\(\int \frac {48 x+141 x^3-42 x^4+3 x^5+e^{4+x} (69 x-27 x^2+3 x^3)+(-48 x+21 x^2-51 x^3+21 x^4-3 x^5+e^{4+x} (-48+21 x-3 x^2)) \log (\frac {16-7 x+x^2}{e^{4+x}+x+x^3})}{(16 x^3-7 x^4+17 x^5-7 x^6+x^7+e^{4+x} (16 x^2-7 x^3+x^4)) \log ^2(\frac {16-7 x+x^2}{e^{4+x}+x+x^3})} \, dx\) [5857]

Optimal result

Integrand size = 173, antiderivative size = 28 \[ \int \frac {48 x+141 x^3-42 x^4+3 x^5+e^{4+x} \left (69 x-27 x^2+3 x^3\right )+\left (-48 x+21 x^2-51 x^3+21 x^4-3 x^5+e^{4+x} \left (-48+21 x-3 x^2\right )\right ) \log \left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )}{\left (16 x^3-7 x^4+17 x^5-7 x^6+x^7+e^{4+x} \left (16 x^2-7 x^3+x^4\right )\right ) \log ^2\left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )} \, dx=\frac {3}{x \log \left (\frac {(-4+x)^2+x}{e^{4+x}+x+x^3}\right )} \]

[Out]

3/ln((x+(x-4)^2)/(exp(4+x)+x^3+x))/x

Rubi [F]

\[ \int \frac {48 x+141 x^3-42 x^4+3 x^5+e^{4+x} \left (69 x-27 x^2+3 x^3\right )+\left (-48 x+21 x^2-51 x^3+21 x^4-3 x^5+e^{4+x} \left (-48+21 x-3 x^2\right )\right ) \log \left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )}{\left (16 x^3-7 x^4+17 x^5-7 x^6+x^7+e^{4+x} \left (16 x^2-7 x^3+x^4\right )\right ) \log ^2\left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )} \, dx=\int \frac {48 x+141 x^3-42 x^4+3 x^5+e^{4+x} \left (69 x-27 x^2+3 x^3\right )+\left (-48 x+21 x^2-51 x^3+21 x^4-3 x^5+e^{4+x} \left (-48+21 x-3 x^2\right )\right ) \log \left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )}{\left (16 x^3-7 x^4+17 x^5-7 x^6+x^7+e^{4+x} \left (16 x^2-7 x^3+x^4\right )\right ) \log ^2\left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )} \, dx \]

[In]

Int[(48*x + 141*x^3 - 42*x^4 + 3*x^5 + E^(4 + x)*(69*x - 27*x^2 + 3*x^3) + (-48*x + 21*x^2 - 51*x^3 + 21*x^4 -
3*x^5 + E^(4 + x)*(-48 + 21*x - 3*x^2))*Log[(16 - 7*x + x^2)/(E^(4 + x) + x + x^3)])/((16*x^3 - 7*x^4 + 17*x^
5 - 7*x^6 + x^7 + E^(4 + x)*(16*x^2 - 7*x^3 + x^4))*Log[(16 - 7*x + x^2)/(E^(4 + x) + x + x^3)]^2),x]

[Out]

