\(\int \frac {-90 x-3 x^2+3 x^3+(-44 x-33 x^2) \log (4+3 x)+(-120-94 x+x^2+3 x^3) \log (4+3 x) \log (\frac {6-x}{(10+2 x) \log (4+3 x)})}{(-120-94 x+x^2+3 x^3) \log (4+3 x) \log ^2(\frac {6-x}{(10+2 x) \log (4+3 x)})} \, dx\) [7830]

Optimal result

Integrand size = 120, antiderivative size = 30 \[ \int \frac {-90 x-3 x^2+3 x^3+\left (-44 x-33 x^2\right ) \log (4+3 x)+\left (-120-94 x+x^2+3 x^3\right ) \log (4+3 x) \log \left (\frac {6-x}{(10+2 x) \log (4+3 x)}\right )}{\left (-120-94 x+x^2+3 x^3\right ) \log (4+3 x) \log ^2\left (\frac {6-x}{(10+2 x) \log (4+3 x)}\right )} \, dx=\frac {x}{\log \left (\frac {\frac {3 (2-x)}{2}+x}{(5+x) \log (4+3 x)}\right )} \]

[Out]

x/ln((3-1/2*x)/ln(4+3*x)/(5+x))

Rubi [F]

\[ \int \frac {-90 x-3 x^2+3 x^3+\left (-44 x-33 x^2\right ) \log (4+3 x)+\left (-120-94 x+x^2+3 x^3\right ) \log (4+3 x) \log \left (\frac {6-x}{(10+2 x) \log (4+3 x)}\right )}{\left (-120-94 x+x^2+3 x^3\right ) \log (4+3 x) \log ^2\left (\frac {6-x}{(10+2 x) \log (4+3 x)}\right )} \, dx=\int \frac {-90 x-3 x^2+3 x^3+\left (-44 x-33 x^2\right ) \log (4+3 x)+\left (-120-94 x+x^2+3 x^3\right ) \log (4+3 x) \log \left (\frac {6-x}{(10+2 x) \log (4+3 x)}\right )}{\left (-120-94 x+x^2+3 x^3\right ) \log (4+3 x) \log ^2\left (\frac {6-x}{(10+2 x) \log (4+3 x)}\right )} \, dx \]

[In]

Int[(-90*x - 3*x^2 + 3*x^3 + (-44*x - 33*x^2)*Log[4 + 3*x] + (-120 - 94*x + x^2 + 3*x^3)*Log[4 + 3*x]*Log[(6 -
x)/((10 + 2*x)*Log[4 + 3*x])])/((-120 - 94*x + x^2 + 3*x^3)*Log[4 + 3*x]*Log[(6 - x)/((10 + 2*x)*Log[4 + 3*x]
)]^2),x]

[Out]

-6*Defer[Int][1/((-6 + x)*Log[-1/2*(-6 + x)/((5 + x)*Log[4 + 3*x])]^2), x] - 5*Defer[Int][1/((5 + x)*Log[-1/2*
(-6 + x)/((5 + x)*Log[4 + 3*x])]^2), x] + Defer[Int][1/(Log[4 + 3*x]*Log[-1/2*(-6 + x)/((5 + x)*Log[4 + 3*x])]
^2), x] - 4*Defer[Int][1/((4 + 3*x)*Log[4 + 3*x]*Log[-1/2*(-6 + x)/((5 + x)*Log[4 + 3*x])]^2), x] + Defer[Int]
[Log[-1/2*(-6 + x)/((5 + x)*Log[4 + 3*x])]^(-1), x]

Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {x \left (-90-3 x+3 x^2-44 \log (4+3 x)-33 x \log (4+3 x)\right )}{(-6+x) (5+x) (4+3 x) \log (4+3 x) \log ^2\left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )}+\frac {1}{\log \left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )}\right ) \, dx \\ & = \int \frac {x \left (-90-3 x+3 x^2-44 \log (4+3 x)-33 x \log (4+3 x)\right )}{(-6+x) (5+x) (4+3 x) \log (4+3 x) \log ^2\left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )} \, dx+\int \frac {1}{\log \left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )} \, dx \\ & = \int \left (\frac {3 \left (-90-3 x+3 x^2-44 \log (4+3 x)-33 x \log (4+3 x)\right )}{121 (-6+x) \log (4+3 x) \log ^2\left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )}-\frac {5 \left (-90-3 x+3 x^2-44 \log (4+3 x)-33 x \log (4+3 x)\right )}{121 (5+x) \log (4+3 x) \log ^2\left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )}+\frac {6 \left (-90-3 x+3 x^2-44 \log (4+3 x)-33 x \log (4+3 x)\right )}{121 (4+3 x) \log (4+3 x) \log ^2\left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )}\right ) \, dx+\int \frac {1}{\log \left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )} \, dx \\ & = \frac {3}{121} \int \frac {-90-3 x+3 x^2-44 \log (4+3 x)-33 x \log (4+3 x)}{(-6+x) \log (4+3 x) \log ^2\left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )} \, dx-\frac {5}{121} \int \frac {-90-3 x+3 x^2-44 \log (4+3 x)-33 x \log (4+3 x)}{(5+x) \log (4+3 x) \log ^2\left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )} \, dx+\frac {6}{121} \int \frac {-90-3 x+3 x^2-44 \log (4+3 x)-33 x \log (4+3 x)}{(4+3 x) \log (4+3 x) \log ^2\left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )} \, dx+\int \frac {1}{\log \left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )} \, dx \\ & = \frac {3}{121} \int \left (-\frac {44}{(-6+x) \log ^2\left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )}-\frac {33 x}{(-6+x) \log ^2\left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )}-\frac {90}{(-6+x) \log (4+3 x) \log ^2\left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )}-\frac {3 x}{(-6+x) \log (4+3 x) \log ^2\left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )}+\frac {3 x^2}{(-6+x) \log (4+3 x) \log ^2\left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )}\right ) \, dx-\frac {5}{121} \int \left (-\frac {44}{(5+x) \log ^2\left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )}-\frac {33 x}{(5+x) \log ^2\left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )}-\frac {90}{(5+x) \log (4+3 x) \log ^2\left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )}-\frac {3 x}{(5+x) \log (4+3 x) \log ^2\left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )}+\frac {3 x^2}{(5+x) \log (4+3 x) \log ^2\left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )}\right ) \, dx+\frac {6}{121} \int \left (-\frac {44}{(4+3 x) \log ^2\left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )}-\frac {33 x}{(4+3 x) \log ^2\left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )}-\frac {90}{(4+3 x) \log (4+3 x) \log ^2\left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )}-\frac {3 x}{(4+3 x) \log (4+3 x) \log ^2\left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )}+\frac {3 x^2}{(4+3 x) \log (4+3 x) \log ^2\left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )}\right ) \, dx+\int \frac {1}{\log \left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )} \, dx \\ & = -\left (\frac {9}{121} \int \frac {x}{(-6+x) \log (4+3 x) \log ^2\left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )} \, dx\right )+\frac {9}{121} \int \frac {x^2}{(-6+x) \log (4+3 x) \log ^2\left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )} \, dx+\frac {15}{121} \int \frac {x}{(5+x) \log (4+3 x) \log ^2\left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )} \, dx-\frac {15}{121} \int \frac {x^2}{(5+x) \log (4+3 x) \log ^2\left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )} \, dx-\frac {18}{121} \int \frac {x}{(4+3 x) \log (4+3 x) \log ^2\left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )} \, dx+\frac {18}{121} \int \frac {x^2}{(4+3 x) \log (4+3 x) \log ^2\left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )} \, dx-\frac {9}{11} \int \frac {x}{(-6+x) \log ^2\left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )} \, dx-\frac {12}{11} \int \frac {1}{(-6+x) \log ^2\left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )} \, dx+\frac {15}{11} \int \frac {x}{(5+x) \log ^2\left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )} \, dx-\frac {18}{11} \int \frac {x}{(4+3 x) \log ^2\left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )} \, dx+\frac {20}{11} \int \frac {1}{(5+x) \log ^2\left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )} \, dx-\frac {24}{11} \int \frac {1}{(4+3 x) \log ^2\left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )} \, dx-\frac {270}{121} \int \frac {1}{(-6+x) \log (4+3 x) \log ^2\left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )} \, dx+\frac {450}{121} \int \frac {1}{(5+x) \log (4+3 x) \log ^2\left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )} \, dx-\frac {540}{121} \int \frac {1}{(4+3 x) \log (4+3 x) \log ^2\left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )} \, dx+\int \frac {1}{\log \left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )} \, dx \\ & = -\left (\frac {9}{121} \int \left (\frac {1}{\log (4+3 x) \log ^2\left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )}+\frac {6}{(-6+x) \log (4+3 x) \log ^2\left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )}\right ) \, dx\right )+\frac {9}{121} \int \left (\frac {6}{\log (4+3 x) \log ^2\left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )}+\frac {36}{(-6+x) \log (4+3 x) \log ^2\left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )}+\frac {x}{\log (4+3 x) \log ^2\left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )}\right ) \, dx+\frac {15}{121} \int \left (\frac {1}{\log (4+3 x) \log ^2\left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )}-\frac {5}{(5+x) \log (4+3 x) \log ^2\left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )}\right ) \, dx-\frac {15}{121} \int \left (-\frac {5}{\log (4+3 x) \log ^2\left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )}+\frac {x}{\log (4+3 x) \log ^2\left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )}+\frac {25}{(5+x) \log (4+3 x) \log ^2\left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )}\right ) \, dx-\frac {18}{121} \int \left (\frac {1}{3 \log (4+3 x) \log ^2\left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )}-\frac {4}{3 (4+3 x) \log (4+3 x) \log ^2\left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )}\right ) \, dx+\frac {18}{121} \int \left (-\frac {4}{9 \log (4+3 x) \log ^2\left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )}+\frac {x}{3 \log (4+3 x) \log ^2\left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )}+\frac {16}{9 (4+3 x) \log (4+3 x) \log ^2\left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )}\right ) \, dx-\frac {9}{11} \int \left (\frac {1}{\log ^2\left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )}+\frac {6}{(-6+x) \log ^2\left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )}\right ) \, dx-\frac {12}{11} \int \frac {1}{(-6+x) \log ^2\left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )} \, dx+\frac {15}{11} \int \left (\frac {1}{\log ^2\left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )}-\frac {5}{(5+x) \log ^2\left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )}\right ) \, dx-\frac {18}{11} \int \left (\frac {1}{3 \log ^2\left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )}-\frac {4}{3 (4+3 x) \log ^2\left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )}\right ) \, dx+\frac {20}{11} \int \frac {1}{(5+x) \log ^2\left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )} \, dx-\frac {24}{11} \int \frac {1}{(4+3 x) \log ^2\left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )} \, dx-\frac {270}{121} \int \frac {1}{(-6+x) \log (4+3 x) \log ^2\left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )} \, dx+\frac {450}{121} \int \frac {1}{(5+x) \log (4+3 x) \log ^2\left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )} \, dx-\frac {540}{121} \int \frac {1}{(4+3 x) \log (4+3 x) \log ^2\left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )} \, dx+\int \frac {1}{\log \left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )} \, dx \\ & = -\left (\frac {6}{121} \int \frac {1}{\log (4+3 x) \log ^2\left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )} \, dx\right )+\frac {6}{121} \int \frac {x}{\log (4+3 x) \log ^2\left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )} \, dx-\frac {8}{121} \int \frac {1}{\log (4+3 x) \log ^2\left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )} \, dx-\frac {9}{121} \int \frac {1}{\log (4+3 x) \log ^2\left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )} \, dx+\frac {9}{121} \int \frac {x}{\log (4+3 x) \log ^2\left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )} \, dx+\frac {15}{121} \int \frac {1}{\log (4+3 x) \log ^2\left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )} \, dx-\frac {15}{121} \int \frac {x}{\log (4+3 x) \log ^2\left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )} \, dx+\frac {24}{121} \int \frac {1}{(4+3 x) \log (4+3 x) \log ^2\left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )} \, dx+\frac {32}{121} \int \frac {1}{(4+3 x) \log (4+3 x) \log ^2\left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )} \, dx+\frac {54}{121} \int \frac {1}{\log (4+3 x) \log ^2\left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )} \, dx-\frac {54}{121} \int \frac {1}{(-6+x) \log (4+3 x) \log ^2\left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )} \, dx-\frac {6}{11} \int \frac {1}{\log ^2\left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )} \, dx+\frac {75}{121} \int \frac {1}{\log (4+3 x) \log ^2\left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )} \, dx-\frac {75}{121} \int \frac {1}{(5+x) \log (4+3 x) \log ^2\left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )} \, dx-\frac {9}{11} \int \frac {1}{\log ^2\left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )} \, dx-\frac {12}{11} \int \frac {1}{(-6+x) \log ^2\left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )} \, dx+\frac {15}{11} \int \frac {1}{\log ^2\left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )} \, dx+\frac {20}{11} \int \frac {1}{(5+x) \log ^2\left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )} \, dx-\frac {270}{121} \int \frac {1}{(-6+x) \log (4+3 x) \log ^2\left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )} \, dx+\frac {324}{121} \int \frac {1}{(-6+x) \log (4+3 x) \log ^2\left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )} \, dx-\frac {375}{121} \int \frac {1}{(5+x) \log (4+3 x) \log ^2\left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )} \, dx+\frac {450}{121} \int \frac {1}{(5+x) \log (4+3 x) \log ^2\left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )} \, dx-\frac {540}{121} \int \frac {1}{(4+3 x) \log (4+3 x) \log ^2\left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )} \, dx-\frac {54}{11} \int \frac {1}{(-6+x) \log ^2\left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )} \, dx-\frac {75}{11} \int \frac {1}{(5+x) \log ^2\left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )} \, dx+\int \frac {1}{\log \left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )} \, dx \\ \end{align*}

