The definitions corresponding to the hyperbolic functions was already given in the unit corresponding to the justification of the formulas for their derivatives. From those rules, the corresponding formulas to compute their antiderivatives can be readily deduced.
In this unit some other basic formulas to compute antiderivatives of hyperbolic functions are justified.
Antiderivative of the hyperbolic tangent function
To compute the antiderivative of this function, apply a change of variable setting so that its differential appears at the numerator of the fraction. With this definition, the formula is applicable:
The application of the chain rule leads to the general rule for this antiderivative: