Optimal. Leaf size=47 \[ \frac{1}{3} x^3 (a e+b d)+\frac{1}{2} a d x^2+\frac{1}{4} x^4 (b e+c d)+\frac{1}{5} c e x^5 \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0373681, antiderivative size = 47, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.059, Rules used = {765} \[ \frac{1}{3} x^3 (a e+b d)+\frac{1}{2} a d x^2+\frac{1}{4} x^4 (b e+c d)+\frac{1}{5} c e x^5 \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 765
Rubi steps
\begin{align*} \int x (d+e x) \left (a+b x+c x^2\right ) \, dx &=\int \left (a d x+(b d+a e) x^2+(c d+b e) x^3+c e x^4\right ) \, dx\\ &=\frac{1}{2} a d x^2+\frac{1}{3} (b d+a e) x^3+\frac{1}{4} (c d+b e) x^4+\frac{1}{5} c e x^5\\ \end{align*}
Mathematica [A] time = 0.0143395, size = 41, normalized size = 0.87 \[ \frac{1}{60} x^2 \left (20 x (a e+b d)+30 a d+15 x^2 (b e+c d)+12 c e x^3\right ) \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.001, size = 40, normalized size = 0.9 \begin{align*}{\frac{ad{x}^{2}}{2}}+{\frac{ \left ( ae+bd \right ){x}^{3}}{3}}+{\frac{ \left ( be+cd \right ){x}^{4}}{4}}+{\frac{ce{x}^{5}}{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.08952, size = 53, normalized size = 1.13 \begin{align*} \frac{1}{5} \, c e x^{5} + \frac{1}{4} \,{\left (c d + b e\right )} x^{4} + \frac{1}{2} \, a d x^{2} + \frac{1}{3} \,{\left (b d + a e\right )} x^{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.12767, size = 112, normalized size = 2.38 \begin{align*} \frac{1}{5} x^{5} e c + \frac{1}{4} x^{4} d c + \frac{1}{4} x^{4} e b + \frac{1}{3} x^{3} d b + \frac{1}{3} x^{3} e a + \frac{1}{2} x^{2} d a \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.062983, size = 42, normalized size = 0.89 \begin{align*} \frac{a d x^{2}}{2} + \frac{c e x^{5}}{5} + x^{4} \left (\frac{b e}{4} + \frac{c d}{4}\right ) + x^{3} \left (\frac{a e}{3} + \frac{b d}{3}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.13966, size = 62, normalized size = 1.32 \begin{align*} \frac{1}{5} \, c x^{5} e + \frac{1}{4} \, c d x^{4} + \frac{1}{4} \, b x^{4} e + \frac{1}{3} \, b d x^{3} + \frac{1}{3} \, a x^{3} e + \frac{1}{2} \, a d x^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]