Optimal. Leaf size=361 \[ \frac {(b c-a d)^3 (b e-a f)^3 (a+b x)^4}{4 b^7}+\frac {3 (b c-a d)^2 (b e-a f)^2 (b d e+b c f-2 a d f) (a+b x)^5}{5 b^7}+\frac {(b c-a d) (b e-a f) \left (5 a^2 d^2 f^2-5 a b d f (d e+c f)+b^2 \left (d^2 e^2+3 c d e f+c^2 f^2\right )\right ) (a+b x)^6}{2 b^7}+\frac {(b d e+b c f-2 a d f) \left (10 a^2 d^2 f^2-10 a b d f (d e+c f)+b^2 \left (d^2 e^2+8 c d e f+c^2 f^2\right )\right ) (a+b x)^7}{7 b^7}+\frac {3 d f \left (5 a^2 d^2 f^2-5 a b d f (d e+c f)+b^2 \left (d^2 e^2+3 c d e f+c^2 f^2\right )\right ) (a+b x)^8}{8 b^7}+\frac {d^2 f^2 (b d e+b c f-2 a d f) (a+b x)^9}{3 b^7}+\frac {d^3 f^3 (a+b x)^{10}}{10 b^7} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.46, antiderivative size = 361, normalized size of antiderivative = 1.00, 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 = {90}
\begin {gather*} \frac {3 d f (a+b x)^8 \left (5 a^2 d^2 f^2-5 a b d f (c f+d e)+b^2 \left (c^2 f^2+3 c d e f+d^2 e^2\right )\right )}{8 b^7}+\frac {(a+b x)^7 (-2 a d f+b c f+b d e) \left (10 a^2 d^2 f^2-10 a b d f (c f+d e)+b^2 \left (c^2 f^2+8 c d e f+d^2 e^2\right )\right )}{7 b^7}+\frac {(a+b x)^6 (b c-a d) (b e-a f) \left (5 a^2 d^2 f^2-5 a b d f (c f+d e)+b^2 \left (c^2 f^2+3 c d e f+d^2 e^2\right )\right )}{2 b^7}+\frac {d^2 f^2 (a+b x)^9 (-2 a d f+b c f+b d e)}{3 b^7}+\frac {3 (a+b x)^5 (b c-a d)^2 (b e-a f)^2 (-2 a d f+b c f+b d e)}{5 b^7}+\frac {(a+b x)^4 (b c-a d)^3 (b e-a f)^3}{4 b^7}+\frac {d^3 f^3 (a+b x)^{10}}{10 b^7} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 90
Rubi steps
\begin {align*} \int (a+b x)^3 (c+d x)^3 (e+f x)^3 \, dx &=\int \left (\frac {(b c-a d)^3 (b e-a f)^3 (a+b x)^3}{b^6}+\frac {3 (b c-a d)^2 (b e-a f)^2 (b d e+b c f-2 a d f) (a+b x)^4}{b^6}+\frac {3 (b c-a d) (b e-a f) \left (5 a^2 d^2 f^2-5 a b d f (d e+c f)+b^2 \left (d^2 e^2+3 c d e f+c^2 f^2\right )\right ) (a+b x)^5}{b^6}+\frac {(b d e+b c f-2 a d f) \left (b^2 d^2 e^2+8 b^2 c d e f-10 a b d^2 e f+b^2 c^2 f^2-10 a b c d f^2+10 a^2 d^2 f^2\right ) (a+b x)^6}{b^6}+\frac {3 d f \left (5 a^2 d^2 f^2-5 a b d f (d e+c f)+b^2 \left (d^2 e^2+3 c d e f+c^2 f^2\right )\right ) (a+b x)^7}{b^6}+\frac {3 d^2 f^2 (b d e+b c f-2 a d f) (a+b