((17*I)/8)*Sqrt[3/5]*Defer[Int][1/((7 + I*Sqrt[15] - 2*x)*Log[(16 - 7*x + x^2)/(E^(4 + x) + x + x^3)]^2), x] +
(69*Defer[Int][1/(x*Log[(16 - 7*x + x^2)/(E^(4 + x) + x + x^3)]^2), x])/16 - (7*(15 - (7*I)*Sqrt[15])*Defer[I
nt][1/((-7 - I*Sqrt[15] + 2*x)*Log[(16 - 7*x + x^2)/(E^(4 + x) + x + x^3)]^2), x])/80 + ((17*I)/8)*Sqrt[3/5]*D
efer[Int][1/((-7 + I*Sqrt[15] + 2*x)*Log[(16 - 7*x + x^2)/(E^(4 + x) + x + x^3)]^2), x] - (7*(15 + (7*I)*Sqrt[
15])*Defer[Int][1/((-7 + I*Sqrt[15] + 2*x)*Log[(16 - 7*x + x^2)/(E^(4 + x) + x + x^3)]^2), x])/80 - 3*Defer[In
t][1/((E^(4 + x) + x + x^3)*Log[(16 - 7*x + x^2)/(E^(4 + x) + x + x^3)]^2), x] + 3*Defer[Int][1/(x*(E^(4 + x)
+ x + x^3)*Log[(16 - 7*x + x^2)/(E^(4 + x) + x + x^3)]^2), x] + 9*Defer[Int][x/((E^(4 + x) + x + x^3)*Log[(16
- 7*x + x^2)/(E^(4 + x) + x + x^3)]^2), x] - 3*Defer[Int][x^2/((E^(4 + x) + x + x^3)*Log[(16 - 7*x + x^2)/(E^(
4 + x) + x + x^3)]^2), x] - 3*Defer[Int][1/(x^2*Log[(16 - 7*x + x^2)/(E^(4 + x) + x + x^3)]), x]