Mathematica [A] (verified)

Time = 0.10 (sec) , antiderivative size = 25, normalized size of antiderivative = 0.83 \[ \int \frac {-90 x-3 x^2+3 x^3+\left (-44 x-33 x^2\right ) \log (4+3 x)+\left (-120-94 x+x^2+3 x^3\right ) \log (4+3 x) \log \left (\frac {6-x}{(10+2 x) \log (4+3 x)}\right )}{\left (-120-94 x+x^2+3 x^3\right ) \log (4+3 x) \log ^2\left (\frac {6-x}{(10+2 x) \log (4+3 x)}\right )} \, dx=\frac {x}{\log \left (-\frac {-6+x}{2 (5+x) \log (4+3 x)}\right )} \]

[In]

Integrate[(-90*x - 3*x^2 + 3*x^3 + (-44*x - 33*x^2)*Log[4 + 3*x] + (-120 - 94*x + x^2 + 3*x^3)*Log[4 + 3*x]*Lo
g[(6 - x)/((10 + 2*x)*Log[4 + 3*x])])/((-120 - 94*x + x^2 + 3*x^3)*Log[4 + 3*x]*Log[(6 - x)/((10 + 2*x)*Log[4
+ 3*x])]^2),x]

[Out]

x/Log[-1/2*(-6 + x)/((5 + x)*Log[4 + 3*x])]

Maple [A] (verified)

Time = 2.90 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.87

method	result	size
parallelrisch	\(\frac {x}{\ln \left (-\frac {-6+x}{\left (2 x +10\right ) \ln \left (4+3 x \right )}\right )}\)	\(26\)
risch	\(\frac {2 i x}{2 \pi \operatorname {csgn}\left (\frac {i \left (-6+x \right )}{\left (5+x \right ) \ln \left (4+3 x \right )}\right )^{2}+\pi \,\operatorname {csgn}\left (i \left (-6+x \right )\right ) \operatorname {csgn}\left (\frac {i}{5+x}\right ) \operatorname {csgn}\left (\frac {i \left (-6+x \right )}{5+x}\right )-\pi \,\operatorname {csgn}\left (i \left (-6+x \right )\right ) \operatorname {csgn}\left (\frac {i \left (-6+x \right )}{5+x}\right )^{2}-\pi \,\operatorname {csgn}\left (\frac {i}{5+x}\right ) \operatorname {csgn}\left (\frac {i \left (-6+x \right )}{5+x}\right )^{2}+\pi \,\operatorname {csgn}\left (\frac {i}{\ln \left (4+3 x \right )}\right ) \operatorname {csgn}\left (\frac {i \left (-6+x \right )}{5+x}\right ) \operatorname {csgn}\left (\frac {i \left (-6+x \right )}{\left (5+x \right ) \ln \left (4+3 x \right )}\right )-\pi \,\operatorname {csgn}\left (\frac {i}{\ln \left (4+3 x \right )}\right ) \operatorname {csgn}\left (\frac {i \left (-6+x \right )}{\left (5+x \right ) \ln \left (4+3 x \right )}\right )^{2}+\pi \operatorname {csgn}\left (\frac {i \left (-6+x \right )}{5+x}\right )^{3}-\pi \,\operatorname {csgn}\left (\frac {i \left (-6+x \right )}{5+x}\right ) \operatorname {csgn}\left (\frac {i \left (-6+x \right )}{\left (5+x \right ) \ln \left (4+3 x \right )}\right )^{2}-\pi \operatorname {csgn}\left (\frac {i \left (-6+x \right )}{\left (5+x \right ) \ln \left (4+3 x \right )}\right )^{3}-2 \pi +2 i \ln \left (-6+x \right )-2 i \ln \left (5+x \right )-2 i \ln \left (2\right )-2 i \ln \left (\ln \left (4+3 x \right )\right )}\)	\(306\)
default	\(\text {Expression too large to display}\)	\(795\)