x)^8}{b^6}+\frac {d^3 f^3 (a+b x)^9}{b^6}\right ) \, dx\\ &=\frac {(b c-a d)^3 (b e-a f)^3 (a+b x)^4}{4 b^7}+\frac {3 (b c-a d)^2 (b e-a f)^2 (b d e+b c f-2 a d f) (a+b x)^5}{5 b^7}+\frac {(b c-a d) (b e-a f) \left (5 a^2 d^2 f^2-5 a b d f (d e+c f)+b^2 \left (d^2 e^2+3 c d e f+c^2 f^2\right )\right ) (a+b x)^6}{2 b^7}+\frac {(b d e+b c f-2 a d f) \left (10 a^2 d^2 f^2-10 a b d f (d e+c f)+b^2 \left (d^2 e^2+8 c d e f+c^2 f^2\right )\right ) (a+b x)^7}{7 b^7}+\frac {3 d f \left (5 a^2 d^2 f^2-5 a b d f (d e+c f)+b^2 \left (d^2 e^2+3 c d e f+c^2 f^2\right )\right ) (a+b x)^8}{8 b^7}+\frac {d^2 f^2 (b d e+b c f-2 a d f) (a+b x)^9}{3 b^7}+\frac {d^3 f^3 (a+b x)^{10}}{10 b^7}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.18, size = 653, normalized size = 1.81 \begin {gather*} a^3 c^3 e^3 x+\frac {3}{2} a^2 c^2 e^2 (b c e+a d e+a c f) x^2+a c e \left (b^2 c^2 e^2+3 a b c e (d e+c f)+a^2 \left (d^2 e^2+3 c d e f+c^2 f^2\right )\right ) x^3+\frac {1}{4} \left (b^3 c^3 e^3+9 a b^2 c^2 e^2 (d e+c f)+9 a^2 b c e \left (d^2 e^2+3 c d e f+c^2 f^2\right )+a^3 \left (d^3 e^3+9 c d^2 e^2 f+9 c^2 d e f^2+c^3 f^3\right )\right ) x^4+\frac {3}{5} \left (b^3 c^2 e^2 (d e+c f)+3 a b^2 c e \left (d^2 e^2+3 c d e f+c^2 f^2\right )+a^3 d f \left (d^2 e^2+3 c d e f+c^2 f^2\right )+a^2 b \left (d^3 e^3+9 c d^2 e^2 f+9 c^2 d e f^2+c^3 f^3\right )\right ) x^5+\frac {1}{2} \left (a^3 d^2 f^2 (d e+c f)+b^3 c e \left (d^2 e^2+3 c d e f+c^2 f^2\right )+3 a^2 b d f \left (d^2 e^2+3 c d e f+c^2 f^2\right )+a b^2 \left (d^3 e^3+9 c d^2 e^2 f+9 c^2 d e f^2+c^3 f^3\right )\right ) x^6+\frac {1}{7} \left (a^3 d^3 f^3+9 a^2 b d^2 f^2 (d e+c f)+9 a b^2 d f \left (d^2 e^2+3 c d e f+c^2 f^2\right )+b^3 \left (d^3 e^3+9 c d^2 e^2 f+9 c^2 d e f^2+c^3 f^3\right )\right ) x^7+\frac {3}{8} b d f \left (a^2 d^2 f^2+3 a b d f (d e+c f)+b^2 \left (d^2 e^2+3 c d e f+c^2 f^2\right )\right ) x^8+\frac {1}{3} b^2 d^2 f^2 (b d e+b c f+a d f) x^9+\frac {1}{10} b^3 d^3 f^3 x^{10} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(766\) vs.
\(2(347)=694\).
time = 0.12, size = 767, normalized size = 2.12 Too large to display
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 764 vs.
\(2 (356) = 712\).
