfrac{x - 1}{x + 1}
2
x
+
2
5
ln
x
+
1
x
−
1
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← For -1 < x < 1 the function sin⁻¹x has no obvious product in it. Treating it as sin⁻¹x · 1, which is its antiderivative, apart from the constant?
The function F is an antiderivative of f on [a, b], and f is continuous there. Which expression is equal to ∫aᵇ f(x) dx? →
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