Optimal. Leaf size=37 \[ 3 a^2 b \log (x)-\frac{a^3}{3 x^3}+a b^2 x^3+\frac{b^3 x^6}{6} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0202246, antiderivative size = 37, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154, Rules used = {266, 43} \[ 3 a^2 b \log (x)-\frac{a^3}{3 x^3}+a b^2 x^3+\frac{b^3 x^6}{6} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 266
Rule 43
Rubi steps
\begin{align*} \int \frac{\left (a+b x^3\right )^3}{x^4} \, dx &=\frac{1}{3} \operatorname{Subst}\left (\int \frac{(a+b x)^3}{x^2} \, dx,x,x^3\right )\\ &=\frac{1}{3} \operatorname{Subst}\left (\int \left (3 a b^2+\frac{a^3}{x^2}+\frac{3 a^2 b}{x}+b^3 x\right ) \, dx,x,x^3\right )\\ &=-\frac{a^3}{3 x^3}+a b^2 x^3+\frac{b^3 x^6}{6}+3 a^2 b \log (x)\\ \end{align*}
Mathematica [A] time = 0.0042985, size = 37, normalized size = 1. \[ 3 a^2 b \log (x)-\frac{a^3}{3 x^3}+a b^2 x^3+\frac{b^3 x^6}{6} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.006, size = 34, normalized size = 0.9 \begin{align*} -{\frac{{a}^{3}}{3\,{x}^{3}}}+{x}^{3}a{b}^{2}+{\frac{{b}^{3}{x}^{6}}{6}}+3\,{a}^{2}b\ln \left ( x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0.946854, size = 46, normalized size = 1.24 \begin{align*} \frac{1}{6} \, b^{3} x^{6} + a b^{2} x^{3} + a^{2} b \log \left (x^{3}\right ) - \frac{a^{3}}{3 \, x^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.6092, size = 85, normalized size = 2.3 \begin{align*} \frac{b^{3} x^{9} + 6 \, a b^{2} x^{6} + 18 \, a^{2} b x^{3} \log \left (x\right ) - 2 \, a^{3}}{6 \, x^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.397016, size = 34, normalized size = 0.92 \begin{align*} - \frac{a^{3}}{3 x^{3}} + 3 a^{2} b \log{\left (x \right )} + a b^{2} x^{3} + \frac{b^{3} x^{6}}{6} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.11797, size = 59, normalized size = 1.59 \begin{align*} \frac{1}{6} \, b^{3} x^{6} + a b^{2} x^{3} + 3 \, a^{2} b \log \left ({\left | x \right |}\right ) - \frac{3 \, a^{2} b x^{3} + a^{3}}{3 \, x^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]