Optimal. Leaf size=59 \[ \frac {3 a^2 (b x-a)^{2/3}}{2 b^3}+\frac {3 (b x-a)^{8/3}}{8 b^3}+\frac {6 a (b x-a)^{5/3}}{5 b^3} \]
________________________________________________________________________________________
Rubi [A] time = 0.01, antiderivative size = 59, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {43} \begin {gather*} \frac {3 a^2 (b x-a)^{2/3}}{2 b^3}+\frac {3 (b x-a)^{8/3}}{8 b^3}+\frac {6 a (b x-a)^{5/3}}{5 b^3} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 43
Rubi steps
\begin {align*} \int \frac {x^2}{\sqrt [3]{-a+b x}} \, dx &=\int \left (\frac {a^2}{b^2 \sqrt [3]{-a+b x}}+\frac {2 a (-a+b x)^{2/3}}{b^2}+\frac {(-a+b x)^{5/3}}{b^2}\right ) \, dx\\ &=\frac {3 a^2 (-a+b x)^{2/3}}{2 b^3}+\frac {6 a (-a+b x)^{5/3}}{5 b^3}+\frac {3 (-a+b x)^{8/3}}{8 b^3}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.02, size = 37, normalized size = 0.63 \begin {gather*} \frac {3 (b x-a)^{2/3} \left (9 a^2+6 a b x+5 b^2 x^2\right )}{40 b^3} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
IntegrateAlgebraic [A] time = 0.02, size = 51, normalized size = 0.86 \begin {gather*} \frac {3 \left (20 a^2 (b x-a)^{2/3}+5 (b x-a)^{8/3}+16 a (b x-a)^{5/3}\right )}{40 b^3} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.94, size = 33, normalized size = 0.56 \begin {gather*} \frac {3 \, {\left (5 \, b^{2} x^{2} + 6 \, a b x + 9 \, a^{2}\right )} {\left (b x - a\right )}^{\frac {2}{3}}}{40 \, b^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 1.07, size = 43, normalized size = 0.73 \begin {gather*} \frac {3 \, {\left (5 \, {\left (b x - a\right )}^{\frac {8}{3}} + 16 \, {\left (b x - a\right )}^{\frac {5}{3}} a + 20 \, {\left (b x - a\right )}^{\frac {2}{3}} a^{2}\right )}}{40 \, b^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.00, size = 34, normalized size = 0.58 \begin {gather*} \frac {3 \left (5 b^{2} x^{2}+6 a b x +9 a^{2}\right ) \left (b x -a \right )^{\frac {2}{3}}}{40 b^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 1.33, size = 47, normalized size = 0.80 \begin {gather*} \frac {3 \, {\left (b x - a\right )}^{\frac {8}{3}}}{8 \, b^{3}} + \frac {6 \, {\left (b x - a\right )}^{\frac {5}{3}} a}{5 \, b^{3}} + \frac {3 \, {\left (b x - a\right )}^{\frac {2}{3}} a^{2}}{2 \, b^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.04, size = 43, normalized size = 0.73 \begin {gather*} \frac {48\,a\,{\left (b\,x-a\right )}^{5/3}+15\,{\left (b\,x-a\right )}^{8/3}+60\,a^2\,{\left (b\,x-a\right )}^{2/3}}{40\,b^3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [C] time = 1.90, size = 1326, normalized size = 22.47
result too large to display
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________