[In]

int(((3*x^3+x^2-94*x-120)*ln(4+3*x)*ln((-x+6)/(2*x+10)/ln(4+3*x))+(-33*x^2-44*x)*ln(4+3*x)+3*x^3-3*x^2-90*x)/(
3*x^3+x^2-94*x-120)/ln(4+3*x)/ln((-x+6)/(2*x+10)/ln(4+3*x))^2,x,method=_RETURNVERBOSE)

[Out]

x/ln(-1/(2*x+10)/ln(4+3*x)*(-6+x))

Fricas [A] (verification not implemented)

none

Time = 0.26 (sec) , antiderivative size = 23, normalized size of antiderivative = 0.77 \[ \int \frac {-90 x-3 x^2+3 x^3+\left (-44 x-33 x^2\right ) \log (4+3 x)+\left (-120-94 x+x^2+3 x^3\right ) \log (4+3 x) \log \left (\frac {6-x}{(10+2 x) \log (4+3 x)}\right )}{\left (-120-94 x+x^2+3 x^3\right ) \log (4+3 x) \log ^2\left (\frac {6-x}{(10+2 x) \log (4+3 x)}\right )} \, dx=\frac {x}{\log \left (-\frac {x - 6}{2 \, {\left (x + 5\right )} \log \left (3 \, x + 4\right )}\right )} \]

[In]

integrate(((3*x^3+x^2-94*x-120)*log(4+3*x)*log((-x+6)/(2*x+10)/log(4+3*x))+(-33*x^2-44*x)*log(4+3*x)+3*x^3-3*x
^2-90*x)/(3*x^3+x^2-94*x-120)/log(4+3*x)/log((-x+6)/(2*x+10)/log(4+3*x))^2,x, algorithm="fricas")

[Out]

x/log(-1/2*(x - 6)/((x + 5)*log(3*x + 4)))

Sympy [A] (verification not implemented)

Time = 0.16 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.57 \[ \int \frac {-90 x-3 x^2+3 x^3+\left (-44 x-33 x^2\right ) \log (4+3 x)+\left (-120-94 x+x^2+3 x^3\right ) \log (4+3 x) \log \left (\frac {6-x}{(10+2 x) \log (4+3 x)}\right )}{\left (-120-94 x+x^2+3 x^3\right ) \log (4+3 x) \log ^2\left (\frac {6-x}{(10+2 x) \log (4+3 x)}\right )} \, dx=\frac {x}{\log {\left (\frac {6 - x}{\left (2 x + 10\right ) \log {\left (3 x + 4 \right )}} \right )}} \]

[In]

integrate(((3*x**3+x**2-94*x-120)*ln(4+3*x)*ln((-x+6)/(2*x+10)/ln(4+3*x))+(-33*x**2-44*x)*ln(4+3*x)+3*x**3-3*x
**2-90*x)/(3*x**3+x**2-94*x-120)/ln(4+3*x)/ln((-x+6)/(2*x+10)/ln(4+3*x))**2,x)

[Out]

x/log((6 - x)/((2*x + 10)*log(3*x + 4)))

Maxima [A] (verification not implemented)

none

Time = 0.34 (sec) , antiderivative size = 27, normalized size of antiderivative = 0.90 \[ \int \frac {-90 x-3 x^2+3 x^3+\left (-44 x-33 x^2\right ) \log (4+3 x)+\left (-120-94 x+x^2+3 x^3\right ) \log (4+3 x) \log \left (\frac {6-x}{(10+2 x) \log (4+3 x)}\right )}{\left (-120-94 x+x^2+3 x^3\right ) \log (4+3 x) \log ^2\left (\frac {6-x}{(10+2 x) \log (4+3 x)}\right )} \, dx=-\frac {x}{\log \left (2\right ) + \log \left (x + 5\right ) - \log \left (-x + 6\right ) + \log \left (\log \left (3 \, x + 4\right )\right )} \]

