Optimal. Leaf size=23 \[ -\frac {4}{5} (1+t)^{5/4}+\frac {4}{9} (1+t)^{9/4} \]
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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 = {45}
\begin {gather*} \frac {4}{9} (t+1)^{9/4}-\frac {4}{5} (t+1)^{5/4} \end {gather*}
Antiderivative was successfully verified.
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Rule 45
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 = 18, normalized size = 0.78 \begin {gather*} \frac {4}{45} (1+t)^{5/4} (-9+5 (1+t)) \end {gather*}
Antiderivative was successfully verified.
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Mathics [A]
time = 2.08, size = 15, normalized size = 0.65 \begin {gather*} \frac {4 \left (-4+t+5 t^2\right ) \left (1+t\right )^{\frac {1}{4}}}{45} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.06, size = 16, normalized size = 0.70
method | result | size |
gosper | \(\frac {4 \left (1+t \right )^{\frac {5}{4}} \left (5 t -4\right )}{45}\) | \(13\) |
meijerg | \(\frac {t^{2} \hypergeom \left (\left [-\frac {1}{4}, 2\right ], \left [3\right ], -t \right )}{2}\) | \(15\) |
derivativedivides | \(-\frac {4 \left (1+t \right )^{\frac {5}{4}}}{5}+\frac {4 \left (1+t \right )^{\frac {9}{4}}}{9}\) | \(16\) |
default | \(-\frac {4 \left (1+t \right )^{\frac {5}{4}}}{5}+\frac {4 \left (1+t \right )^{\frac {9}{4}}}{9}\) | \(16\) |
risch | \(\frac {4 \left (1+t \right )^{\frac {1}{4}} \left (5 t^{2}+t -4\right )}{45}\) | \(16\) |
trager | \(\left (\frac {4}{9} t^{2}+\frac {4}{45} t -\frac {16}{45}\right ) \left (1+t \right )^{\frac {1}{4}}\) | \(17\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 15, normalized size = 0.65 \begin {gather*} \frac {4}{9} \, {\left (t + 1\right )}^{\frac {9}{4}} - \frac {4}{5} \, {\left (t + 1\right )}^{\frac {5}{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.32, size = 15, normalized size = 0.65 \begin {gather*} \frac {4}{45} \, {\left (5 \, t^{2} + t - 4\right )} {\left (t + 1\right )}^{\frac {1}{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.50, size = 34, normalized size = 1.48 \begin {gather*} \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 {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.00, size = 65, normalized size = 2.83 \begin {gather*} 4 \left (\frac {1}{5} \left (t+1\right )^{\frac {1}{4}} \left (t+1\right )-\left (t+1\right )^{\frac {1}{4}}\right )+4 \left (\frac {1}{9} \left (t+1\right )^{\frac {1}{4}} \left (t+1\right )^{2}-\frac {2}{5} \left (t+1\right )^{\frac {1}{4}} \left (t+1\right )+\left (t+1\right )^{\frac {1}{4}}\right ) \end {gather*}
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 \begin {gather*} \frac {4\,\left (5\,t-4\right )\,{\left (t+1\right )}^{5/4}}{45} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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