Optimal. Leaf size=16 \[ \frac{3 (a+b x)^{7/3}}{7 b} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0015413, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.111, Rules used = {32} \[ \frac{3 (a+b x)^{7/3}}{7 b} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 32
Rubi steps
\begin{align*} \int (a+b x)^{4/3} \, dx &=\frac{3 (a+b x)^{7/3}}{7 b}\\ \end{align*}
Mathematica [A] time = 0.012641, size = 16, normalized size = 1. \[ \frac{3 (a+b x)^{7/3}}{7 b} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.001, size = 13, normalized size = 0.8 \begin{align*}{\frac{3}{7\,b} \left ( bx+a \right ) ^{{\frac{7}{3}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.06903, size = 16, normalized size = 1. \begin{align*} \frac{3 \,{\left (b x + a\right )}^{\frac{7}{3}}}{7 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [B] time = 1.46872, size = 66, normalized size = 4.12 \begin{align*} \frac{3 \,{\left (b^{2} x^{2} + 2 \, a b x + a^{2}\right )}{\left (b x + a\right )}^{\frac{1}{3}}}{7 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.069693, size = 12, normalized size = 0.75 \begin{align*} \frac{3 \left (a + b x\right )^{\frac{7}{3}}}{7 b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.25241, size = 16, normalized size = 1. \begin{align*} \frac{3 \,{\left (b x + a\right )}^{\frac{7}{3}}}{7 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]