∫11−x2 dx\int \frac{1}{\sqrt{1-x^{2}}}\:dx∫1−x21dx
sin−1(x)+C \sin^{-1}(x) + C sin−1(x)+C
∫11+x2 dx\int\frac{1}{\sqrt{1+x^{2}}}\:dx∫1+x21dx
sinh−1(x)+C \sinh^{-1}(x) + C sinh−1(x)+C
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Calculus
Derivatives & Differentiation
AP Calculus BC
Unit 3: Differentiation: Composite, Implicit, and Inverse Functions
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∫−11−x2 dx\int -\frac{1}{\sqrt{1-x^{2}}}\:dx∫−1−x21dx
cos−1(x)+C\cos^{-1}(x) + Ccos−1(x)+C
∫1x2−1 dx\int\frac{1}{\sqrt{x^{2}-1}}\:dx∫x2−11dx
cosh−1(x)+C\cosh^{-1}(x) + Ccosh−1(x)+C
∫11+x2 dx\int \frac{1}{1+x^{2}}\:dx∫1+x21dx
tan−1(x)+C\tan^{-1}(x) + Ctan−1(x)+C
∫11−x2 dx\int \frac{1}{1-x^{2}}\:dx∫1−x21dx
tanh−1(x)+C\tanh^{-1}(x) + C tanh−1(x)+C