3.39.80 \(\int \frac {(-3 x+6 x^2-x^3+2 x^4+(-5 x^3+10 x^4) \log (4)) \log (-3-x^2-5 x^2 \log (4))+\log (5-x+x^2) (-10 x^2+2 x^3-2 x^4+(-50 x^2+10 x^3-10 x^4) \log (4)+(15-3 x+8 x^2-x^3+x^4+(25 x^2-5 x^3+5 x^4) \log (4)) \log (-3-x^2-5 x^2 \log (4)))}{(15-3 x+8 x^2-x^3+x^4+(25 x^2-5 x^3+5 x^4) \log (4)) \log ^2(-3-x^2-5 x^2 \log (4))} \, dx\)

Optimal. Leaf size=28 \[ \frac {x \log \left (5-x+x^2\right )}{\log \left (-3-x^2-5 x^2 \log (4)\right )} \]

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Rubi [F]  time = 11.09, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {\left (-3 x+6 x^2-x^3+2 x^4+\left (-5 x^3+10 x^4\right ) \log (4)\right ) \log \left (-3-x^2-5 x^2 \log (4)\right )+\log \left (5-x+x^2\right ) \left (-10 x^2+2 x^3-2 x^4+\left (-50 x^2+10 x^3-10 x^4\right ) \log (4)+\left (15-3 x+8 x^2-x^3+x^4+\left (25 x^2-5 x^3+5 x^4\right ) \log (4)\right ) \log \left (-3-x^2-5 x^2 \log (4)\right )\right )}{\left (15-3 x+8 x^2-x^3+x^4+\left (25 x^2-5 x^3+5 x^4\right ) \log (4)\right ) \log ^2\left (-3-x^2-5 x^2 \log (4)\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[((-3*x + 6*x^2 - x^3 + 2*x^4 + (-5*x^3 + 10*x^4)*Log[4])*Log[-3 - x^2 - 5*x^2*Log[4]] + Log[5 - x + x^2]*(
-10*x^2 + 2*x^3 - 2*x^4 + (-50*x^2 + 10*x^3 - 10*x^4)*Log[4] + (15 - 3*x + 8*x^2 - x^3 + x^4 + (25*x^2 - 5*x^3
+ 5*x^4)*Log[4])*Log[-3 - x^2 - 5*x^2*Log[4]]))/((15 - 3*x + 8*x^2 - x^3 + x^4 + (25*x^2 - 5*x^3 + 5*x^4)*Log
[4])*Log[-3 - x^2 - 5*x^2*Log[4]]^2),x]

[Out]

