Optimal. Leaf size=34 \[ -\frac {7}{108} (2+3 x)^4+\frac {37}{135} (2+3 x)^5-\frac {5}{81} (2+3 x)^6 \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.01, antiderivative size = 34, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.056, Rules used = {78}
\begin {gather*} -\frac {5}{81} (3 x+2)^6+\frac {37}{135} (3 x+2)^5-\frac {7}{108} (3 x+2)^4 \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 78
Rubi steps
\begin {align*} \int (1-2 x) (2+3 x)^3 (3+5 x) \, dx &=\int \left (-\frac {7}{9} (2+3 x)^3+\frac {37}{9} (2+3 x)^4-\frac {10}{9} (2+3 x)^5\right ) \, dx\\ &=-\frac {7}{108} (2+3 x)^4+\frac {37}{135} (2+3 x)^5-\frac {5}{81} (2+3 x)^6\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.00, size = 35, normalized size = 1.03 \begin {gather*} 24 x+50 x^2+\frac {46 x^3}{3}-\frac {333 x^4}{4}-\frac {567 x^5}{5}-45 x^6 \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.10, size = 30, normalized size = 0.88
method | result | size |
gosper | \(-\frac {x \left (2700 x^{5}+6804 x^{4}+4995 x^{3}-920 x^{2}-3000 x -1440\right )}{60}\) | \(29\) |
default | \(-45 x^{6}-\frac {567}{5} x^{5}-\frac {333}{4} x^{4}+\frac {46}{3} x^{3}+50 x^{2}+24 x\) | \(30\) |
norman | \(-45 x^{6}-\frac {567}{5} x^{5}-\frac {333}{4} x^{4}+\frac {46}{3} x^{3}+50 x^{2}+24 x\) | \(30\) |
risch | \(-45 x^{6}-\frac {567}{5} x^{5}-\frac {333}{4} x^{4}+\frac {46}{3} x^{3}+50 x^{2}+24 x\) | \(30\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.28, size = 29, normalized size = 0.85 \begin {gather*} -45 \, x^{6} - \frac {567}{5} \, x^{5} - \frac {333}{4} \, x^{4} + \frac {46}{3} \, x^{3} + 50 \, x^{2} + 24 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.48, size = 29, normalized size = 0.85 \begin {gather*} -45 \, x^{6} - \frac {567}{5} \, x^{5} - \frac {333}{4} \, x^{4} + \frac {46}{3} \, x^{3} + 50 \, x^{2} + 24 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.01, size = 32, normalized size = 0.94 \begin {gather*} - 45 x^{6} - \frac {567 x^{5}}{5} - \frac {333 x^{4}}{4} + \frac {46 x^{3}}{3} + 50 x^{2} + 24 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 1.02, size = 29, normalized size = 0.85 \begin {gather*} -45 \, x^{6} - \frac {567}{5} \, x^{5} - \frac {333}{4} \, x^{4} + \frac {46}{3} \, x^{3} + 50 \, x^{2} + 24 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.02, size = 29, normalized size = 0.85 \begin {gather*} -45\,x^6-\frac {567\,x^5}{5}-\frac {333\,x^4}{4}+\frac {46\,x^3}{3}+50\,x^2+24\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________