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  • 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 […]

  • Antiderivative of the Natural Log Function

    In this case the technique of Integration by parts works. To this end, define $u = ln v$ and therefore, $du = nicefrac{dv}{v}$.
    Also, let $dw = dv$, so that $w = […]

  • In this unit some formulas to calculate the antiderivative of functions that include $a^2 + u^2$, $a^2 – u^2$ or $u^2 – a^2$ are deduced.

    Antiderivative of $y = nicefrac{1}{(a^2 + u^2)}$

    Rewrite the […]

  • Antiderivative of the Arcsine function

    Define $y = arcsin v$. Then, $v = sin y$. From this, it follows that $dv = cos y cdot dy$.

    In order to calculate the antiderivative for the arcsine function, […]

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