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 = 0.00, antiderivative size = 23, normalized size of antiderivative = 1.00, 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*}
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Mathematica [A] time = 0.01, size = 16, normalized size = 0.70 \[ \frac {4}{45} (t+1)^{5/4} (5 t-4) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.39, size = 15, normalized size = 0.65 \[ \frac {4}{45} \, {\left (5 \, t^{2} + t - 4\right )} {\left (t + 1\right )}^{\frac {1}{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.01, size = 15, normalized size = 0.65 \[ \frac {4}{9} \, {\left (t + 1\right )}^{\frac {9}{4}} - \frac {4}{5} \, {\left (t + 1\right )}^{\frac {5}{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 13, normalized size = 0.57 \[ \frac {4 \left (t +1\right )^{\frac {5}{4}} \left (5 t -4\right )}{45} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.50, size = 15, normalized size = 0.65 \[ \frac {4}{9} \, {\left (t + 1\right )}^{\frac {9}{4}} - \frac {4}{5} \, {\left (t + 1\right )}^{\frac {5}{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 12, normalized size = 0.52 \[ \frac {4\,\left (5\,t-4\right )\,{\left (t+1\right )}^{5/4}}{45} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 1.01, size = 34, normalized size = 1.48 \[ \frac {4 t^{2} \sqrt [4]{t + 1}}{9} + \frac {4 t \sqrt [4]{t + 1}}{45} - \frac {16 \sqrt [4]{t + 1}}{45} \]
Verification of antiderivative is not currently implemented for this CAS.
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