Optimal. Leaf size=23 \[ \frac{4}{9} (t+1)^{9/4}-\frac{4}{5} (t+1)^{5/4} \]
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Rubi [A] time = 0.0037507, antiderivative size = 23, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.111, Rules used = {43} \[ \frac{4}{9} (t+1)^{9/4}-\frac{4}{5} (t+1)^{5/4} \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin{align*} \int t \sqrt [4]{1+t} \, dt &=\int \left (-\sqrt [4]{1+t}+(1+t)^{5/4}\right ) \, dt\\ &=-\frac{4}{5} (1+t)^{5/4}+\frac{4}{9} (1+t)^{9/4}\\ \end{align*}
Mathematica [A] time = 0.0040473, size = 16, normalized size = 0.7 \[ \frac{4}{45} (t+1)^{5/4} (5 t-4) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 13, normalized size = 0.6 \begin{align*}{\frac{20\,t-16}{45} \left ( 1+t \right ) ^{{\frac{5}{4}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.955077, size = 20, normalized size = 0.87 \begin{align*} \frac{4}{9} \,{\left (t + 1\right )}^{\frac{9}{4}} - \frac{4}{5} \,{\left (t + 1\right )}^{\frac{5}{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0.419432, size = 49, normalized size = 2.13 \begin{align*} \frac{4}{45} \,{\left (5 \, t^{2} + t - 4\right )}{\left (t + 1\right )}^{\frac{1}{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.882601, size = 34, normalized size = 1.48 \begin{align*} \frac{4 t^{2} \sqrt [4]{t + 1}}{9} + \frac{4 t \sqrt [4]{t + 1}}{45} - \frac{16 \sqrt [4]{t + 1}}{45} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.06519, size = 20, normalized size = 0.87 \begin{align*} \frac{4}{9} \,{\left (t + 1\right )}^{\frac{9}{4}} - \frac{4}{5} \,{\left (t + 1\right )}^{\frac{5}{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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