Integrand size = 19, antiderivative size = 74 \[ \int (a+b x)^{5/6} (c+d x)^{5/6} \, dx=\frac {6 (a+b x)^{11/6} (c+d x)^{5/6} \operatorname {Hypergeometric2F1}\left (-\frac {5}{6},\frac {11}{6},\frac {17}{6},-\frac {d (a+b x)}{b c-a d}\right )}{11 b \left (\frac {b (c+d x)}{b c-a d}\right )^{5/6}} \]
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Time = 0.02 (sec) , antiderivative size = 74, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.105, Rules used = {72, 71} \[ \int (a+b x)^{5/6} (c+d x)^{5/6} \, dx=\frac {6 (a+b x)^{11/6} (c+d x)^{5/6} \operatorname {Hypergeometric2F1}\left (-\frac {5}{6},\frac {11}{6},\frac {17}{6},-\frac {d (a+b x)}{b c-a d}\right )}{11 b \left (\frac {b (c+d x)}{b c-a d}\right )^{5/6}} \]
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Rule 71
Rule 72
Rubi steps \begin{align*} \text {integral}& = \frac {(c+d x)^{5/6} \int (a+b x)^{5/6} \left (\frac {b c}{b c-a d}+\frac {b d x}{b c-a d}\right )^{5/6} \, dx}{\left (\frac {b (c+d x)}{b c-a d}\right )^{5/6}} \\ & = \frac {6 (a+b x)^{11/6} (c+d x)^{5/6} \, _2F_1\left (-\frac {5}{6},\frac {11}{6};\frac {17}{6};-\frac {d (a+b x)}{b c-a d}\right )}{11 b \left (\frac {b (c+d x)}{b c-a d}\right )^{5/6}} \\ \end{align*}
Time = 0.02 (sec) , antiderivative size = 73, normalized size of antiderivative = 0.99 \[ \int (a+b x)^{5/6} (c+d x)^{5/6} \, dx=\frac {6 (a+b x)^{11/6} (c+d x)^{5/6} \operatorname {Hypergeometric2F1}\left (-\frac {5}{6},\frac {11}{6},\frac {17}{6},\frac {d (a+b x)}{-b c+a d}\right )}{11 b \left (\frac {b (c+d x)}{b c-a d}\right )^{5/6}} \]
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\[\int \left (b x +a \right )^{\frac {5}{6}} \left (d x +c \right )^{\frac {5}{6}}d x\]
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\[ \int (a+b x)^{5/6} (c+d x)^{5/6} \, dx=\int { {\left (b x + a\right )}^{\frac {5}{6}} {\left (d x + c\right )}^{\frac {5}{6}} \,d x } \]
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\[ \int (a+b x)^{5/6} (c+d x)^{5/6} \, dx=\int \left (a + b x\right )^{\frac {5}{6}} \left (c + d x\right )^{\frac {5}{6}}\, dx \]
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\[ \int (a+b x)^{5/6} (c+d x)^{5/6} \, dx=\int { {\left (b x + a\right )}^{\frac {5}{6}} {\left (d x + c\right )}^{\frac {5}{6}} \,d x } \]
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Timed out. \[ \int (a+b x)^{5/6} (c+d x)^{5/6} \, dx=\text {Timed out} \]
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Timed out. \[ \int (a+b x)^{5/6} (c+d x)^{5/6} \, dx=\int {\left (a+b\,x\right )}^{5/6}\,{\left (c+d\,x\right )}^{5/6} \,d x \]
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