2*Defer[Int][Log[-3 + x^2*(-1 - 5*Log[4])]^(-1), x] - ((20*I)*Defer[Int][1/((1 + I*Sqrt[19] - 2*x)*Log[-3 + x^
2*(-1 - 5*Log[4])]), x])/Sqrt[19] + ((19 - I*Sqrt[19])*Defer[Int][1/((-1 - I*Sqrt[19] + 2*x)*Log[-3 + x^2*(-1
- 5*Log[4])]), x])/19 - ((20*I)*Defer[Int][1/((-1 + I*Sqrt[19] + 2*x)*Log[-3 + x^2*(-1 - 5*Log[4])]), x])/Sqrt
[19] + ((19 + I*Sqrt[19])*Defer[Int][1/((-1 + I*Sqrt[19] + 2*x)*Log[-3 + x^2*(-1 - 5*Log[4])]), x])/19 - 2*Def
er[Int][Log[5 - x + x^2]/Log[-3 - x^2*(1 + 5*Log[4])]^2, x] + I*Sqrt[3/(1 + 5*Log[4])]*Defer[Int][Log[5 - x +
x^2]/((-x + I*Sqrt[3/(1 + 5*Log[4])])*Log[-3 - x^2*(1 + 5*Log[4])]^2), x] + I*Sqrt[3/(1 + 5*Log[4])]*Defer[Int
][Log[5 - x + x^2]/((x + I*Sqrt[3/(1 + 5*Log[4])])*Log[-3 - x^2*(1 + 5*Log[4])]^2), x] + Defer[Int][Log[5 - x
+ x^2]/Log[-3 - x^2*(1 + 5*Log[4])], x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-\frac {2 x^2 (1+5 \log (4)) \log \left (5-x+x^2\right )}{3+x^2 (1+5 \log (4))}+\frac {x (-1+2 x) \log \left (-3-x^2 (1+5 \log (4))\right )}{5-x+x^2}+\log \left (5-x+x^2\right ) \log \left (-3-x^2 (1+5 \log (4))\right )}{\log ^2\left (-3-x^2 (1+5 \log (4))\right )} \, dx\\ &=\int \left (\frac {2 x^2 (-1-5 \log (4)) \log \left (5-x+x^2\right )}{\left (3+x^2 (1+5 \log (4))\right ) \log ^2\left (-3-x^2 (1+5 \log (4))\right )}+\frac {-x+2 x^2+5 \log \left (5-x+x^2\right )-x \log \left (5-x+x^2\right )+x^2 \log \left (5-x+x^2\right )}{\left (5-x+x^2\right ) \log \left (-3-x^2 (1+5 \log (4))\right )}\right ) \, dx\\ &=-\left ((2 (1+5 \log (4))) \int \frac {x^2 \log \left (5-x+x^2\right )}{\left (3+x^2 (1+5 \log (4))\right ) \log ^2\left (-3-x^2 (1+5 \log (4))\right )} \, dx\right )+\int \frac {-x+2 x^2+5 \log \left (5-x+x^2\right )-x \log \left (5-x+x^2\right )+x^2 \log \left (5-x+x^2\right )}{\left (5-x+x^2\right ) \log \left (-3-x^2 (1+5 \log (4))\right )} \, dx\\ &=-\left ((2 (1+5 \log (4))) \int \left (\frac {\log \left (5-x+x^2\right )}{(1+5 \log (4)) \log ^2\left (-3-x^2 (1+5 \log (4))\right )}+\frac {3 \log \left (5-x+x^2\right )}{(-1-5 \log (4)) \left (3+x^2 (1+5 \log (4))\right ) \log ^2\left (-3-x^2 (1+5 \log (4))\right )}\right ) \, dx\right )+\int \frac {x (-1+2 x)+\left (5-x+x^2\right ) \log \left (5-x+x^2\right )}{\left (5-x+x^2\right ) \log \left (-3-x^2 (1+5 \log (4))\right )} \, dx\\ &=-\left (2 \int \frac {\log \left (5-x+x^2\right )}{\log ^2\left (-3-x^2 (1+5 \log (4))\right )} \, dx\right )+6 \int \frac {\log \left (5-x+x^2\right )}{\left (3+x^2 (1+5 \log (4))\right ) \log ^2\left (-3-x^2 (1+5 \log (4))\right )} \, dx+\int \left (-\frac {x}{\left (5-x+x^2\right ) \log \left (-3-x^2 (1+5 \log (4))\right )}+\frac {2 x^2}{\left (5-x+x^2\right ) \log \left (-3-x^2 (1+5 \log (4))\right )}+\frac {5 \log \left (5-x+x^2\right )}{\left (5-x+x^2\right ) \log \left (-3-x^2 (1+5 \log (4))\right )}-\frac {x \log \left (5-x+x^2\right )}{\left (5-x+x^2\right ) \log \left (-3-x^2 (1+5 \log (4))\right )}+\frac {x^2 \log \left (5-x+x^2\right )}{\left (5-x+x^2\right ) \log \left (-3-x^2 (1+5 \log (4))\right )}\right ) \, dx\\ &=-\left (2 \int \frac {\log \left (5-x+x^2\right )}{\log ^2\left (-3-x^2 (1+5 \log (4))\right )} \, dx\right )+2 \int \frac {x^2}{\left (5-x+x^2\right ) \log \left (-3-x^2 (1+5 \log (4))\right )} \, dx+5 \int \frac {\log \left (5-x+x^2\right )}{\left (5-x+x^2\right ) \log \left (-3-x^2 (1+5 \log (4))\right )} \, dx+6 \int \left (\frac {i \log \left (5-x+x^2\right )}{2 \sqrt {3 (1+5 \log (4))} \left (-x+i \sqrt {\frac {3}{1+5 \log (4)}}\right ) \log ^2\left (-3-x^2 (1+5 \log (4))\right )}+\frac {i \log \left (5-x+x^2\right )}{2 \sqrt {3 (1+5 \log (4))} \left (x+i \sqrt {\frac {3}{1+5 \log (4)}}\right ) \log ^2\left (-3-x^2 (1+5 \log (4))\right )}\right ) \, dx-\int \frac {x}{\left (5-x+x^2\right ) \log \left (-3-x^2 (1+5 \log (4))\right )} \, dx-\int \frac {x \log \left (5-x+x^2\right )}{\left (5-x+x^2\right ) \log \left (-3-x^2 (1+5 \log (4))\right )} \, dx+\int \frac {x^2 \log \left (5-x+x^2\right )}{\left (5-x+x^2\right ) \log \left (-3-x^2 (1+5 \log (4))\right )} \, dx\\ &=2 \int \left (\frac {1}{\log \left (-3-x^2 (1+5 \log (4))\right )}+\frac {-5+x}{\left (5-x+x^2\right ) \log \left (-3-x^2 (1+5 \log (4))\right )}\right ) \, dx-2 \int \frac {\log \left (5-x+x^2\right )}{\log ^2\left (-3-x^2 (1+5 \log (4))\right )} \, dx+5 \int \left (\frac {2 i \log \left (5-x+x^2\right )}{\sqrt {19} \left (1+i \sqrt {19}-2 x\right ) \log \left (-3-x^2 (1+5 \log (4))\right )}+\frac {2 i \log \left (5-x+x^2\right )}{\sqrt {19} \left (-1+i \sqrt {19}+2 x\right ) \log \left (-3-x^2 (1+5 \log (4))\right )}\right ) \, dx+\left (i \sqrt {\frac {3}{1+5 \log (4)}}\right ) \int \frac {\log \left (5-x+x^2\right )}{\left (-x+i \sqrt {\frac {3}{1+5 \log (4)}}\right ) \log ^2\left (-3-x^2 (1+5 \log (4))\right )} \, dx+\left (i \sqrt {\frac {3}{1+5 \log (4)}}\right ) \int \frac {\log \left (5-x+x^2\right )}{\left (x+i \sqrt {\frac {3}{1+5 \log (4)}}\right ) \log ^2\left (-3-x^2 (1+5 \log (4))\right )} \, dx-\int \left (\frac {1-\frac {i}{\sqrt {19}}}{\left (-1-i \sqrt {19}+2 x\right ) \log \left (-3-x^2 (1+5 \log (4))\right )}+\frac {1+\frac {i}{\sqrt {19}}}{\left (-1+i \sqrt {19}+2 x\right ) \log \left (-3-x^2 (1+5 \log (4))\right )}\right ) \, dx-\int \left (\frac {\left (1-\frac {i}{\sqrt {19}}\right ) \log \left (5-x+x^2\right )}{\left (-1-i \sqrt {19}+2 x\right ) \log \left (-3-x^2 (1+5 \log (4))\right )}+\frac {\left (1+\frac {i}{\sqrt {19}}\right ) \log \left (5-x+x^2\right )}{\left (-1+i \sqrt {19}+2 x\right ) \log \left (-3-x^2 (1+5 \log (4))\right )}\right ) \, dx+\int \left (\frac {\log \left (5-x+x^2\right )}{\log \left (-3-x^2 (1+5 \log (4))\right )}+\frac {(-5+x) \log \left (5-x+x^2\right )}{\left (5-x+x^2\right ) \log \left (-3-x^2 (1+5 \log (4))\right )}\right ) \, dx\\ &=2 \int \frac {1}{\log \left (-3+x^2 (-1-5 \log (4))\right )} \, dx-2 \int \frac {\log \left (5-x+x^2\right )}{\log ^2\left (-3-x^2 (1+5 \log (4))\right )} \, dx+2 \int \frac {-5+x}{\left (5-x+x^2\right ) \log \left (-3-x^2 (1+5 \log (4))\right )} \, dx+\frac {(10 i) \int \frac {\log \left (5-x+x^2\right )}{\left (1+i \sqrt {19}-2 x\right ) \log \left (-3-x^2 (1+5 \log (4))\right )} \, dx}{\sqrt {19}}+\frac {(10 i) \int \frac {\log \left (5-x+x^2\right )}{\left (-1+i \sqrt {19}+2 x\right ) \log \left (-3-x^2 (1+5 \log (4))\right )} \, dx}{\sqrt {19}}-\frac {1}{19} \left (19-i \sqrt {19}\right ) \int \frac {1}{\left (-1-i \sqrt {19}+2 x\right ) \log \left (-3+x^2 (-1-5 \log (4))\right )} \, dx-\frac {1}{19} \left (19-i \sqrt {19}\right ) \int \frac {\log \left (5-x+x^2\right )}{\left (-1-i \sqrt {19}+2 x\right ) \log \left (-3-x^2 (1+5 \log (4))\right )} \, dx-\frac {1}{19} \left (19+i \sqrt {19}\right ) \int \frac {1}{\left (-1+i \sqrt {19}+2 x\right ) \log \left (-3+x^2 (-1-5 \log (4))\right )} \, dx-\frac {1}{19} \left (19+i \sqrt {19}\right ) \int \frac {\log \left (5-x+x^2\right )}{\left (-1+i \sqrt {19}+2 x\right ) \log \left (-3-x^2 (1+5 \log (4))\right )} \, dx+\left (i \sqrt {\frac {3}{1+5 \log (4)}}\right ) \int \frac {\log \left (5-x+x^2\right )}{\left (-x+i \sqrt {\frac {3}{1+5 \log (4)}}\right ) \log ^2\left (-3-x^2 (1+5 \log (4))\right )} \, dx+\left (i \sqrt {\frac {3}{1+5 \log (4)}}\right ) \int \frac {\log \left (5-x+x^2\right )}{\left (x+i \sqrt {\frac {3}{1+5 \log (4)}}\right ) \log ^2\left (-3-x^2 (1+5 \log (4))\right )} \, dx+\int \frac {\log \left (5-x+x^2\right )}{\log \left (-3-x^2 (1+5 \log (4))\right )} \, dx+\int \frac {(-5+x) \log \left (5-x+x^2\right )}{\left (5-x+x^2\right ) \log \left (-3-x^2 (1+5 \log (4))\right )} \, dx\\ &=2 \int \frac {1}{\log \left (-3+x^2 (-1-5 \log (4))\right )} \, dx+2 \int \left (-\frac {5}{\left (5-x+x^2\right ) \log \left (-3-x^2 (1+5 \log (4))\right )}+\frac {x}{\left (5-x+x^2\right ) \log \left (-3-x^2 (1+5 \log (4))\right )}\right ) \, dx-2 \int \frac {\log \left (5-x+x^2\right )}{\log ^2\left (-3-x^2 (1+5 \log (4))\right )} \, dx+\frac {(10 i) \int \frac {\log \left (5-x+x^2\right )}{\left (1+i \sqrt {19}-2 x\right ) \log \left (-3-x^2 (1+5 \log (4))\right )} \, dx}{\sqrt {19}}+\frac {(10 i) \int \frac {\log \left (5-x+x^2\right )}{\left (-1+i \sqrt {19}+2 x\right ) \log \left (-3-x^2 (1+5 \log (4))\right )} \, dx}{\sqrt {19}}-\frac {1}{19} \left (19-i \sqrt {19}\right ) \int \frac {1}{\left (-1-i \sqrt {19}+2 x\right ) \log \left (-3+x^2 (-1-5 \log (4))\right )} \, dx-\frac {1}{19} \left (19-i \sqrt {19}\right ) \int \frac {\log \left (5-x+x^2\right )}{\left (-1-i \sqrt {19}+2 x\right ) \log \left (-3-x^2 (1+5 \log (4))\right )} \, dx-\frac {1}{19} \left (19+i \sqrt {19}\right ) \int \frac {1}{\left (-1+i \sqrt {19}+2 x\right ) \log \left (-3+x^2 (-1-5 \log (4))\right )} \, dx-\frac {1}{19} \left (19+i \sqrt {19}\right ) \int \frac {\log \left (5-x+x^2\right )}{\left (-1+i \sqrt {19}+2 x\right ) \log \left (-3-x^2 (1+5 \log (4))\right )} \, dx+\left (i \sqrt {\frac {3}{1+5 \log (4)}}\right ) \int \frac {\log \left (5-x+x^2\right )}{\left (-x+i \sqrt {\frac {3}{1+5 \log (4)}}\right ) \log ^2\left (-3-x^2 (1+5 \log (4))\right )} \, dx+\left (i \sqrt {\frac {3}{1+5 \log (4)}}\right ) \int \frac {\log \left (5-x+x^2\right )}{\left (x+i \sqrt {\frac {3}{1+5 \log (4)}}\right ) \log ^2\left (-3-x^2 (1+5 \log (4))\right )} \, dx+\int \left (-\frac {5 \log \left (5-x+x^2\right )}{\left (5-x+x^2\right ) \log \left (-3-x^2 (1+5 \log (4))\right )}+\frac {x \log \left (5-x+x^2\right )}{\left (5-x+x^2\right ) \log \left (-3-x^2 (1+5 \log (4))\right )}\right ) \, dx+\int \frac {\log \left (5-x+x^2\right )}{\log \left (-3-x^2 (1+5 \log (4))\right )} \, dx\\ &=2 \int \frac {1}{\log \left (-3+x^2 (-1-5 \log (4))\right )} \, dx-2 \int \frac {\log \left (5-x+x^2\right )}{\log ^2\left (-3-x^2 (1+5 \log (4))\right )} \, dx+2 \int \frac {x}{\left (5-x+x^2\right ) \log \left (-3-x^2 (1+5 \log (4))\right )} \, dx-5 \int \frac {\log \left (5-x+x^2\right )}{\left (5-x+x^2\right ) \log \left (-3-x^2 (1+5 \log (4))\right )} \, dx-10 \int \frac {1}{\left (5-x+x^2\right ) \log \left (-3-x^2 (1+5 \log (4))\right )} \, dx+\frac {(10 i) \int \frac {\log \left (5-x+x^2\right )}{\left (1+i \sqrt {19}-2 x\right ) \log \left (-3-x^2 (1+5 \log (4))\right )} \, dx}{\sqrt {19}}+\frac {(10 i) \int \frac {\log \left (5-x+x^2\right )}{\left (-1+i \sqrt {19}+2 x\right ) \log \left (-3-x^2 (1+5 \log (4))\right )} \, dx}{\sqrt {19}}-\frac {1}{19} \left (19-i \sqrt {19}\right ) \int \frac {1}{\left (-1-i \sqrt {19}+2 x\right ) \log \left (-3+x^2 (-1-5 \log (4))\right )} \, dx-\frac {1}{19} \left (19-i \sqrt {19}\right ) \int \frac {\log \left (5-x+x^2\right )}{\left (-1-i \sqrt {19}+2 x\right ) \log \left (-3-x^2 (1+5 \log (4))\right )} \, dx-\frac {1}{19} \left (19+i \sqrt {19}\right ) \int \frac {1}{\left (-1+i \sqrt {19}+2 x\right ) \log \left (-3+x^2 (-1-5 \log (4))\right )} \, dx-\frac {1}{19} \left (19+i \sqrt {19}\right ) \int \frac {\log \left (5-x+x^2\right )}{\left (-1+i \sqrt {19}+2 x\right ) \log \left (-3-x^2 (1+5 \log (4))\right )} \, dx+\left (i \sqrt {\frac {3}{1+5 \log (4)}}\right ) \int \frac {\log \left (5-x+x^2\right )}{\left (-x+i \sqrt {\frac {3}{1+5 \log (4)}}\right ) \log ^2\left (-3-x^2 (1+5 \log (4))\right )} \, dx+\left (i \sqrt {\frac {3}{1+5 \log (4)}}\right ) \int \frac {\log \left (5-x+x^2\right )}{\left (x+i \sqrt {\frac {3}{1+5 \log (4)}}\right ) \log ^2\left (-3-x^2 (1+5 \log (4))\right )} \, dx+\int \frac {\log \left (5-x+x^2\right )}{\log \left (-3-x^2 (1+5 \log (4))\right )} \, dx+\int \frac {x \log \left (5-x+x^2\right )}{\left (5-x+x^2\right ) \log \left (-3-x^2 (1+5 \log (4))\right )} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.10, size = 27, normalized size = 0.96 \begin {gather*} \frac {x \log \left (5-x+x^2\right )}{\log \left (-3-x^2 (1+5 \log (4))\right )} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[((-3*x + 6*x^2 - x^3 + 2*x^4 + (-5*x^3 + 10*x^4)*Log[4])*Log[-3 - x^2 - 5*x^2*Log[4]] + Log[5 - x +
x^2]*(-10*x^2 + 2*x^3 - 2*x^4 + (-50*x^2 + 10*x^3 - 10*x^4)*Log[4] + (15 - 3*x + 8*x^2 - x^3 + x^4 + (25*x^2 -
5*x^3 + 5*x^4)*Log[4])*Log[-3 - x^2 - 5*x^2*Log[4]]))/((15 - 3*x + 8*x^2 - x^3 + x^4 + (25*x^2 - 5*x^3 + 5*x^
4)*Log[4])*Log[-3 - x^2 - 5*x^2*Log[4]]^2),x]