Rubi steps \begin{align*} \text {integral}& = \int \frac {3 \left (\frac {x \left (16+47 x^2-14 x^3+x^4+e^{4+x} \left (23-9 x+x^2\right )\right )}{\left (16-7 x+x^2\right ) \left (e^{4+x}+x+x^3\right )}-\log \left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )\right )}{x^2 \log ^2\left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )} \, dx \\ & = 3 \int \frac {\frac {x \left (16+47 x^2-14 x^3+x^4+e^{4+x} \left (23-9 x+x^2\right )\right )}{\left (16-7 x+x^2\right ) \left (e^{4+x}+x+x^3\right )}-\log \left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )}{x^2 \log ^2\left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )} \, dx \\ & = 3 \int \left (-\frac {-1+x-3 x^2+x^3}{x \left (e^{4+x}+x+x^3\right ) \log ^2\left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )}+\frac {23 x-9 x^2+x^3-16 \log \left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )+7 x \log \left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )-x^2 \log \left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )}{x^2 \left (16-7 x+x^2\right ) \log ^2\left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )}\right ) \, dx \\ & = -\left (3 \int \frac {-1+x-3 x^2+x^3}{x \left (e^{4+x}+x+x^3\right ) \log ^2\left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )} \, dx\right )+3 \int \frac {23 x-9 x^2+x^3-16 \log \left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )+7 x \log \left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )-x^2 \log \left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )}{x^2 \left (16-7 x+x^2\right ) \log ^2\left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )} \, dx \\ & = -\left (3 \int \left (\frac {1}{\left (e^{4+x}+x+x^3\right ) \log ^2\left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )}-\frac {1}{x \left (e^{4+x}+x+x^3\right ) \log ^2\left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )}-\frac {3 x}{\left (e^{4+x}+x+x^3\right ) \log ^2\left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )}+\frac {x^2}{\left (e^{4+x}+x+x^3\right ) \log ^2\left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )}\right ) \, dx\right )+3 \int \frac {\frac {x \left (23-9 x+x^2\right )}{16-7 x+x^2}-\log \left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )}{x^2 \log ^2\left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )} \, dx \\ & = 3 \int \left (\frac {23-9 x+x^2}{x \left (16-7 x+x^2\right ) \log ^2\left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )}-\frac {1}{x^2 \log \left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )}\right ) \, dx-3 \int \frac {1}{\left (e^{4+x}+x+x^3\right ) \log ^2\left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )} \, dx+3 \int \frac {1}{x \left (e^{4+x}+x+x^3\right ) \log ^2\left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )} \, dx-3 \int \frac {x^2}{\left (e^{4+x}+x+x^3\right ) \log ^2\left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )} \, dx+9 \int \frac {x}{\left (e^{4+x}+x+x^3\right ) \log ^2\left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )} \, dx \\ & = 3 \int \frac {23-9 x+x^2}{x \left (16-7 x+x^2\right ) \log ^2\left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )} \, dx-3 \int \frac {1}{\left (e^{4+x}+x+x^3\right ) \log ^2\left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )} \, dx+3 \int \frac {1}{x \left (e^{4+x}+x+x^3\right ) \log ^2\left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )} \, dx-3 \int \frac {x^2}{\left (e^{4+x}+x+x^3\right ) \log ^2\left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )} \, dx-3 \int \frac {1}{x^2 \log \left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )} \, dx+9 \int \frac {x}{\left (e^{4+x}+x+x^3\right ) \log ^2\left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )} \, dx \\ & = 3 \int \left (\frac {23}{16 x \log ^2\left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )}+\frac {17-7 x}{16 \left (16-7 x+x^2\right ) \log ^2\left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )}\right ) \, dx-3 \int \frac {1}{\left (e^{4+x}+x+x^3\right ) \log ^2\left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )} \, dx+3 \int \frac {1}{x \left (e^{4+x}+x+x^3\right ) \log ^2\left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )} \, dx-3 \int \frac {x^2}{\left (e^{4+x}+x+x^3\right ) \log ^2\left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )} \, dx-3 \int \frac {1}{x^2 \log \left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )} \, dx+9 \int \frac {x}{\left (e^{4+x}+x+x^3\right ) \log ^2\left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )} \, dx \\ & = \frac {3}{16} \int \frac {17-7 x}{\left (16-7 x+x^2\right ) \log ^2\left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )} \, dx-3 \int \frac {1}{\left (e^{4+x}+x+x^3\right ) \log ^2\left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )} \, dx+3 \int \frac {1}{x \left (e^{4+x}+x+x^3\right ) \log ^2\left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )} \, dx-3 \int \frac {x^2}{\left (e^{4+x}+x+x^3\right ) \log ^2\left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )} \, dx-3 \int \frac {1}{x^2 \log \left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )} \, dx+\frac {69}{16} \int \frac {1}{x \log ^2\left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )} \, dx+9 \int \frac {x}{\left (e^{4+x}+x+x^3\right ) \log ^2\left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )} \, dx \\ & = \frac {3}{16} \int \left (\frac {17}{\left (16-7 x+x^2\right ) \log ^2\left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )}-\frac {7 x}{\left (16-7 x+x^2\right ) \log ^2\left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )}\right ) \, dx-3 \int \frac {1}{\left (e^{4+x}+x+x^3\right ) \log ^2\left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )} \, dx+3 \int \frac {1}{x \left (e^{4+x}+x+x^3\right ) \log ^2\left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )} \, dx-3 \int \frac {x^2}{\left (e^{4+x}+x+x^3\right ) \log ^2\left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )} \, dx-3 \int \frac {1}{x^2 \log \left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )} \, dx+\frac {69}{16} \int \frac {1}{x \log ^2\left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )} \, dx+9 \int \frac {x}{\left (e^{4+x}+x+x^3\right ) \log ^2\left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )} \, dx \\ & = -\left (\frac {21}{16} \int \frac {x}{\left (16-7 x+x^2\right ) \log ^2\left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )} \, dx\right )-3 \int \frac {1}{\left (e^{4+x}+x+x^3\right ) \log ^2\left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )} \, dx+3 \int \frac {1}{x \left (e^{4+x}+x+x^3\right ) \log ^2\left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )} \, dx-3 \int \frac {x^2}{\left (e^{4+x}+x+x^3\right ) \log ^2\left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )} \, dx-3 \int \frac {1}{x^2 \log \left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )} \, dx+\frac {51}{16} \int \frac {1}{\left (16-7 x+x^2\right ) \log ^2\left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )} \, dx+\frac {69}{16} \int \frac {1}{x \log ^2\left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )} \, dx+9 \int \frac {x}{\left (e^{4+x}+x+x^3\right ) \log ^2\left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )} \, dx \\ & = -\left (\frac {21}{16} \int \left (\frac {1-\frac {7 i}{\sqrt {15}}}{\left (-7-i \sqrt {15}+2 x\right ) \log ^2\left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )}+\frac {1+\frac {7 i}{\sqrt {15}}}{\left (-7+i \sqrt {15}+2 x\right ) \log ^2\left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )}\right ) \, dx\right )-3 \int \frac {1}{\left (e^{4+x}+x+x^3\right ) \log ^2\left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )} \, dx+3 \int \frac {1}{x \left (e^{4+x}+x+x^3\right ) \log ^2\left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )} \, dx-3 \int \frac {x^2}{\left (e^{4+x}+x+x^3\right ) \log ^2\left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )} \, dx-3 \int \frac {1}{x^2 \log \left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )} \, dx+\frac {51}{16} \int \left (\frac {2 i}{\sqrt {15} \left (7+i \sqrt {15}-2 x\right ) \log ^2\left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )}+\frac {2 i}{\sqrt {15} \left (-7+i \sqrt {15}+2 x\right ) \log ^2\left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )}\right ) \, dx+\frac {69}{16} \int \frac {1}{x \log ^2\left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )} \, dx+9 \int \frac {x}{\left (e^{4+x}+x+x^3\right ) \log ^2\left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )} \, dx \\ & = -\left (3 \int \frac {1}{\left (e^{4+x}+x+x^3\right ) \log ^2\left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )} \, dx\right )+3 \int \frac {1}{x \left (e^{4+x}+x+x^3\right ) \log ^2\left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )} \, dx-3 \int \frac {x^2}{\left (e^{4+x}+x+x^3\right ) \log ^2\left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )} \, dx-3 \int \frac {1}{x^2 \log \left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )} \, dx+\frac {69}{16} \int \frac {1}{x \log ^2\left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )} \, dx+9 \int \frac {x}{\left (e^{4+x}+x+x^3\right ) \log ^2\left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )} \, dx+\frac {1}{8} \left (17 i \sqrt {\frac {3}{5}}\right ) \int \frac {1}{\left (7+i \sqrt {15}-2 x\right ) \log ^2\left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )} \, dx+\frac {1}{8} \left (17 i \sqrt {\frac {3}{5}}\right ) \int \frac {1}{\left (-7+i \sqrt {15}+2 x\right ) \log ^2\left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )} \, dx-\frac {1}{80} \left (7 \left (15-7 i \sqrt {15}\right )\right ) \int \frac {1}{\left (-7-i \sqrt {15}+2 x\right ) \log ^2\left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )} \, dx-\frac {1}{80} \left (7 \left (15+7 i \sqrt {15}\right )\right ) \int \frac {1}{\left (-7+i \sqrt {15}+2 x\right ) \log ^2\left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )} \, dx \\ \end{align*}

