Optimal. Leaf size=32 \[ -\frac{4 (c+d x)^{3/4}}{3 (a+b x)^{3/4} (b c-a d)} \]
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Rubi [A] time = 0.0032892, 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} \[ -\frac{4 (c+d x)^{3/4}}{3 (a+b x)^{3/4} (b c-a d)} \]
Antiderivative was successfully verified.
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Rule 37
Rubi steps
\begin{align*} \int \frac{1}{(a+b x)^{7/4} \sqrt [4]{c+d x}} \, dx &=-\frac{4 (c+d x)^{3/4}}{3 (b c-a d) (a+b x)^{3/4}}\\ \end{align*}
Mathematica [A] time = 0.0110246, size = 32, normalized size = 1. \[ -\frac{4 (c+d x)^{3/4}}{3 (a+b x)^{3/4} (b c-a d)} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 27, normalized size = 0.8 \begin{align*}{\frac{4}{3\,ad-3\,bc} \left ( dx+c \right ) ^{{\frac{3}{4}}} \left ( bx+a \right ) ^{-{\frac{3}{4}}}} \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{1}{{\left (b x + a\right )}^{\frac{7}{4}}{\left (d x + c\right )}^{\frac{1}{4}}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.93565, size = 100, normalized size = 3.12 \begin{align*} -\frac{4 \,{\left (b x + a\right )}^{\frac{1}{4}}{\left (d x + c\right )}^{\frac{3}{4}}}{3 \,{\left (a b c - a^{2} d +{\left (b^{2} c - a 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{1}{\left (a + b x\right )^{\frac{7}{4}} \sqrt [4]{c + d x}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F(-1)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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