Optimal. Leaf size=121 \[ \frac{5}{9} x^9 (20 d-9 e)-\frac{3}{8} x^8 (15 d-37 e)+\frac{37}{7} x^7 (3 d-e)-\frac{37}{6} x^6 (d-4 e)+\frac{1}{5} x^5 (148 d+65 e)+\frac{1}{4} x^4 (65 d+107 e)+\frac{1}{3} x^3 (107 d+33 e)+\frac{3}{2} x^2 (11 d+6 e)+18 d x+10 e x^{10} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.160346, antiderivative size = 121, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 36, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.028, Rules used = {1628} \[ \frac{5}{9} x^9 (20 d-9 e)-\frac{3}{8} x^8 (15 d-37 e)+\frac{37}{7} x^7 (3 d-e)-\frac{37}{6} x^6 (d-4 e)+\frac{1}{5} x^5 (148 d+65 e)+\frac{1}{4} x^4 (65 d+107 e)+\frac{1}{3} x^3 (107 d+33 e)+\frac{3}{2} x^2 (11 d+6 e)+18 d x+10 e x^{10} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 1628
Rubi steps
\begin{align*} \int (d+e x) \left (3+2 x+5 x^2\right )^2 \left (2+x+3 x^2-5 x^3+4 x^4\right ) \, dx &=\int \left (18 d+3 (11 d+6 e) x+(107 d+33 e) x^2+(65 d+107 e) x^3+(148 d+65 e) x^4-37 (d-4 e) x^5+37 (3 d-e) x^6-3 (15 d-37 e) x^7+5 (20 d-9 e) x^8+100 e x^9\right ) \, dx\\ &=18 d x+\frac{3}{2} (11 d+6 e) x^2+\frac{1}{3} (107 d+33 e) x^3+\frac{1}{4} (65 d+107 e) x^4+\frac{1}{5} (148 d+65 e) x^5-\frac{37}{6} (d-4 e) x^6+\frac{37}{7} (3 d-e) x^7-\frac{3}{8} (15 d-37 e) x^8+\frac{5}{9} (20 d-9 e) x^9+10 e x^{10}\\ \end{align*}
Mathematica [A] time = 0.0175363, size = 121, normalized size = 1. \[ \frac{5}{9} x^9 (20 d-9 e)-\frac{3}{8} x^8 (15 d-37 e)+\frac{37}{7} x^7 (3 d-e)-\frac{37}{6} x^6 (d-4 e)+\frac{1}{5} x^5 (148 d+65 e)+\frac{1}{4} x^4 (65 d+107 e)+\frac{1}{3} x^3 (107 d+33 e)+\frac{3}{2} x^2 (11 d+6 e)+18 d x+10 e x^{10} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.043, size = 108, normalized size = 0.9 \begin{align*} 10\,e{x}^{10}+{\frac{ \left ( 100\,d-45\,e \right ){x}^{9}}{9}}+{\frac{ \left ( -45\,d+111\,e \right ){x}^{8}}{8}}+{\frac{ \left ( 111\,d-37\,e \right ){x}^{7}}{7}}+{\frac{ \left ( -37\,d+148\,e \right ){x}^{6}}{6}}+{\frac{ \left ( 148\,d+65\,e \right ){x}^{5}}{5}}+{\frac{ \left ( 65\,d+107\,e \right ){x}^{4}}{4}}+{\frac{ \left ( 107\,d+33\,e \right ){x}^{3}}{3}}+{\frac{ \left ( 33\,d+18\,e \right ){x}^{2}}{2}}+18\,dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0.964713, size = 142, normalized size = 1.17 \begin{align*} 10 \, e x^{10} + \frac{5}{9} \,{\left (20 \, d - 9 \, e\right )} x^{9} - \frac{3}{8} \,{\left (15 \, d - 37 \, e\right )} x^{8} + \frac{37}{7} \,{\left (3 \, d - e\right )} x^{7} - \frac{37}{6} \,{\left (d - 4 \, e\right )} x^{6} + \frac{1}{5} \,{\left (148 \, d + 65 \, e\right )} x^{5} + \frac{1}{4} \,{\left (65 \, d + 107 \, e\right )} x^{4} + \frac{1}{3} \,{\left (107 \, d + 33 \, e\right )} x^{3} + \frac{3}{2} \,{\left (11 \, d + 6 \, e\right )} x^{2} + 18 \, d x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 0.871077, size = 302, normalized size = 2.5 \begin{align*} 10 x^{10} e - 5 x^{9} e + \frac{100}{9} x^{9} d + \frac{111}{8} x^{8} e - \frac{45}{8} x^{8} d - \frac{37}{7} x^{7} e + \frac{111}{7} x^{7} d + \frac{74}{3} x^{6} e - \frac{37}{6} x^{6} d + 13 x^{5} e + \frac{148}{5} x^{5} d + \frac{107}{4} x^{4} e + \frac{65}{4} x^{4} d + 11 x^{3} e + \frac{107}{3} x^{3} d + 9 x^{2} e + \frac{33}{2} x^{2} d + 18 x d \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.089445, size = 112, normalized size = 0.93 \begin{align*} 18 d x + 10 e x^{10} + x^{9} \left (\frac{100 d}{9} - 5 e\right ) + x^{8} \left (- \frac{45 d}{8} + \frac{111 e}{8}\right ) + x^{7} \left (\frac{111 d}{7} - \frac{37 e}{7}\right ) + x^{6} \left (- \frac{37 d}{6} + \frac{74 e}{3}\right ) + x^{5} \left (\frac{148 d}{5} + 13 e\right ) + x^{4} \left (\frac{65 d}{4} + \frac{107 e}{4}\right ) + x^{3} \left (\frac{107 d}{3} + 11 e\right ) + x^{2} \left (\frac{33 d}{2} + 9 e\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.13902, size = 157, normalized size = 1.3 \begin{align*} 10 \, x^{10} e + \frac{100}{9} \, d x^{9} - 5 \, x^{9} e - \frac{45}{8} \, d x^{8} + \frac{111}{8} \, x^{8} e + \frac{111}{7} \, d x^{7} - \frac{37}{7} \, x^{7} e - \frac{37}{6} \, d x^{6} + \frac{74}{3} \, x^{6} e + \frac{148}{5} \, d x^{5} + 13 \, x^{5} e + \frac{65}{4} \, d x^{4} + \frac{107}{4} \, x^{4} e + \frac{107}{3} \, d x^{3} + 11 \, x^{3} e + \frac{33}{2} \, d x^{2} + 9 \, x^{2} e + 18 \, d x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]