Mathematica [A] (verified)

Time = 0.12 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.04 \[ \int \frac {48 x+141 x^3-42 x^4+3 x^5+e^{4+x} \left (69 x-27 x^2+3 x^3\right )+\left (-48 x+21 x^2-51 x^3+21 x^4-3 x^5+e^{4+x} \left (-48+21 x-3 x^2\right )\right ) \log \left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )}{\left (16 x^3-7 x^4+17 x^5-7 x^6+x^7+e^{4+x} \left (16 x^2-7 x^3+x^4\right )\right ) \log ^2\left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )} \, dx=\frac {3}{x \log \left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )} \]

[In]

Integrate[(48*x + 141*x^3 - 42*x^4 + 3*x^5 + E^(4 + x)*(69*x - 27*x^2 + 3*x^3) + (-48*x + 21*x^2 - 51*x^3 + 21
*x^4 - 3*x^5 + E^(4 + x)*(-48 + 21*x - 3*x^2))*Log[(16 - 7*x + x^2)/(E^(4 + x) + x + x^3)])/((16*x^3 - 7*x^4 +
17*x^5 - 7*x^6 + x^7 + E^(4 + x)*(16*x^2 - 7*x^3 + x^4))*Log[(16 - 7*x + x^2)/(E^(4 + x) + x + x^3)]^2),x]

[Out]

3/(x*Log[(16 - 7*x + x^2)/(E^(4 + x) + x + x^3)])

Maple [A] (verified)

