Optimal. Leaf size=11 \[ x-\frac{4 x^{5/4}}{5} \]
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Rubi [A] time = 0.0015401, antiderivative size = 11, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 19, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.053, Rules used = {26} \[ x-\frac{4 x^{5/4}}{5} \]
Antiderivative was successfully verified.
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Rule 26
Rubi steps
\begin{align*} \int \frac{1-\sqrt{x}}{1+\sqrt [4]{x}} \, dx &=\int \left (1-\sqrt [4]{x}\right ) \, dx\\ &=x-\frac{4 x^{5/4}}{5}\\ \end{align*}
Mathematica [A] time = 0.0003907, size = 11, normalized size = 1. \[ x-\frac{4 x^{5/4}}{5} \]
Antiderivative was successfully verified.
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Maple [C] time = 0.009, size = 44, normalized size = 4. \begin{align*} -{\frac{4}{5}{x}^{{\frac{5}{4}}}}+x+2\,\ln \left ( 1+\sqrt [4]{x} \right ) +2\,\ln \left ( \sqrt [4]{x}-1 \right ) -\ln \left ( x-1 \right ) -\ln \left ( -1+\sqrt{x} \right ) +\ln \left ( 1+\sqrt{x} \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.999827, size = 9, normalized size = 0.82 \begin{align*} -\frac{4}{5} \, x^{\frac{5}{4}} + x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.42162, size = 24, normalized size = 2.18 \begin{align*} -\frac{4}{5} \, x^{\frac{5}{4}} + x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 5.64295, size = 8, normalized size = 0.73 \begin{align*} - \frac{4 x^{\frac{5}{4}}}{5} + x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.20375, size = 9, normalized size = 0.82 \begin{align*} -\frac{4}{5} \, x^{\frac{5}{4}} + x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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