time = 0.33, size = 764, normalized size = 2.12 \begin {gather*} \frac {1}{10} \, b^{3} d^{3} f^{3} x^{10} + \frac {1}{3} \, {\left (b^{3} d^{3} f^{2} e + {\left (b^{3} c d^{2} + a b^{2} d^{3}\right )} f^{3}\right )} x^{9} + \frac {3}{8} \, {\left (b^{3} d^{3} f e^{2} + {\left (b^{3} c^{2} d + 3 \, a b^{2} c d^{2} + a^{2} b d^{3}\right )} f^{3} + 3 \, {\left (b^{3} c d^{2} e + a b^{2} d^{3} e\right )} f^{2}\right )} x^{8} + \frac {1}{7} \, {\left (b^{3} d^{3} e^{3} + {\left (b^{3} c^{3} + 9 \, a b^{2} c^{2} d + 9 \, a^{2} b c d^{2} + a^{3} d^{3}\right )} f^{3} + 9 \, {\left (b^{3} c^{2} d e + 3 \, a b^{2} c d^{2} e + a^{2} b d^{3} e\right )} f^{2} + 9 \, {\left (b^{3} c d^{2} e^{2} + a b^{2} d^{3} e^{2}\right )} f\right )} x^{7} + a^{3} c^{3} x e^{3} + \frac {1}{2} \, {\left (b^{3} c d^{2} e^{3} + a b^{2} d^{3} e^{3} + {\left (a b^{2} c^{3} + 3 \, a^{2} b c^{2} d + a^{3} c d^{2}\right )} f^{3} + {\left (b^{3} c^{3} e + 9 \, a b^{2} c^{2} d e + 9 \, a^{2} b c d^{2} e + a^{3} d^{3} e\right )} f^{2} + 3 \, {\left (b^{3} c^{2} d e^{2} + 3 \, a b^{2} c d^{2} e^{2} + a^{2} b d^{3} e^{2}\right )} f\right )} x^{6} + \frac {3}{5} \, {\left (b^{3} c^{2} d e^{3} + 3 \, a b^{2} c d^{2} e^{3} + a^{2} b d^{3} e^{3} + {\left (a^{2} b c^{3} + a^{3} c^{2} d\right )} f^{3} + 3 \, {\left (a b^{2} c^{3} e + 3 \, a^{2} b c^{2} d e + a^{3} c d^{2} e\right )} f^{2} + {\left (b^{3} c^{3} e^{2} + 9 \, a b^{2} c^{2} d e^{2} + 9 \, a^{2} b c d^{2} e^{2} + a^{3} d^{3} e^{2}\right )} f\right )} x^{5} + \frac {1}{4} \, {\left (a^{3} c^{3} f^{3} + b^{3} c^{3} e^{3} + 9 \, a b^{2} c^{2} d e^{3} + 9 \, a^{2} b c d^{2} e^{3} + a^{3} d^{3} e^{3} + 9 \, {\left (a^{2} b c^{3} e + a^{3} c^{2} d e\right )} f^{2} + 9 \, {\left (a b^{2} c^{3} e^{2} + 3 \, a^{2} b c^{2} d e^{2} + a^{3} c d^{2} e^{2}\right )} f\right )} x^{4} + {\left (a^{3} c^{3} f^{2} e + a b^{2} c^{3} e^{3} + 3 \, a^{2} b c^{2} d e^{3} + a^{3} c d^{2} e^{3} + 3 \, {\left (a^{2} b c^{3} e^{2} + a^{3} c^{2} d e^{2}\right )} f\right )} x^{3} + \frac {3}{2} \, {\left (a^{3} c^{3} f e^{2} + a^{2} b c^{3} e^{3} + a^{3} c^{2} d e^{3}\right )} x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 743 vs.
\(2 (356) = 712\).
