Optimal. Leaf size=32 \[ \frac{6 (a+b x)^{13/6}}{13 (c+d x)^{13/6} (b c-a d)} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0030103, 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} \[ \frac{6 (a+b x)^{13/6}}{13 (c+d x)^{13/6} (b c-a d)} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 37
Rubi steps
\begin{align*} \int \frac{(a+b x)^{7/6}}{(c+d x)^{19/6}} \, dx &=\frac{6 (a+b x)^{13/6}}{13 (b c-a d) (c+d x)^{13/6}}\\ \end{align*}
Mathematica [A] time = 0.0129569, size = 32, normalized size = 1. \[ \frac{6 (a+b x)^{13/6}}{13 (c+d x)^{13/6} (b c-a d)} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.004, size = 27, normalized size = 0.8 \begin{align*} -{\frac{6}{13\,ad-13\,bc} \left ( bx+a \right ) ^{{\frac{13}{6}}} \left ( dx+c \right ) ^{-{\frac{13}{6}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{{\left (b x + a\right )}^{\frac{7}{6}}}{{\left (d x + c\right )}^{\frac{19}{6}}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [B] time = 1.76069, size = 221, normalized size = 6.91 \begin{align*} \frac{6 \,{\left (b^{2} x^{2} + 2 \, a b x + a^{2}\right )}{\left (b x + a\right )}^{\frac{1}{6}}{\left (d x + c\right )}^{\frac{5}{6}}}{13 \,{\left (b c^{4} - a c^{3} d +{\left (b c d^{3} - a d^{4}\right )} x^{3} + 3 \,{\left (b c^{2} d^{2} - a c d^{3}\right )} x^{2} + 3 \,{\left (b c^{3} d - a c^{2} d^{2}\right )} x\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [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.
[In]
[Out]
________________________________________________________________________________________
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.
[In]
[Out]