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→Standard integrals: Fixed an inaccuracy in a standard formula. Tags: Reverted Mobile edit Mobile web edit |
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\int \tanh (ax)\,dx &= a^{-1} \ln (\cosh (ax)) + C \\
\int \coth (ax)\,dx &= a^{-1} \ln \left|\sinh (ax)\right| + C \\
\int \operatorname{sech} (ax)\,dx &= a^{-1} \arctan (\
\int \operatorname{csch} (ax)\,dx &= a^{-1} \ln \left| \tanh \left( \frac{ax}{2} \right) \right| + C = a^{-1} \ln\left|\coth \left(ax\right) - \operatorname{csch} \left(ax\right)\right| + C = -a^{-1}\operatorname{arcoth} \left(\cosh\left(ax\right)\right) +C
\end{align}</math>
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