Integrand size = 9, antiderivative size = 23 \[ \int t \sqrt [4]{1+t} \, dt=-\frac {4}{5} (1+t)^{5/4}+\frac {4}{9} (1+t)^{9/4} \]
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Time = 0.00 (sec) , antiderivative size = 23, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {45} \[ \int t \sqrt [4]{1+t} \, dt=\frac {4}{9} (t+1)^{9/4}-\frac {4}{5} (t+1)^{5/4} \]
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Rule 45
Rubi steps \begin{align*} \text {integral}& = \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*}
Time = 0.01 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.78 \[ \int t \sqrt [4]{1+t} \, dt=\frac {4}{45} (1+t)^{5/4} (-9+5 (1+t)) \]
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Time = 0.05 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.57
method | result | size |
gosper | \(\frac {4 \left (1+t \right )^{\frac {5}{4}} \left (5 t -4\right )}{45}\) | \(13\) |
meijerg | \(\frac {t^{2} {}_{2}^{}{\moversetsp {}{\mundersetsp {}{F_{1}^{}}}}\left (-\frac {1}{4},2;3;-t \right )}{2}\) | \(15\) |
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 | \(\left (\frac {4}{9} t^{2}+\frac {4}{45} t -\frac {16}{45}\right ) \left (1+t \right )^{\frac {1}{4}}\) | \(17\) |
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Time = 0.24 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.65 \[ \int t \sqrt [4]{1+t} \, dt=\frac {4}{45} \, {\left (5 \, t^{2} + t - 4\right )} {\left (t + 1\right )}^{\frac {1}{4}} \]
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Time = 0.62 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.48 \[ \int t \sqrt [4]{1+t} \, dt=\frac {4 t^{2} \sqrt [4]{t + 1}}{9} + \frac {4 t \sqrt [4]{t + 1}}{45} - \frac {16 \sqrt [4]{t + 1}}{45} \]
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none
Time = 0.19 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.65 \[ \int t \sqrt [4]{1+t} \, dt=\frac {4}{9} \, {\left (t + 1\right )}^{\frac {9}{4}} - \frac {4}{5} \, {\left (t + 1\right )}^{\frac {5}{4}} \]
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none
Time = 0.27 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.65 \[ \int t \sqrt [4]{1+t} \, dt=\frac {4}{9} \, {\left (t + 1\right )}^{\frac {9}{4}} - \frac {4}{5} \, {\left (t + 1\right )}^{\frac {5}{4}} \]
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Time = 0.02 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.52 \[ \int t \sqrt [4]{1+t} \, dt=\frac {4\,\left (5\,t-4\right )\,{\left (t+1\right )}^{5/4}}{45} \]
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