time = 1.06, size = 743, normalized size = 2.06 \begin {gather*} \frac {1}{10} \, b^{3} d^{3} f^{3} x^{10} + \frac {1}{4} \, a^{3} c^{3} f^{3} x^{4} + \frac {1}{3} \, {\left (b^{3} c d^{2} + a b^{2} d^{3}\right )} f^{3} x^{9} + \frac {3}{8} \, {\left (b^{3} c^{2} d + 3 \, a b^{2} c d^{2} + a^{2} b d^{3}\right )} f^{3} x^{8} + \frac {1}{7} \, {\left (b^{3} c^{3} + 9 \, a b^{2} c^{2} d + 9 \, a^{2} b c d^{2} + a^{3} d^{3}\right )} f^{3} x^{7} + \frac {1}{2} \, {\left (a b^{2} c^{3} + 3 \, a^{2} b c^{2} d + a^{3} c d^{2}\right )} f^{3} x^{6} + \frac {3}{5} \, {\left (a^{2} b c^{3} + a^{3} c^{2} d\right )} f^{3} x^{5} + \frac {1}{140} \, {\left (20 \, b^{3} d^{3} x^{7} + 140 \, a^{3} c^{3} x + 70 \, {\left (b^{3} c d^{2} + a b^{2} d^{3}\right )} x^{6} + 84 \, {\left (b^{3} c^{2} d + 3 \, a b^{2} c d^{2} + a^{2} b d^{3}\right )} x^{5} + 35 \, {\left (b^{3} c^{3} + 9 \, a b^{2} c^{2} d + 9 \, a^{2} b c d^{2} + a^{3} d^{3}\right )} x^{4} + 140 \, {\left (a b^{2} c^{3} + 3 \, a^{2} b c^{2} d + a^{3} c d^{2}\right )} x^{3} + 210 \, {\left (a^{2} b c^{3} + a^{3} c^{2} d\right )} x^{2}\right )} e^{3} + \frac {3}{280} \, {\left (35 \, b^{3} d^{3} f x^{8} + 140 \, a^{3} c^{3} f x^{2} + 120 \, {\left (b^{3} c d^{2} + a b^{2} d^{3}\right )} f x^{7} + 140 \, {\left (b^{3} c^{2} d + 3 \, a b^{2} c d^{2} + a^{2} b d^{3}\right )} f x^{6} + 56 \, {\left (b^{3} c^{3} + 9 \, a b^{2} c^{2} d + 9 \, a^{2} b c d^{2} + a^{3} d^{3}\right )} f x^{5} + 210 \, {\left (a b^{2} c^{3} + 3 \, a^{2} b c^{2} d + a^{3} c d^{2}\right )} f x^{4} + 280 \, {\left (a^{2} b c^{3} + a^{3} c^{2} d\right )} f x^{3}\right )} e^{2} + \frac {1}{840} \, {\left (280 \, b^{3} d^{3} f^{2} x^{9} + 840 \, a^{3} c^{3} f^{2} x^{3} + 945 \, {\left (b^{3} c d^{2} + a b^{2} d^{3}\right )} f^{2} x^{8} + 1080 \, {\left (b^{3} c^{2} d + 3 \, a b^{2} c d^{2} + a^{2} b d^{3}\right )} f^{2} x^{7} + 420 \, {\left (b^{3} c^{3} + 9 \, a b^{2} c^{2} d + 9 \, a^{2} b c d^{2} + a^{3} d^{3}\right )} f^{2} x^{6} + 1512 \, {\left (a b^{2} c^{3} + 3 \, a^{2} b c^{2} d + a^{3} c d^{2}\right )} f^{2} x^{5} + 1890 \, {\left (a^{2} b c^{3} + a^{3} c^{2} d\right )} f^{2} x^{4}\right )} e \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 1018 vs.
\(2 (364) = 728\).
