Optimal. Leaf size=55 \[ \frac{1}{2} a c x^2+\frac{1}{3} a d x^3+\frac{1}{4} a e x^4+\frac{1}{5} b c x^5+\frac{1}{6} b d x^6+\frac{1}{7} b e x^7 \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0376349, antiderivative size = 55, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 19, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.053, Rules used = {1628} \[ \frac{1}{2} a c x^2+\frac{1}{3} a d x^3+\frac{1}{4} a e x^4+\frac{1}{5} b c x^5+\frac{1}{6} b d x^6+\frac{1}{7} b e x^7 \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 1628
Rubi steps
\begin{align*} \int x \left (c+d x+e x^2\right ) \left (a+b x^3\right ) \, dx &=\int \left (a c x+a d x^2+a e x^3+b c x^4+b d x^5+b e x^6\right ) \, dx\\ &=\frac{1}{2} a c x^2+\frac{1}{3} a d x^3+\frac{1}{4} a e x^4+\frac{1}{5} b c x^5+\frac{1}{6} b d x^6+\frac{1}{7} b e x^7\\ \end{align*}
Mathematica [A] time = 0.0022814, size = 55, normalized size = 1. \[ \frac{1}{2} a c x^2+\frac{1}{3} a d x^3+\frac{1}{4} a e x^4+\frac{1}{5} b c x^5+\frac{1}{6} b d x^6+\frac{1}{7} b e x^7 \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.001, size = 44, normalized size = 0.8 \begin{align*}{\frac{ac{x}^{2}}{2}}+{\frac{ad{x}^{3}}{3}}+{\frac{ae{x}^{4}}{4}}+{\frac{bc{x}^{5}}{5}}+{\frac{bd{x}^{6}}{6}}+{\frac{be{x}^{7}}{7}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0.945712, size = 58, normalized size = 1.05 \begin{align*} \frac{1}{7} \, b e x^{7} + \frac{1}{6} \, b d x^{6} + \frac{1}{5} \, b c x^{5} + \frac{1}{4} \, a e x^{4} + \frac{1}{3} \, a d x^{3} + \frac{1}{2} \, a c x^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.28433, size = 112, normalized size = 2.04 \begin{align*} \frac{1}{7} x^{7} e b + \frac{1}{6} x^{6} d b + \frac{1}{5} x^{5} c b + \frac{1}{4} x^{4} e a + \frac{1}{3} x^{3} d a + \frac{1}{2} x^{2} c a \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.063504, size = 49, normalized size = 0.89 \begin{align*} \frac{a c x^{2}}{2} + \frac{a d x^{3}}{3} + \frac{a e x^{4}}{4} + \frac{b c x^{5}}{5} + \frac{b d x^{6}}{6} + \frac{b e x^{7}}{7} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.06715, size = 61, normalized size = 1.11 \begin{align*} \frac{1}{7} \, b x^{7} e + \frac{1}{6} \, b d x^{6} + \frac{1}{5} \, b c x^{5} + \frac{1}{4} \, a x^{4} e + \frac{1}{3} \, a d x^{3} + \frac{1}{2} \, a c x^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]