Optimal. Leaf size=21 \[ \frac {4 \left (x^3+x^4\right )^{3/4}}{x^2 (1+x)} \]
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Rubi [A]
time = 0.02, antiderivative size = 14, normalized size of antiderivative = 0.67, number of steps
used = 2, number of rules used = 2, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.118, Rules used = {2081, 37}
\begin {gather*} \frac {4 x}{\sqrt [4]{x^4+x^3}} \end {gather*}
Antiderivative was successfully verified.
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Rule 37
Rule 2081
Rubi steps
\begin {align*} \int \frac {1}{(1+x) \sqrt [4]{x^3+x^4}} \, dx &=\frac {\left (x^{3/4} \sqrt [4]{1+x}\right ) \int \frac {1}{x^{3/4} (1+x)^{5/4}} \, dx}{\sqrt [4]{x^3+x^4}}\\ &=\frac {4 x}{\sqrt [4]{x^3+x^4}}\\ \end {align*}
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Mathematica [A]
time = 0.02, size = 14, normalized size = 0.67 \begin {gather*} \frac {4 x}{\sqrt [4]{x^3 (1+x)}} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.39, size = 11, normalized size = 0.52
method | result | size |
meijerg | \(\frac {4 x^{\frac {1}{4}}}{\left (1+x \right )^{\frac {1}{4}}}\) | \(11\) |
gosper | \(\frac {4 x}{\left (x^{4}+x^{3}\right )^{\frac {1}{4}}}\) | \(13\) |
risch | \(\frac {4 x}{\left (x^{3} \left (1+x \right )\right )^{\frac {1}{4}}}\) | \(13\) |
trager | \(\frac {4 \left (x^{4}+x^{3}\right )^{\frac {3}{4}}}{x^{2} \left (1+x \right )}\) | \(20\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.34, size = 20, normalized size = 0.95 \begin {gather*} \frac {4 \, {\left (x^{4} + x^{3}\right )}^{\frac {3}{4}}}{x^{3} + x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{\sqrt [4]{x^{3} \left (x + 1\right )} \left (x + 1\right )}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.39, size = 9, normalized size = 0.43 \begin {gather*} \frac {4}{{\left (\frac {1}{x} + 1\right )}^{\frac {1}{4}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.17, size = 19, normalized size = 0.90 \begin {gather*} \frac {4\,{\left (x^4+x^3\right )}^{3/4}}{x^2\,\left (x+1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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