Optimal. Leaf size=81 \[ \frac {6 (a+b x)^{7/6} \left (\frac {b (c+d x)}{b c-a d}\right )^{5/6} \, _2F_1\left (\frac {7}{6},\frac {11}{6};\frac {13}{6};-\frac {d (a+b x)}{b c-a d}\right )}{7 (b c-a d) (c+d x)^{5/6}} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.02, antiderivative size = 81, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 2, integrand size = 19, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.105, Rules used = {72, 71}
\begin {gather*} \frac {6 (a+b x)^{7/6} \left (\frac {b (c+d x)}{b c-a d}\right )^{5/6} \, _2F_1\left (\frac {7}{6},\frac {11}{6};\frac {13}{6};-\frac {d (a+b x)}{b c-a d}\right )}{7 (c+d x)^{5/6} (b c-a d)} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 71
Rule 72
Rubi steps
\begin {align*} \int \frac {\sqrt [6]{a+b x}}{(c+d x)^{11/6}} \, dx &=\frac {\left (b \left (\frac {b (c+d x)}{b c-a d}\right )^{5/6}\right ) \int \frac {\sqrt [6]{a+b x}}{\left (\frac {b c}{b c-a d}+\frac {b d x}{b c-a d}\right )^{11/6}} \, dx}{(b c-a d) (c+d x)^{5/6}}\\ &=\frac {6 (a+b x)^{7/6} \left (\frac {b (c+d x)}{b c-a d}\right )^{5/6} \, _2F_1\left (\frac {7}{6},\frac {11}{6};\frac {13}{6};-\frac {d (a+b x)}{b c-a d}\right )}{7 (b c-a d) (c+d x)^{5/6}}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 10.05, size = 73, normalized size = 0.90 \begin {gather*} \frac {6 (a+b x)^{7/6} \left (\frac {b (c+d x)}{b c-a d}\right )^{11/6} \, _2F_1\left (\frac {7}{6},\frac {11}{6};\frac {13}{6};\frac {d (a+b x)}{-b c+a d}\right )}{7 b (c+d x)^{11/6}} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [F]
time = 0.06, size = 0, normalized size = 0.00 \[\int \frac {\left (b x +a \right )^{\frac {1}{6}}}{\left (d x +c \right )^{\frac {11}{6}}}\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\sqrt [6]{a + b x}}{\left (c + d x\right )^{\frac {11}{6}}}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [F]
time = 0.00, size = -1, normalized size = -0.01 \begin {gather*} \int \frac {{\left (a+b\,x\right )}^{1/6}}{{\left (c+d\,x\right )}^{11/6}} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________