Optimal. Leaf size=16 \[ -\frac {4 \left (x^3+1\right )^{3/4}}{3 x^3} \]
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Rubi [A] time = 0.01, antiderivative size = 16, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {446, 74} \begin {gather*} -\frac {4 \left (x^3+1\right )^{3/4}}{3 x^3} \end {gather*}
Antiderivative was successfully verified.
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Rule 74
Rule 446
Rubi steps
\begin {align*} \int \frac {4+x^3}{x^4 \sqrt [4]{1+x^3}} \, dx &=\frac {1}{3} \operatorname {Subst}\left (\int \frac {4+x}{x^2 \sqrt [4]{1+x}} \, dx,x,x^3\right )\\ &=-\frac {4 \left (1+x^3\right )^{3/4}}{3 x^3}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 16, normalized size = 1.00 \begin {gather*} -\frac {4 \left (x^3+1\right )^{3/4}}{3 x^3} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.04, size = 16, normalized size = 1.00 \begin {gather*} -\frac {4 \left (x^3+1\right )^{3/4}}{3 x^3} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.40, size = 12, normalized size = 0.75 \begin {gather*} -\frac {4 \, {\left (x^{3} + 1\right )}^{\frac {3}{4}}}{3 \, x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.31, size = 12, normalized size = 0.75 \begin {gather*} -\frac {4 \, {\left (x^{3} + 1\right )}^{\frac {3}{4}}}{3 \, x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 24, normalized size = 1.50 \begin {gather*} -\frac {4 \left (1+x \right ) \left (x^{2}-x +1\right )}{3 x^{3} \left (x^{3}+1\right )^{\frac {1}{4}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.56, size = 12, normalized size = 0.75 \begin {gather*} -\frac {4 \, {\left (x^{3} + 1\right )}^{\frac {3}{4}}}{3 \, x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.15, size = 12, normalized size = 0.75 \begin {gather*} -\frac {4\,{\left (x^3+1\right )}^{3/4}}{3\,x^3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 46.79, size = 49, normalized size = 3.06 \begin {gather*} \frac {1}{3 \left (1 + \frac {1}{\sqrt [4]{x^{3} + 1}}\right )} - \frac {2}{3 \left (1 + \frac {1}{\sqrt {x^{3} + 1}}\right ) \sqrt [4]{x^{3} + 1}} + \frac {1}{3 \left (-1 + \frac {1}{\sqrt [4]{x^{3} + 1}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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