Inverse Regular & Hyperbolic Trig Integrals

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Calculus

Derivatives & Differentiation

AP Calculus BC

Unit 3: Differentiation: Composite, Implicit, and Inverse Functions

Last updated 5:40 PM on 5/3/24

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1

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$\int \frac{1}{\sqrt{1-x^{2}}}\:dx$

$\sin^{-1}(x) + C$

2

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$\int\frac{1}{\sqrt{1+x^{2}}}\:dx$

$\sinh^{-1}(x) + C$

3

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$\int -\frac{1}{\sqrt{1-x^{2}}}\:dx$

$\cos^{-1}(x) + C$

4

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$\int\frac{1}{\sqrt{x^{2}-1}}\:dx$

$\cosh^{-1}(x) + C$

5

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$\int \frac{1}{1+x^{2}}\:dx$

$\tan^{-1}(x) + C$

6

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$\int \frac{1}{1-x^{2}}\:dx$

$\tanh^{-1}(x) + C$