time = 0.06, size = 1018, normalized size = 2.82 \begin {gather*} a^{3} c^{3} e^{3} x + \frac {b^{3} d^{3} f^{3} x^{10}}{10} + x^{9} \left (\frac {a b^{2} d^{3} f^{3}}{3} + \frac {b^{3} c d^{2} f^{3}}{3} + \frac {b^{3} d^{3} e f^{2}}{3}\right ) + x^{8} \cdot \left (\frac {3 a^{2} b d^{3} f^{3}}{8} + \frac {9 a b^{2} c d^{2} f^{3}}{8} + \frac {9 a b^{2} d^{3} e f^{2}}{8} + \frac {3 b^{3} c^{2} d f^{3}}{8} + \frac {9 b^{3} c d^{2} e f^{2}}{8} + \frac {3 b^{3} d^{3} e^{2} f}{8}\right ) + x^{7} \left (\frac {a^{3} d^{3} f^{3}}{7} + \frac {9 a^{2} b c d^{2} f^{3}}{7} + \frac {9 a^{2} b d^{3} e f^{2}}{7} + \frac {9 a b^{2} c^{2} d f^{3}}{7} + \frac {27 a b^{2} c d^{2} e f^{2}}{7} + \frac {9 a b^{2} d^{3} e^{2} f}{7} + \frac {b^{3} c^{3} f^{3}}{7} + \frac {9 b^{3} c^{2} d e f^{2}}{7} + \frac {9 b^{3} c d^{2} e^{2} f}{7} + \frac {b^{3} d^{3} e^{3}}{7}\right ) + x^{6} \left (\frac {a^{3} c d^{2} f^{3}}{2} + \frac {a^{3} d^{3} e f^{2}}{2} + \frac {3 a^{2} b c^{2} d f^{3}}{2} + \frac {9 a^{2} b c d^{2} e f^{2}}{2} + \frac {3 a^{2} b d^{3} e^{2} f}{2} + \frac {a b^{2} c^{3} f^{3}}{2} + \frac {9 a b^{2} c^{2} d e f^{2}}{2} + \frac {9 a b^{2} c d^{2} e^{2} f}{2} + \frac {a b^{2} d^{3} e^{3}}{2} + \frac {b^{3} c^{3} e f^{2}}{2} + \frac {3 b^{3} c^{2} d e^{2} f}{2} + \frac {b^{3} c d^{2} e^{3}}{2}\right ) + x^{5} \cdot \left (\frac {3 a^{3} c^{2} d f^{3}}{5} + \frac {9 a^{3} c d^{2} e f^{2}}{5} + \frac {3 a^{3} d^{3} e^{2} f}{5} + \frac {3 a^{2} b c^{3} f^{3}}{5} + \frac {27 a^{2} b c^{2} d e f^{2}}{5} + \frac {27 a^{2} b c d^{2} e^{2} f}{5} + \frac {3 a^{2} b d^{3} e^{3}}{5} + \frac {9 a b^{2} c^{3} e f^{2}}{5} + \frac {27 a b^{2} c^{2} d e^{2} f}{5} + \frac {9 a b^{2} c d^{2} e^{3}}{5} + \frac {3 b^{3} c^{3} e^{2} f}{5} + \frac {3 b^{3} c^{2} d e^{3}}{5}\right ) + x^{4} \left (\frac {a^{3} c^{3} f^{3}}{4} + \frac {9 a^{3} c^{2} d e f^{2}}{4} + \frac {9 a^{3} c d^{2} e^{2} f}{4} + \frac {a^{3} d^{3} e^{3}}{4} + \frac {9 a^{2} b c^{3} e f^{2}}{4} + \frac {27 a^{2} b c^{2} d e^{2} f}{4} + \frac {9 a^{2} b c d^{2} e^{3}}{4} + \frac {9 a b^{2} c^{3} e^{2} f}{4} + \frac {9 a b^{2} c^{2} d e^{3}}{4} + \frac {b^{3} c^{3} e^{3}}{4}\right ) + x^{3} \left (a^{3} c^{3} e f^{2} + 3 a^{3} c^{2} d e^{2} f + a^{3} c d^{2} e^{3} + 3 a^{2} b c^{3} e^{2} f + 3 a^{2} b c^{2} d e^{3} + a b^{2} c^{3} e^{3}\right ) + x^{2} \cdot \left (\frac {3 a^{3} c^{3} e^{2} f}{2} + \frac {3 a^{3} c^{2} d e^{3}}{2} + \frac {3 a^{2} b c^{3} e^{3}}{2}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 971 vs.
\(2 (356) = 712\).