[Out]

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

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fricas [A]  time = 0.53, size = 28, normalized size = 1.00 \begin {gather*} \frac {x \log \left (x^{2} - x + 5\right )}{\log \left (-10 \, x^{2} \log \relax (2) - x^{2} - 3\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((2*(5*x^4-5*x^3+25*x^2)*log(2)+x^4-x^3+8*x^2-3*x+15)*log(-10*x^2*log(2)-x^2-3)+2*(-10*x^4+10*x^3-5
0*x^2)*log(2)-2*x^4+2*x^3-10*x^2)*log(x^2-x+5)+(2*(10*x^4-5*x^3)*log(2)+2*x^4-x^3+6*x^2-3*x)*log(-10*x^2*log(2
)-x^2-3))/(2*(5*x^4-5*x^3+25*x^2)*log(2)+x^4-x^3+8*x^2-3*x+15)/log(-10*x^2*log(2)-x^2-3)^2,x, algorithm="frica
s")

[Out]

x*log(x^2 - x + 5)/log(-10*x^2*log(2) - x^2 - 3)

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giac [F(-2)]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: TypeError} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((2*(5*x^4-5*x^3+25*x^2)*log(2)+x^4-x^3+8*x^2-3*x+15)*log(-10*x^2*log(2)-x^2-3)+2*(-10*x^4+10*x^3-5
0*x^2)*log(2)-2*x^4+2*x^3-10*x^2)*log(x^2-x+5)+(2*(10*x^4-5*x^3)*log(2)+2*x^4-x^3+6*x^2-3*x)*log(-10*x^2*log(2
)-x^2-3))/(2*(5*x^4-5*x^3+25*x^2)*log(2)+x^4-x^3+8*x^2-3*x+15)/log(-10*x^2*log(2)-x^2-3)^2,x, algorithm="giac"
)

[Out]

Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,sageVARx):;OUTP
UT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value

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maple [A]  time = 0.13, size = 29, normalized size = 1.04

method	result	size
risch	\(\frac {x \ln \left (x^{2}-x +5\right )}{\ln \left (-10 x^{2} \ln \relax (2)-x^{2}-3\right )}\)	\(29\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((2*(5*x^4-5*x^3+25*x^2)*ln(2)+x^4-x^3+8*x^2-3*x+15)*ln(-10*x^2*ln(2)-x^2-3)+2*(-10*x^4+10*x^3-50*x^2)*ln
(2)-2*x^4+2*x^3-10*x^2)*ln(x^2-x+5)+(2*(10*x^4-5*x^3)*ln(2)+2*x^4-x^3+6*x^2-3*x)*ln(-10*x^2*ln(2)-x^2-3))/(2*(
5*x^4-5*x^3+25*x^2)*ln(2)+x^4-x^3+8*x^2-3*x+15)/ln(-10*x^2*ln(2)-x^2-3)^2,x,method=_RETURNVERBOSE)

[Out]

x*ln(x^2-x+5)/ln(-10*x^2*ln(2)-x^2-3)

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maxima [A]  time = 0.51, size = 27, normalized size = 0.96 \begin {gather*} \frac {x \log \left (x^{2} - x + 5\right )}{\log \left (-x^{2} {\left (10 \, \log \relax (2) + 1\right )} - 3\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((2*(5*x^4-5*x^3+25*x^2)*log(2)+x^4-x^3+8*x^2-3*x+15)*log(-10*x^2*log(2)-x^2-3)+2*(-10*x^4+10*x^3-5
0*x^2)*log(2)-2*x^4+2*x^3-10*x^2)*log(x^2-x+5)+(2*(10*x^4-5*x^3)*log(2)+2*x^4-x^3+6*x^2-3*x)*log(-10*x^2*log(2
)-x^2-3))/(2*(5*x^4-5*x^3+25*x^2)*log(2)+x^4-x^3+8*x^2-3*x+15)/log(-10*x^2*log(2)-x^2-3)^2,x, algorithm="maxim
a")