Time = 7.57 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.04

method	result	size
parallelrisch	\(\frac {3}{\ln \left (\frac {x^{2}-7 x +16}{{\mathrm e}^{4+x}+x^{3}+x}\right ) x}\)	\(29\)
risch	\(\frac {6 i}{x \left (\pi \,\operatorname {csgn}\left (\frac {i}{{\mathrm e}^{4+x}+x^{3}+x}\right ) \operatorname {csgn}\left (i \left (x^{2}-7 x +16\right )\right ) \operatorname {csgn}\left (\frac {i \left (x^{2}-7 x +16\right )}{{\mathrm e}^{4+x}+x^{3}+x}\right )-\pi \,\operatorname {csgn}\left (\frac {i}{{\mathrm e}^{4+x}+x^{3}+x}\right ) {\operatorname {csgn}\left (\frac {i \left (x^{2}-7 x +16\right )}{{\mathrm e}^{4+x}+x^{3}+x}\right )}^{2}-\pi \,\operatorname {csgn}\left (i \left (x^{2}-7 x +16\right )\right ) {\operatorname {csgn}\left (\frac {i \left (x^{2}-7 x +16\right )}{{\mathrm e}^{4+x}+x^{3}+x}\right )}^{2}+\pi {\operatorname {csgn}\left (\frac {i \left (x^{2}-7 x +16\right )}{{\mathrm e}^{4+x}+x^{3}+x}\right )}^{3}+2 i \ln \left (x^{2}-7 x +16\right )-2 i \ln \left ({\mathrm e}^{4+x}+x^{3}+x \right )\right )}\)	\(197\)

[In]

int((((-3*x^2+21*x-48)*exp(4+x)-3*x^5+21*x^4-51*x^3+21*x^2-48*x)*ln((x^2-7*x+16)/(exp(4+x)+x^3+x))+(3*x^3-27*x
^2+69*x)*exp(4+x)+3*x^5-42*x^4+141*x^3+48*x)/((x^4-7*x^3+16*x^2)*exp(4+x)+x^7-7*x^6+17*x^5-7*x^4+16*x^3)/ln((x
^2-7*x+16)/(exp(4+x)+x^3+x))^2,x,method=_RETURNVERBOSE)

[Out]

3/ln((x^2-7*x+16)/(exp(4+x)+x^3+x))/x

Fricas [A] (verification not implemented)

none

Time = 0.24 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.00 \[ \int \frac {48 x+141 x^3-42 x^4+3 x^5+e^{4+x} \left (69 x-27 x^2+3 x^3\right )+\left (-48 x+21 x^2-51 x^3+21 x^4-3 x^5+e^{4+x} \left (-48+21 x-3 x^2\right )\right ) \log \left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )}{\left (16 x^3-7 x^4+17 x^5-7 x^6+x^7+e^{4+x} \left (16 x^2-7 x^3+x^4\right )\right ) \log ^2\left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )} \, dx=\frac {3}{x \log \left (\frac {x^{2} - 7 \, x + 16}{x^{3} + x + e^{\left (x + 4\right )}}\right )} \]

[In]

integrate((((-3*x^2+21*x-48)*exp(4+x)-3*x^5+21*x^4-51*x^3+21*x^2-48*x)*log((x^2-7*x+16)/(exp(4+x)+x^3+x))+(3*x
^3-27*x^2+69*x)*exp(4+x)+3*x^5-42*x^4+141*x^3+48*x)/((x^4-7*x^3+16*x^2)*exp(4+x)+x^7-7*x^6+17*x^5-7*x^4+16*x^3
)/log((x^2-7*x+16)/(exp(4+x)+x^3+x))^2,x, algorithm="fricas")

[Out]

3/(x*log((x^2 - 7*x + 16)/(x^3 + x + e^(x + 4))))

Sympy [A] (verification not implemented)

Time = 0.25 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.79 \[ \int \frac {48 x+141 x^3-42 x^4+3 x^5+e^{4+x} \left (69 x-27 x^2+3 x^3\right )+\left (-48 x+21 x^2-51 x^3+21 x^4-3 x^5+e^{4+x} \left (-48+21 x-3 x^2\right )\right ) \log \left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )}{\left (16 x^3-7 x^4+17 x^5-7 x^6+x^7+e^{4+x} \left (16 x^2-7 x^3+x^4\right )\right ) \log ^2\left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )} \, dx=\frac {3}{x \log {\left (\frac {x^{2} - 7 x + 16}{x^{3} + x + e^{x + 4}} \right )}} \]