time = 0.57, size = 971, normalized size = 2.69 \begin {gather*} \frac {1}{10} \, b^{3} d^{3} f^{3} x^{10} + \frac {1}{3} \, b^{3} c d^{2} f^{3} x^{9} + \frac {1}{3} \, a b^{2} d^{3} f^{3} x^{9} + \frac {1}{3} \, b^{3} d^{3} f^{2} x^{9} e + \frac {3}{8} \, b^{3} c^{2} d f^{3} x^{8} + \frac {9}{8} \, a b^{2} c d^{2} f^{3} x^{8} + \frac {3}{8} \, a^{2} b d^{3} f^{3} x^{8} + \frac {9}{8} \, b^{3} c d^{2} f^{2} x^{8} e + \frac {9}{8} \, a b^{2} d^{3} f^{2} x^{8} e + \frac {1}{7} \, b^{3} c^{3} f^{3} x^{7} + \frac {9}{7} \, a b^{2} c^{2} d f^{3} x^{7} + \frac {9}{7} \, a^{2} b c d^{2} f^{3} x^{7} + \frac {1}{7} \, a^{3} d^{3} f^{3} x^{7} + \frac {3}{8} \, b^{3} d^{3} f x^{8} e^{2} + \frac {9}{7} \, b^{3} c^{2} d f^{2} x^{7} e + \frac {27}{7} \, a b^{2} c d^{2} f^{2} x^{7} e + \frac {9}{7} \, a^{2} b d^{3} f^{2} x^{7} e + \frac {1}{2} \, a b^{2} c^{3} f^{3} x^{6} + \frac {3}{2} \, a^{2} b c^{2} d f^{3} x^{6} + \frac {1}{2} \, a^{3} c d^{2} f^{3} x^{6} + \frac {9}{7} \, b^{3} c d^{2} f x^{7} e^{2} + \frac {9}{7} \, a b^{2} d^{3} f x^{7} e^{2} + \frac {1}{2} \, b^{3} c^{3} f^{2} x^{6} e + \frac {9}{2} \, a b^{2} c^{2} d f^{2} x^{6} e + \frac {9}{2} \, a^{2} b c d^{2} f^{2} x^{6} e + \frac {1}{2} \, a^{3} d^{3} f^{2} x^{6} e + \frac {3}{5} \, a^{2} b c^{3} f^{3} x^{5} + \frac {3}{5} \, a^{3} c^{2} d f^{3} x^{5} + \frac {1}{7} \, b^{3} d^{3} x^{7} e^{3} + \frac {3}{2} \, b^{3} c^{2} d f x^{6} e^{2} + \frac {9}{2} \, a b^{2} c d^{2} f x^{6} e^{2} + \frac {3}{2} \, a^{2} b d^{3} f x^{6} e^{2} + \frac {9}{5} \, a b^{2} c^{3} f^{2} x^{5} e + \frac {27}{5} \, a^{2} b c^{2} d f^{2} x^{5} e + \frac {9}{5} \, a^{3} c d^{2} f^{2} x^{5} e + \frac {1}{4} \, a^{3} c^{3} f^{3} x^{4} + \frac {1}{2} \, b^{3} c d^{2} x^{6} e^{3} + \frac {1}{2} \, a b^{2} d^{3} x^{6} e^{3} + \frac {3}{5} \, b^{3} c^{3} f x^{5} e^{2} + \frac {27}{5} \, a b^{2} c^{2} d f x^{5} e^{2} + \frac {27}{5} \, a^{2} b c d^{2} f x^{5} e^{2} + \frac {3}{5} \, a^{3} d^{3} f x^{5} e^{2} + \frac {9}{4} \, a^{2} b c^{3} f^{2} x^{4} e + \frac {9}{4} \, a^{3} c^{2} d f^{2} x^{4} e + \frac {3}{5} \, b^{3} c^{2} d x^{5} e^{3} + \frac {9}{5} \, a b^{2} c d^{2} x^{5} e^{3} + \frac {3}{5} \, a^{2} b d^{3} x^{5} e^{3} + \frac {9}{4} \, a b^{2} c^{3} f x^{4} e^{2} + \frac {27}{4} \, a^{2} b c^{2} d f x^{4} e^{2} + \frac {9}{4} \, a^{3} c d^{2} f x^{4} e^{2} + a^{3} c^{3} f^{2} x^{3} e + \frac {1}{4} \, b^{3} c^{3} x^{4} e^{3} + \frac {9}{4} \, a b^{2} c^{2} d x^{4} e^{3} + \frac {9}{4} \, a^{2} b c d^{2} x^{4} e^{3} + \frac {1}{4} \, a^{3} d^{3} x^{4} e^{3} + 3 \, a^{2} b c^{3} f x^{3} e^{2} + 3 \, a^{3} c^{2} d f