Optimal. Leaf size=23 \[ \frac {4 (4 x-3) \left (x^4+x^3\right )^{3/4}}{21 x^4} \]
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Rubi [A] time = 0.05, antiderivative size = 37, normalized size of antiderivative = 1.61, number of steps used = 2, number of rules used = 2, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.133, Rules used = {2016, 2014} \begin {gather*} \frac {16 \left (x^4+x^3\right )^{3/4}}{21 x^3}-\frac {4 \left (x^4+x^3\right )^{3/4}}{7 x^4} \end {gather*}
Antiderivative was successfully verified.
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Rule 2014
Rule 2016
Rubi steps
\begin {align*} \int \frac {1}{x^2 \sqrt [4]{x^3+x^4}} \, dx &=-\frac {4 \left (x^3+x^4\right )^{3/4}}{7 x^4}-\frac {4}{7} \int \frac {1}{x \sqrt [4]{x^3+x^4}} \, dx\\ &=-\frac {4 \left (x^3+x^4\right )^{3/4}}{7 x^4}+\frac {16 \left (x^3+x^4\right )^{3/4}}{21 x^3}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 23, normalized size = 1.00 \begin {gather*} \frac {4 \left (x^3 (x+1)\right )^{3/4} (4 x-3)}{21 x^4} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.20, size = 23, normalized size = 1.00 \begin {gather*} \frac {4 (4 x-3) \left (x^4+x^3\right )^{3/4}}{21 x^4} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.43, size = 19, normalized size = 0.83 \begin {gather*} \frac {4 \, {\left (x^{4} + x^{3}\right )}^{\frac {3}{4}} {\left (4 \, x - 3\right )}}{21 \, x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.32, size = 19, normalized size = 0.83 \begin {gather*} -\frac {4}{7} \, {\left (\frac {1}{x} + 1\right )}^{\frac {7}{4}} + \frac {4}{3} \, {\left (\frac {1}{x} + 1\right )}^{\frac {3}{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 23, normalized size = 1.00 \begin {gather*} \frac {4 \left (1+x \right ) \left (-3+4 x \right )}{21 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}} x^{2}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.13, size = 29, normalized size = 1.26 \begin {gather*} \frac {16\,x\,{\left (x^4+x^3\right )}^{3/4}-12\,{\left (x^4+x^3\right )}^{3/4}}{21\,x^4} \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}{x^{2} \sqrt [4]{x^{3} \left (x + 1\right )}}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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