Optimal. Leaf size=30 \[ \frac{3 \sqrt [3]{a+b x}}{\sqrt [3]{c+d x} (b c-a d)} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0031594, antiderivative size = 30, 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} \[ \frac{3 \sqrt [3]{a+b x}}{\sqrt [3]{c+d x} (b c-a d)} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 37
Rubi steps
\begin{align*} \int \frac{1}{(a+b x)^{2/3} (c+d x)^{4/3}} \, dx &=\frac{3 \sqrt [3]{a+b x}}{(b c-a d) \sqrt [3]{c+d x}}\\ \end{align*}
Mathematica [A] time = 0.0080146, size = 30, normalized size = 1. \[ \frac{3 \sqrt [3]{a+b x}}{\sqrt [3]{c+d x} (b c-a d)} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.004, size = 27, normalized size = 0.9 \begin{align*} -3\,{\frac{\sqrt [3]{bx+a}}{\sqrt [3]{dx+c} \left ( ad-bc \right ) }} \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{1}{{\left (b x + a\right )}^{\frac{2}{3}}{\left (d x + c\right )}^{\frac{4}{3}}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 2.2954, size = 96, normalized size = 3.2 \begin{align*} \frac{3 \,{\left (b x + a\right )}^{\frac{1}{3}}{\left (d x + c\right )}^{\frac{2}{3}}}{b c^{2} - a c d +{\left (b c d - a d^{2}\right )} x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{\left (a + b x\right )^{\frac{2}{3}} \left (c + d x\right )^{\frac{4}{3}}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{{\left (b x + a\right )}^{\frac{2}{3}}{\left (d x + c\right )}^{\frac{4}{3}}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]