Optimal. Leaf size=18 \[ -\frac {1}{2} (5-2 x)^7 (2+3 x)^4 \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.00, antiderivative size = 18, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {75}
\begin {gather*} -\frac {1}{2} (5-2 x)^7 (3 x+2)^4 \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 75
Rubi steps
\begin {align*} \int (5-2 x)^6 (2+3 x)^3 (-16+33 x) \, dx &=-\frac {1}{2} (5-2 x)^7 (2+3 x)^4\\ \end {align*}
________________________________________________________________________________________
Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(56\) vs. \(2(18)=36\).
time = 0.00, size = 56, normalized size = 3.11 \begin {gather*} -2000000 x-37500 x^2+3987500 x^3-\frac {98125 x^4}{2}-3816225 x^5+1497230 x^6+1235404 x^7-1256376 x^8+452304 x^9-76896 x^{10}+5184 x^{11} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(54\) vs.
\(2(16)=32\).
time = 0.09, size = 55, normalized size = 3.06
method | result | size |
gosper | \(\frac {x \left (10368 x^{10}-153792 x^{9}+904608 x^{8}-2512752 x^{7}+2470808 x^{6}+2994460 x^{5}-7632450 x^{4}-98125 x^{3}+7975000 x^{2}-75000 x -4000000\right )}{2}\) | \(54\) |
default | \(5184 x^{11}-76896 x^{10}+452304 x^{9}-1256376 x^{8}+1235404 x^{7}+1497230 x^{6}-3816225 x^{5}-\frac {98125}{2} x^{4}+3987500 x^{3}-37500 x^{2}-2000000 x\) | \(55\) |
norman | \(5184 x^{11}-76896 x^{10}+452304 x^{9}-1256376 x^{8}+1235404 x^{7}+1497230 x^{6}-3816225 x^{5}-\frac {98125}{2} x^{4}+3987500 x^{3}-37500 x^{2}-2000000 x\) | \(55\) |
risch | \(5184 x^{11}-76896 x^{10}+452304 x^{9}-1256376 x^{8}+1235404 x^{7}+1497230 x^{6}-3816225 x^{5}-\frac {98125}{2} x^{4}+3987500 x^{3}-37500 x^{2}-2000000 x\) | \(55\) |
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. 54 vs.
\(2 (16) = 32\).
time = 0.28, size = 54, normalized size = 3.00 \begin {gather*} 5184 \, x^{11} - 76896 \, x^{10} + 452304 \, x^{9} - 1256376 \, x^{8} + 1235404 \, x^{7} + 1497230 \, x^{6} - 3816225 \, x^{5} - \frac {98125}{2} \, x^{4} + 3987500 \, x^{3} - 37500 \, x^{2} - 2000000 \, x \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. 54 vs.
\(2 (16) = 32\).
time = 0.74, size = 54, normalized size = 3.00 \begin {gather*} 5184 \, x^{11} - 76896 \, x^{10} + 452304 \, x^{9} - 1256376 \, x^{8} + 1235404 \, x^{7} + 1497230 \, x^{6} - 3816225 \, x^{5} - \frac {98125}{2} \, x^{4} + 3987500 \, x^{3} - 37500 \, x^{2} - 2000000 \, x \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. 54 vs.
\(2 (15) = 30\).
time = 0.02, size = 54, normalized size = 3.00 \begin {gather*} 5184 x^{11} - 76896 x^{10} + 452304 x^{9} - 1256376 x^{8} + 1235404 x^{7} + 1497230 x^{6} - 3816225 x^{5} - \frac {98125 x^{4}}{2} + 3987500 x^{3} - 37500 x^{2} - 2000000 x \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. 54 vs.
\(2 (16) = 32\).
time = 0.94, size = 54, normalized size = 3.00 \begin {gather*} 5184 \, x^{11} - 76896 \, x^{10} + 452304 \, x^{9} - 1256376 \, x^{8} + 1235404 \, x^{7} + 1497230 \, x^{6} - 3816225 \, x^{5} - \frac {98125}{2} \, x^{4} + 3987500 \, x^{3} - 37500 \, x^{2} - 2000000 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.06, size = 54, normalized size = 3.00 \begin {gather*} 5184\,x^{11}-76896\,x^{10}+452304\,x^9-1256376\,x^8+1235404\,x^7+1497230\,x^6-3816225\,x^5-\frac {98125\,x^4}{2}+3987500\,x^3-37500\,x^2-2000000\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________