Optimal. Leaf size=30 \[ \frac {4 \sqrt [4]{a+b x}}{\sqrt [4]{c+d x} (b c-a d)} \]
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Rubi [A] time = 0.00, antiderivative size = 30, normalized size of antiderivative = 1.00, 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} \[ \frac {4 \sqrt [4]{a+b x}}{\sqrt [4]{c+d x} (b c-a d)} \]
Antiderivative was successfully verified.
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Rule 37
Rubi steps
\begin {align*} \int \frac {1}{(a+b x)^{3/4} (c+d x)^{5/4}} \, dx &=\frac {4 \sqrt [4]{a+b x}}{(b c-a d) \sqrt [4]{c+d x}}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 30, normalized size = 1.00 \[ \frac {4 \sqrt [4]{a+b x}}{\sqrt [4]{c+d x} (b c-a d)} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.65, size = 42, normalized size = 1.40 \[ \frac {4 \, {\left (b x + a\right )}^{\frac {1}{4}} {\left (d x + c\right )}^{\frac {3}{4}}}{b c^{2} - a c d + {\left (b c d - a d^{2}\right )} x} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{{\left (b x + a\right )}^{\frac {3}{4}} {\left (d x + c\right )}^{\frac {5}{4}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 27, normalized size = 0.90 \[ -\frac {4 \left (b x +a \right )^{\frac {1}{4}}}{\left (d x +c \right )^{\frac {1}{4}} \left (a d -b c \right )} \]
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 \[ \int \frac {1}{{\left (b x + a\right )}^{\frac {3}{4}} {\left (d x + c\right )}^{\frac {5}{4}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.03 \[ \int \frac {1}{{\left (a+b\,x\right )}^{3/4}\,{\left (c+d\,x\right )}^{5/4}} \,d x \]
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 \[ \int \frac {1}{\left (a + b x\right )^{\frac {3}{4}} \left (c + d x\right )^{\frac {5}{4}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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