Optimal. Leaf size=10 \[ \frac {1}{4} (x+\sin (x))^4 \]
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Rubi [A] time = 0.04, antiderivative size = 10, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {6686} \[ \frac {1}{4} (x+\sin (x))^4 \]
Antiderivative was successfully verified.
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Rule 6686
Rubi steps
\begin {align*} \int (1+\cos (x)) (x+\sin (x))^3 \, dx &=\frac {1}{4} (x+\sin (x))^4\\ \end {align*}
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Mathematica [A] time = 0.02, size = 10, normalized size = 1.00 \[ \frac {1}{4} (x+\sin (x))^4 \]
Antiderivative was successfully verified.
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fricas [B] time = 0.62, size = 45, normalized size = 4.50 \[ \frac {1}{4} \, x^{4} + \frac {1}{4} \, \cos \relax (x)^{4} - \frac {1}{2} \, {\left (3 \, x^{2} + 1\right )} \cos \relax (x)^{2} + \frac {3}{2} \, x^{2} + {\left (x^{3} - x \cos \relax (x)^{2} + x\right )} \sin \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.15, size = 61, normalized size = 6.10 \[ \frac {1}{4} \, x^{4} + \frac {3}{4} \, x^{2} - \frac {1}{4} \, {\left (3 \, x^{2} - 1\right )} \cos \left (2 \, x\right ) - \frac {1}{4} \, x \sin \left (3 \, x\right ) + \frac {1}{4} \, {\left (4 \, x^{3} - 21 \, x\right )} \sin \relax (x) + 6 \, x \sin \relax (x) + \frac {1}{32} \, \cos \left (4 \, x\right ) - \frac {3}{8} \, \cos \left (2 \, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.09, size = 65, normalized size = 6.50 \[ x^{3} \sin \relax (x )-\frac {3 \left (\cos ^{2}\relax (x )\right ) x^{2}}{2}+3 x \left (\frac {\cos \relax (x ) \sin \relax (x )}{2}+\frac {x}{2}\right )-\frac {3 x^{2}}{2}+x \left (\sin ^{3}\relax (x )\right )+\frac {\left (\sin ^{4}\relax (x )\right )}{4}+\frac {x^{4}}{4}+3 x \left (-\frac {\cos \relax (x ) \sin \relax (x )}{2}+\frac {x}{2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.33, size = 8, normalized size = 0.80 \[ \frac {1}{4} \, {\left (x + \sin \relax (x)\right )}^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.15, size = 8, normalized size = 0.80 \[ \frac {{\left (x+\sin \relax (x)\right )}^4}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.52, size = 36, normalized size = 3.60 \[ \frac {x^{4}}{4} + x^{3} \sin {\relax (x )} + \frac {3 x^{2} \sin ^{2}{\relax (x )}}{2} + x \sin ^{3}{\relax (x )} + \frac {\sin ^{4}{\relax (x )}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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