Optimal. Leaf size=41 \[ -\frac{\left (a+b x^3\right )^5 \sqrt{a^2+2 a b x^3+b^2 x^6}}{18 a x^{18}} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0184203, antiderivative size = 41, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 26, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077, Rules used = {1355, 264} \[ -\frac{\left (a+b x^3\right )^5 \sqrt{a^2+2 a b x^3+b^2 x^6}}{18 a x^{18}} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 1355
Rule 264
Rubi steps
\begin{align*} \int \frac{\left (a^2+2 a b x^3+b^2 x^6\right )^{5/2}}{x^{19}} \, dx &=\frac{\sqrt{a^2+2 a b x^3+b^2 x^6} \int \frac{\left (a b+b^2 x^3\right )^5}{x^{19}} \, dx}{b^4 \left (a b+b^2 x^3\right )}\\ &=-\frac{\left (a+b x^3\right )^5 \sqrt{a^2+2 a b x^3+b^2 x^6}}{18 a x^{18}}\\ \end{align*}
Mathematica [A] time = 0.0164692, size = 81, normalized size = 1.98 \[ -\frac{\sqrt{\left (a+b x^3\right )^2} \left (20 a^2 b^3 x^9+15 a^3 b^2 x^6+6 a^4 b x^3+a^5+15 a b^4 x^{12}+6 b^5 x^{15}\right )}{18 x^{18} \left (a+b x^3\right )} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [B] time = 0.005, size = 78, normalized size = 1.9 \begin{align*} -{\frac{6\,{b}^{5}{x}^{15}+15\,a{b}^{4}{x}^{12}+20\,{a}^{2}{b}^{3}{x}^{9}+15\,{a}^{3}{b}^{2}{x}^{6}+6\,{a}^{4}b{x}^{3}+{a}^{5}}{18\,{x}^{18} \left ( b{x}^{3}+a \right ) ^{5}} \left ( \left ( b{x}^{3}+a \right ) ^{2} \right ) ^{{\frac{5}{2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [F(-2)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: ValueError} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [B] time = 1.80635, size = 128, normalized size = 3.12 \begin{align*} -\frac{6 \, b^{5} x^{15} + 15 \, a b^{4} x^{12} + 20 \, a^{2} b^{3} x^{9} + 15 \, a^{3} b^{2} x^{6} + 6 \, a^{4} b x^{3} + a^{5}}{18 \, x^{18}} \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{\left (\left (a + b x^{3}\right )^{2}\right )^{\frac{5}{2}}}{x^{19}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [B] time = 1.12067, size = 143, normalized size = 3.49 \begin{align*} -\frac{6 \, b^{5} x^{15} \mathrm{sgn}\left (b x^{3} + a\right ) + 15 \, a b^{4} x^{12} \mathrm{sgn}\left (b x^{3} + a\right ) + 20 \, a^{2} b^{3} x^{9} \mathrm{sgn}\left (b x^{3} + a\right ) + 15 \, a^{3} b^{2} x^{6} \mathrm{sgn}\left (b x^{3} + a\right ) + 6 \, a^{4} b x^{3} \mathrm{sgn}\left (b x^{3} + a\right ) + a^{5} \mathrm{sgn}\left (b x^{3} + a\right )}{18 \, x^{18}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]