Optimal. Leaf size=75 \[ \frac {21}{4 (2+3 x)^4}+\frac {103}{(2+3 x)^3}+\frac {1530}{(2+3 x)^2}+\frac {25350}{2+3 x}-\frac {1375}{2 (3+5 x)^2}+\frac {20875}{3+5 x}-189375 \log (2+3 x)+189375 \log (3+5 x) \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.03, antiderivative size = 75, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {78}
\begin {gather*} \frac {25350}{3 x+2}+\frac {20875}{5 x+3}+\frac {1530}{(3 x+2)^2}-\frac {1375}{2 (5 x+3)^2}+\frac {103}{(3 x+2)^3}+\frac {21}{4 (3 x+2)^4}-189375 \log (3 x+2)+189375 \log (5 x+3) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 78
Rubi steps
\begin {align*} \int \frac {1-2 x}{(2+3 x)^5 (3+5 x)^3} \, dx &=\int \left (-\frac {63}{(2+3 x)^5}-\frac {927}{(2+3 x)^4}-\frac {9180}{(2+3 x)^3}-\frac {76050}{(2+3 x)^2}-\frac {568125}{2+3 x}+\frac {6875}{(3+5 x)^3}-\frac {104375}{(3+5 x)^2}+\frac {946875}{3+5 x}\right ) \, dx\\ &=\frac {21}{4 (2+3 x)^4}+\frac {103}{(2+3 x)^3}+\frac {1530}{(2+3 x)^2}+\frac {25350}{2+3 x}-\frac {1375}{2 (3+5 x)^2}+\frac {20875}{3+5 x}-189375 \log (2+3 x)+189375 \log (3+5 x)\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.03, size = 77, normalized size = 1.03 \begin {gather*} \frac {21}{4 (2+3 x)^4}+\frac {103}{(2+3 x)^3}+\frac {1530}{(2+3 x)^2}+\frac {25350}{2+3 x}-\frac {1375}{2 (3+5 x)^2}+\frac {20875}{3+5 x}-189375 \log (2+3 x)+189375 \log (-3 (3+5 x)) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.10, size = 72, normalized size = 0.96
method | result | size |
risch | \(\frac {25565625 x^{5}+\frac {165324375}{2} x^{4}+106845375 x^{3}+\frac {276035525}{4} x^{2}+\frac {44542717}{2} x +\frac {11492725}{4}}{\left (2+3 x \right )^{4} \left (3+5 x \right )^{2}}-189375 \ln \left (2+3 x \right )+189375 \ln \left (3+5 x \right )\) | \(59\) |
norman | \(\frac {-\frac {27269999}{6} x -\frac {2585863125}{64} x^{6}-\frac {4181235375}{32} x^{5}-\frac {2618929975}{24} x^{3}-\frac {2536109975}{72} x^{2}-\frac {10810927725}{64} x^{4}}{\left (2+3 x \right )^{4} \left (3+5 x \right )^{2}}-189375 \ln \left (2+3 x \right )+189375 \ln \left (3+5 x \right )\) | \(62\) |
default | \(\frac {21}{4 \left (2+3 x \right )^{4}}+\frac {103}{\left (2+3 x \right )^{3}}+\frac {1530}{\left (2+3 x \right )^{2}}+\frac {25350}{2+3 x}-\frac {1375}{2 \left (3+5 x \right )^{2}}+\frac {20875}{3+5 x}-189375 \ln \left (2+3 x \right )+189375 \ln \left (3+5 x \right )\) | \(72\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.30, size = 76, normalized size = 1.01 \begin {gather*} \frac {102262500 \, x^{5} + 330648750 \, x^{4} + 427381500 \, x^{3} + 276035525 \, x^{2} + 89085434 \, x + 11492725}{4 \, {\left (2025 \, x^{6} + 7830 \, x^{5} + 12609 \, x^{4} + 10824 \, x^{3} + 5224 \, x^{2} + 1344 \, x + 144\right )}} + 189375 \, \log \left (5 \, x + 3\right ) - 189375 \, \log \left (3 \, x + 2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.93, size = 135, normalized size = 1.80 \begin {gather*} \frac {102262500 \, x^{5} + 330648750 \, x^{4} + 427381500 \, x^{3} + 276035525 \, x^{2} + 757500 \, {\left (2025 \, x^{6} + 7830 \, x^{5} + 12609 \, x^{4} + 10824 \, x^{3} + 5224 \, x^{2} + 1344 \, x + 144\right )} \log \left (5 \, x + 3\right ) - 757500 \, {\left (2025 \, x^{6} + 7830 \, x^{5} + 12609 \, x^{4} + 10824 \, x^{3} + 5224 \, x^{2} + 1344 \, x + 144\right )} \log \left (3 \, x + 2\right ) + 89085434 \, x + 11492725}{4 \, {\left (2025 \, x^{6} + 7830 \, x^{5} + 12609 \, x^{4} + 10824 \, x^{3} + 5224 \, x^{2} + 1344 \, x + 144\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.10, size = 73, normalized size = 0.97 \begin {gather*} - \frac {- 102262500 x^{5} - 330648750 x^{4} - 427381500 x^{3} - 276035525 x^{2} - 89085434 x - 11492725}{8100 x^{6} + 31320 x^{5} + 50436 x^{4} + 43296 x^{3} + 20896 x^{2} + 5376 x + 576} + 189375 \log {\left (x + \frac {3}{5} \right )} - 189375 \log {\left (x + \frac {2}{3} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.56, size = 76, normalized size = 1.01 \begin {gather*} \frac {25350}{3 \, x + 2} - \frac {9375 \, {\left (\frac {80}{3 \, x + 2} - 367\right )}}{2 \, {\left (\frac {1}{3 \, x + 2} - 5\right )}^{2}} + \frac {1530}{{\left (3 \, x + 2\right )}^{2}} + \frac {103}{{\left (3 \, x + 2\right )}^{3}} + \frac {21}{4 \, {\left (3 \, x + 2\right )}^{4}} + 189375 \, \log \left ({\left | -\frac {1}{3 \, x + 2} + 5 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.04, size = 65, normalized size = 0.87 \begin {gather*} \frac {12625\,x^5+\frac {244925\,x^4}{6}+\frac {1424605\,x^3}{27}+\frac {11041421\,x^2}{324}+\frac {44542717\,x}{4050}+\frac {459709}{324}}{x^6+\frac {58\,x^5}{15}+\frac {467\,x^4}{75}+\frac {3608\,x^3}{675}+\frac {5224\,x^2}{2025}+\frac {448\,x}{675}+\frac {16}{225}}-378750\,\mathrm {atanh}\left (30\,x+19\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________