Optimal. Leaf size=103 \[ \frac{1}{10} e x^{10} \left (e (a e+3 b d)+3 c d^2\right )+\frac{1}{7} d x^7 \left (3 e (a e+b d)+c d^2\right )+\frac{1}{4} d^2 x^4 (3 a e+b d)+a d^3 x+\frac{1}{13} e^2 x^{13} (b e+3 c d)+\frac{1}{16} c e^3 x^{16} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0969754, antiderivative size = 103, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.045, Rules used = {1407} \[ \frac{1}{10} e x^{10} \left (e (a e+3 b d)+3 c d^2\right )+\frac{1}{7} d x^7 \left (3 e (a e+b d)+c d^2\right )+\frac{1}{4} d^2 x^4 (3 a e+b d)+a d^3 x+\frac{1}{13} e^2 x^{13} (b e+3 c d)+\frac{1}{16} c e^3 x^{16} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 1407
Rubi steps
\begin{align*} \int \left (d+e x^3\right )^3 \left (a+b x^3+c x^6\right ) \, dx &=\int \left (a d^3+d^2 (b d+3 a e) x^3+d \left (c d^2+3 e (b d+a e)\right ) x^6+e \left (3 c d^2+e (3 b d+a e)\right ) x^9+e^2 (3 c d+b e) x^{12}+c e^3 x^{15}\right ) \, dx\\ &=a d^3 x+\frac{1}{4} d^2 (b d+3 a e) x^4+\frac{1}{7} d \left (c d^2+3 e (b d+a e)\right ) x^7+\frac{1}{10} e \left (3 c d^2+e (3 b d+a e)\right ) x^{10}+\frac{1}{13} e^2 (3 c d+b e) x^{13}+\frac{1}{16} c e^3 x^{16}\\ \end{align*}
Mathematica [A] time = 0.0285729, size = 104, normalized size = 1.01 \[ \frac{1}{10} e x^{10} \left (a e^2+3 b d e+3 c d^2\right )+\frac{1}{7} d x^7 \left (3 a e^2+3 b d e+c d^2\right )+\frac{1}{4} d^2 x^4 (3 a e+b d)+a d^3 x+\frac{1}{13} e^2 x^{13} (b e+3 c d)+\frac{1}{16} c e^3 x^{16} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.002, size = 103, normalized size = 1. \begin{align*}{\frac{c{e}^{3}{x}^{16}}{16}}+{\frac{ \left ({e}^{3}b+3\,cd{e}^{2} \right ){x}^{13}}{13}}+{\frac{ \left ({e}^{3}a+3\,d{e}^{2}b+3\,{d}^{2}ec \right ){x}^{10}}{10}}+{\frac{ \left ( 3\,ad{e}^{2}+3\,b{d}^{2}e+c{d}^{3} \right ){x}^{7}}{7}}+{\frac{ \left ( 3\,{d}^{2}ea+{d}^{3}b \right ){x}^{4}}{4}}+a{d}^{3}x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.05264, size = 138, normalized size = 1.34 \begin{align*} \frac{1}{16} \, c e^{3} x^{16} + \frac{1}{13} \,{\left (3 \, c d e^{2} + b e^{3}\right )} x^{13} + \frac{1}{10} \,{\left (3 \, c d^{2} e + 3 \, b d e^{2} + a e^{3}\right )} x^{10} + \frac{1}{7} \,{\left (c d^{3} + 3 \, b d^{2} e + 3 \, a d e^{2}\right )} x^{7} + a d^{3} x + \frac{1}{4} \,{\left (b d^{3} + 3 \, a d^{2} e\right )} x^{4} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.15749, size = 282, normalized size = 2.74 \begin{align*} \frac{1}{16} x^{16} e^{3} c + \frac{3}{13} x^{13} e^{2} d c + \frac{1}{13} x^{13} e^{3} b + \frac{3}{10} x^{10} e d^{2} c + \frac{3}{10} x^{10} e^{2} d b + \frac{1}{10} x^{10} e^{3} a + \frac{1}{7} x^{7} d^{3} c + \frac{3}{7} x^{7} e d^{2} b + \frac{3}{7} x^{7} e^{2} d a + \frac{1}{4} x^{4} d^{3} b + \frac{3}{4} x^{4} e d^{2} a + x d^{3} a \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.082, size = 117, normalized size = 1.14 \begin{align*} a d^{3} x + \frac{c e^{3} x^{16}}{16} + x^{13} \left (\frac{b e^{3}}{13} + \frac{3 c d e^{2}}{13}\right ) + x^{10} \left (\frac{a e^{3}}{10} + \frac{3 b d e^{2}}{10} + \frac{3 c d^{2} e}{10}\right ) + x^{7} \left (\frac{3 a d e^{2}}{7} + \frac{3 b d^{2} e}{7} + \frac{c d^{3}}{7}\right ) + x^{4} \left (\frac{3 a d^{2} e}{4} + \frac{b d^{3}}{4}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.07675, size = 147, normalized size = 1.43 \begin{align*} \frac{1}{16} \, c x^{16} e^{3} + \frac{3}{13} \, c d x^{13} e^{2} + \frac{1}{13} \, b x^{13} e^{3} + \frac{3}{10} \, c d^{2} x^{10} e + \frac{3}{10} \, b d x^{10} e^{2} + \frac{1}{10} \, a x^{10} e^{3} + \frac{1}{7} \, c d^{3} x^{7} + \frac{3}{7} \, b d^{2} x^{7} e + \frac{3}{7} \, a d x^{7} e^{2} + \frac{1}{4} \, b d^{3} x^{4} + \frac{3}{4} \, a d^{2} x^{4} e + a d^{3} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]