x^{3} e^{2} + a b^{2} c^{3} x^{3} e^{3} + 3 \, a^{2} b c^{2} d x^{3} e^{3} + a^{3} c d^{2} x^{3} e^{3} + \frac {3}{2} \, a^{3} c^{3} f x^{2} e^{2} + \frac {3}{2} \, a^{2} b c^{3} x^{2} e^{3} + \frac {3}{2} \, a^{3} c^{2} d x^{2} e^{3} + a^{3} c^{3} x e^{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 1.23, size = 787, normalized size = 2.18 \begin {gather*} x^7\,\left (\frac {a^3\,d^3\,f^3}{7}+\frac {9\,a^2\,b\,c\,d^2\,f^3}{7}+\frac {9\,a^2\,b\,d^3\,e\,f^2}{7}+\frac {9\,a\,b^2\,c^2\,d\,f^3}{7}+\frac {27\,a\,b^2\,c\,d^2\,e\,f^2}{7}+\frac {9\,a\,b^2\,d^3\,e^2\,f}{7}+\frac {b^3\,c^3\,f^3}{7}+\frac {9\,b^3\,c^2\,d\,e\,f^2}{7}+\frac {9\,b^3\,c\,d^2\,e^2\,f}{7}+\frac {b^3\,d^3\,e^3}{7}\right )+x^5\,\left (\frac {3\,a^3\,c^2\,d\,f^3}{5}+\frac {9\,a^3\,c\,d^2\,e\,f^2}{5}+\frac {3\,a^3\,d^3\,e^2\,f}{5}+\frac {3\,a^2\,b\,c^3\,f^3}{5}+\frac {27\,a^2\,b\,c^2\,d\,e\,f^2}{5}+\frac {27\,a^2\,b\,c\,d^2\,e^2\,f}{5}+\frac {3\,a^2\,b\,d^3\,e^3}{5}+\frac {9\,a\,b^2\,c^3\,e\,f^2}{5}+\frac {27\,a\,b^2\,c^2\,d\,e^2\,f}{5}+\frac {9\,a\,b^2\,c\,d^2\,e^3}{5}+\frac {3\,b^3\,c^3\,e^2\,f}{5}+\frac {3\,b^3\,c^2\,d\,e^3}{5}\right )+x^6\,\left (\frac {a^3\,c\,d^2\,f^3}{2}+\frac {a^3\,d^3\,e\,f^2}{2}+\frac {3\,a^2\,b\,c^2\,d\,f^3}{2}+\frac {9\,a^2\,b\,c\,d^2\,e\,f^2}{2}+\frac {3\,a^2\,b\,d^3\,e^2\,f}{2}+\frac {a\,b^2\,c^3\,f^3}{2}+\frac {9\,a\,b^2\,c^2\,d\,e\,f^2}{2}+\frac {9\,a\,b^2\,c\,d^2\,e^2\,f}{2}+\frac {a\,b^2\,d^3\,e^3}{2}+\frac {b^3\,c^3\,e\,f^2}{2}+\frac {3\,b^3\,c^2\,d\,e^2\,f}{2}+\frac {b^3\,c\,d^2\,e^3}{2}\right )+x^4\,\left (\frac {a^3\,c^3\,f^3}{4}+\frac {9\,a^3\,c^2\,d\,e\,f^2}{4}+\frac {9\,a^3\,c\,d^2\,e^2\,f}{4}+\frac {a^3\,d^3\,e^3}{4}+\frac {9\,a^2\,b\,c^3\,e\,f^2}{4}+\frac {27\,a^2\,b\,c^2\,d\,e^2\,f}{4}+\frac {9\,a^2\,b\,c\,d^2\,e^3}{4}+\frac {9\,a\,b^2\,c^3\,e^2\,f}{4}+\frac {9\,a\,b^2\,c^2\,d\,e^3}{4}+\frac {b^3\,c^3\,e^3}{4}\right )+a^3\,c^3\,e^3\,x+\frac {b^3\,d^3\,f^3\,x^{10}}{10}+\frac {3\,a^2\,c^2\,e^2\,x^2\,\left (a\,c\,f+a\,d\,e+b\,c\,e\right )}{2}+\frac {b^2\,d^2\,f^2\,x^9\,\left (a\,d\,f+b\,c\,f+b\,d\,e\right )}{3}+a\,c\,e\,x^3\,\left (a^2\,c^2\,f^2+3\,a^2\,c\,d\,e\,f+a^2\,d^2\,e^2+3\,a\,b\,c^2\,e\,f+3\,a\,b\,c\,d\,e^2+b^2\,c^2\,e^2\right )+\frac {3\,b\,d\,f\,x^8\,\left (a^2\,d^2\,f^2+3\,a\,b\,c\,d\,f^2+3\,a\,b\,d^2\,e\,f+b^2\,c^2\,f^2+3\,b^2\,c\,d\,e\,f+b^2\,d^2\,e^2\right )}{8} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________