[Out]

x*log(x^2 - x + 5)/log(-x^2*(10*log(2) + 1) - 3)

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mupad [B]  time = 3.26, size = 199, normalized size = 7.11 \begin {gather*} x+\frac {x\,\ln \left (x^2-x+5\right )-\frac {\ln \left (-10\,x^2\,\ln \relax (2)-x^2-3\right )\,\left (10\,x^2\,\ln \relax (2)+x^2+3\right )\,\left (5\,\ln \left (x^2-x+5\right )-x-x\,\ln \left (x^2-x+5\right )+x^2\,\ln \left (x^2-x+5\right )+2\,x^2\right )}{2\,x\,\left (10\,\ln \relax (2)+1\right )\,\left (x^2-x+5\right )}}{\ln \left (-10\,x^2\,\ln \relax (2)-x^2-3\right )}-\frac {50\,\ln \relax (2)+x\,\left (90\,\ln \relax (2)+3\right )+8}{\left (20\,\ln \relax (2)+2\right )\,x^2+\left (-20\,\ln \relax (2)-2\right )\,x+100\,\ln \relax (2)+10}+\frac {\ln \left (x^2-x+5\right )\,\left (\frac {x^2}{2}+\frac {3}{2\,\left (10\,\ln \relax (2)+1\right )}\right )}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(log(- 10*x^2*log(2) - x^2 - 3)*(3*x + 2*log(2)*(5*x^3 - 10*x^4) - 6*x^2 + x^3 - 2*x^4) + log(x^2 - x + 5
)*(2*log(2)*(50*x^2 - 10*x^3 + 10*x^4) - log(- 10*x^2*log(2) - x^2 - 3)*(2*log(2)*(25*x^2 - 5*x^3 + 5*x^4) - 3
*x + 8*x^2 - x^3 + x^4 + 15) + 10*x^2 - 2*x^3 + 2*x^4))/(log(- 10*x^2*log(2) - x^2 - 3)^2*(2*log(2)*(25*x^2 -
5*x^3 + 5*x^4) - 3*x + 8*x^2 - x^3 + x^4 + 15)),x)

[Out]

x + (x*log(x^2 - x + 5) - (log(- 10*x^2*log(2) - x^2 - 3)*(10*x^2*log(2) + x^2 + 3)*(5*log(x^2 - x + 5) - x -
x*log(x^2 - x + 5) + x^2*log(x^2 - x + 5) + 2*x^2))/(2*x*(10*log(2) + 1)*(x^2 - x + 5)))/log(- 10*x^2*log(2) -
x^2 - 3) - (50*log(2) + x*(90*log(2) + 3) + 8)/(100*log(2) - x*(20*log(2) + 2) + x^2*(20*log(2) + 2) + 10) +
(log(x^2 - x + 5)*(3/(2*(10*log(2) + 1)) + x^2/2))/x

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sympy [A]  time = 0.51, size = 26, normalized size = 0.93 \begin {gather*} \frac {x \log {\left (x^{2} - x + 5 \right )}}{\log {\left (- 10 x^{2} \log {\relax (2 )} - x^{2} - 3 \right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((2*(5*x**4-5*x**3+25*x**2)*ln(2)+x**4-x**3+8*x**2-3*x+15)*ln(-10*x**2*ln(2)-x**2-3)+2*(-10*x**4+10
*x**3-50*x**2)*ln(2)-2*x**4+2*x**3-10*x**2)*ln(x**2-x+5)+(2*(10*x**4-5*x**3)*ln(2)+2*x**4-x**3+6*x**2-3*x)*ln(
-10*x**2*ln(2)-x**2-3))/(2*(5*x**4-5*x**3+25*x**2)*ln(2)+x**4-x**3+8*x**2-3*x+15)/ln(-10*x**2*ln(2)-x**2-3)**2
,x)

[Out]

x*log(x**2 - x + 5)/log(-10*x**2*log(2) - x**2 - 3)

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