Optimal. Leaf size=21 \[ \frac {4 \left (x^4+x^3\right )^{3/4}}{x^2 (x+1)} \]
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Rubi [A] time = 0.03, 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 = {2056, 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 2056
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 = 0.01, size = 14, normalized size = 0.67 \begin {gather*} \frac {4 x}{\sqrt [4]{x^3 (x+1)}} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.20, size = 21, normalized size = 1.00 \begin {gather*} \frac {4 \left (x^4+x^3\right )^{3/4}}{x^2 (x+1)} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.38, 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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giac [A] time = 0.62, 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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maple [A] time = 0.00, size = 13, normalized size = 0.62 \begin {gather*} \frac {4 x}{\left (x^{4}+x^{3}\right )^{\frac {1}{4}}} \end {gather*}
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*} \int \frac {1}{{\left (x^{4} + x^{3}\right )}^{\frac {1}{4}} {\left (x + 1\right )}}\,{d x} \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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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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