Optimal. Leaf size=32 \[ -\frac{3 (c+d x)^{4/3}}{4 (a+b x)^{4/3} (b c-a d)} \]
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Rubi [A] time = 0.0029945, antiderivative size = 32, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 19, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.053, Rules used = {37} \[ -\frac{3 (c+d x)^{4/3}}{4 (a+b x)^{4/3} (b c-a d)} \]
Antiderivative was successfully verified.
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Rule 37
Rubi steps
\begin{align*} \int \frac{\sqrt [3]{c+d x}}{(a+b x)^{7/3}} \, dx &=-\frac{3 (c+d x)^{4/3}}{4 (b c-a d) (a+b x)^{4/3}}\\ \end{align*}
Mathematica [A] time = 0.0117813, size = 32, normalized size = 1. \[ -\frac{3 (c+d x)^{4/3}}{4 (a+b x)^{4/3} (b c-a d)} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 27, normalized size = 0.8 \begin{align*}{\frac{3}{4\,ad-4\,bc} \left ( dx+c \right ) ^{{\frac{4}{3}}} \left ( bx+a \right ) ^{-{\frac{4}{3}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{{\left (d x + c\right )}^{\frac{1}{3}}}{{\left (b x + a\right )}^{\frac{7}{3}}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.72426, size = 143, normalized size = 4.47 \begin{align*} -\frac{3 \,{\left (b x + a\right )}^{\frac{2}{3}}{\left (d x + c\right )}^{\frac{4}{3}}}{4 \,{\left (a^{2} b c - a^{3} d +{\left (b^{3} c - a b^{2} d\right )} x^{2} + 2 \,{\left (a b^{2} c - a^{2} b d\right )} x\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\sqrt [3]{c + d x}}{\left (a + b x\right )^{\frac{7}{3}}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{{\left (d x + c\right )}^{\frac{1}{3}}}{{\left (b x + a\right )}^{\frac{7}{3}}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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