[In]

integrate(((3*x^3+x^2-94*x-120)*log(4+3*x)*log((-x+6)/(2*x+10)/log(4+3*x))+(-33*x^2-44*x)*log(4+3*x)+3*x^3-3*x
^2-90*x)/(3*x^3+x^2-94*x-120)/log(4+3*x)/log((-x+6)/(2*x+10)/log(4+3*x))^2,x, algorithm="maxima")

[Out]

-x/(log(2) + log(x + 5) - log(-x + 6) + log(log(3*x + 4)))

Giac [A] (verification not implemented)

none

Time = 0.45 (sec) , antiderivative size = 33, normalized size of antiderivative = 1.10 \[ \int \frac {-90 x-3 x^2+3 x^3+\left (-44 x-33 x^2\right ) \log (4+3 x)+\left (-120-94 x+x^2+3 x^3\right ) \log (4+3 x) \log \left (\frac {6-x}{(10+2 x) \log (4+3 x)}\right )}{\left (-120-94 x+x^2+3 x^3\right ) \log (4+3 x) \log ^2\left (\frac {6-x}{(10+2 x) \log (4+3 x)}\right )} \, dx=-\frac {x}{\log \left (2 \, x \log \left (3 \, x + 4\right ) + 10 \, \log \left (3 \, x + 4\right )\right ) - \log \left (-x + 6\right )} \]

[In]

integrate(((3*x^3+x^2-94*x-120)*log(4+3*x)*log((-x+6)/(2*x+10)/log(4+3*x))+(-33*x^2-44*x)*log(4+3*x)+3*x^3-3*x
^2-90*x)/(3*x^3+x^2-94*x-120)/log(4+3*x)/log((-x+6)/(2*x+10)/log(4+3*x))^2,x, algorithm="giac")

[Out]

-x/(log(2*x*log(3*x + 4) + 10*log(3*x + 4)) - log(-x + 6))

Mupad [F(-1)]

Timed out. \[ \int \frac {-90 x-3 x^2+3 x^3+\left (-44 x-33 x^2\right ) \log (4+3 x)+\left (-120-94 x+x^2+3 x^3\right ) \log (4+3 x) \log \left (\frac {6-x}{(10+2 x) \log (4+3 x)}\right )}{\left (-120-94 x+x^2+3 x^3\right ) \log (4+3 x) \log ^2\left (\frac {6-x}{(10+2 x) \log (4+3 x)}\right )} \, dx=\int \frac {90\,x+\ln \left (3\,x+4\right )\,\left (33\,x^2+44\,x\right )+3\,x^2-3\,x^3+\ln \left (-\frac {x-6}{\ln \left (3\,x+4\right )\,\left (2\,x+10\right )}\right )\,\ln \left (3\,x+4\right )\,\left (-3\,x^3-x^2+94\,x+120\right )}{{\ln \left (-\frac {x-6}{\ln \left (3\,x+4\right )\,\left (2\,x+10\right )}\right )}^2\,\ln \left (3\,x+4\right )\,\left (-3\,x^3-x^2+94\,x+120\right )} \,d x \]

[In]

int((90*x + log(3*x + 4)*(44*x + 33*x^2) + 3*x^2 - 3*x^3 + log(-(x - 6)/(log(3*x + 4)*(2*x + 10)))*log(3*x + 4
)*(94*x - x^2 - 3*x^3 + 120))/(log(-(x - 6)/(log(3*x + 4)*(2*x + 10)))^2*log(3*x + 4)*(94*x - x^2 - 3*x^3 + 12
0)),x)

[Out]

int((90*x + log(3*x + 4)*(44*x + 33*x^2) + 3*x^2 - 3*x^3 + log(-(x - 6)/(log(3*x + 4)*(2*x + 10)))*log(3*x + 4
)*(94*x - x^2 - 3*x^3 + 120))/(log(-(x - 6)/(log(3*x + 4)*(2*x + 10)))^2*log(3*x + 4)*(94*x - x^2 - 3*x^3 + 12
0)), x)