[In]

integrate((((-3*x**2+21*x-48)*exp(4+x)-3*x**5+21*x**4-51*x**3+21*x**2-48*x)*ln((x**2-7*x+16)/(exp(4+x)+x**3+x)
)+(3*x**3-27*x**2+69*x)*exp(4+x)+3*x**5-42*x**4+141*x**3+48*x)/((x**4-7*x**3+16*x**2)*exp(4+x)+x**7-7*x**6+17*
x**5-7*x**4+16*x**3)/ln((x**2-7*x+16)/(exp(4+x)+x**3+x))**2,x)

[Out]

3/(x*log((x**2 - 7*x + 16)/(x**3 + x + exp(x + 4))))

Maxima [A] (verification not implemented)

none

Time = 0.50 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.04 \[ \int \frac {48 x+141 x^3-42 x^4+3 x^5+e^{4+x} \left (69 x-27 x^2+3 x^3\right )+\left (-48 x+21 x^2-51 x^3+21 x^4-3 x^5+e^{4+x} \left (-48+21 x-3 x^2\right )\right ) \log \left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )}{\left (16 x^3-7 x^4+17 x^5-7 x^6+x^7+e^{4+x} \left (16 x^2-7 x^3+x^4\right )\right ) \log ^2\left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )} \, dx=-\frac {3}{x \log \left (x^{3} + x + e^{\left (x + 4\right )}\right ) - x \log \left (x^{2} - 7 \, x + 16\right )} \]

[In]

integrate((((-3*x^2+21*x-48)*exp(4+x)-3*x^5+21*x^4-51*x^3+21*x^2-48*x)*log((x^2-7*x+16)/(exp(4+x)+x^3+x))+(3*x
^3-27*x^2+69*x)*exp(4+x)+3*x^5-42*x^4+141*x^3+48*x)/((x^4-7*x^3+16*x^2)*exp(4+x)+x^7-7*x^6+17*x^5-7*x^4+16*x^3
)/log((x^2-7*x+16)/(exp(4+x)+x^3+x))^2,x, algorithm="maxima")

[Out]

-3/(x*log(x^3 + x + e^(x + 4)) - x*log(x^2 - 7*x + 16))

Giac [A] (verification not implemented)

none

Time = 0.58 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.00 \[ \int \frac {48 x+141 x^3-42 x^4+3 x^5+e^{4+x} \left (69 x-27 x^2+3 x^3\right )+\left (-48 x+21 x^2-51 x^3+21 x^4-3 x^5+e^{4+x} \left (-48+21 x-3 x^2\right )\right ) \log \left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )}{\left (16 x^3-7 x^4+17 x^5-7 x^6+x^7+e^{4+x} \left (16 x^2-7 x^3+x^4\right )\right ) \log ^2\left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )} \, dx=\frac {3}{x \log \left (\frac {x^{2} - 7 \, x + 16}{x^{3} + x + e^{\left (x + 4\right )}}\right )} \]

[In]

integrate((((-3*x^2+21*x-48)*exp(4+x)-3*x^5+21*x^4-51*x^3+21*x^2-48*x)*log((x^2-7*x+16)/(exp(4+x)+x^3+x))+(3*x
^3-27*x^2+69*x)*exp(4+x)+3*x^5-42*x^4+141*x^3+48*x)/((x^4-7*x^3+16*x^2)*exp(4+x)+x^7-7*x^6+17*x^5-7*x^4+16*x^3
)/log((x^2-7*x+16)/(exp(4+x)+x^3+x))^2,x, algorithm="giac")

[Out]

3/(x*log((x^2 - 7*x + 16)/(x^3 + x + e^(x + 4))))

Mupad [B] (verification not implemented)

Time = 12.55 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.04 \[ \int \frac {48 x+141 x^3-42 x^4+3 x^5+e^{4+x} \left (69 x-27 x^2+3 x^3\right )+\left (-48 x+21 x^2-51 x^3+21 x^4-3 x^5+e^{4+x} \left (-48+21 x-3 x^2\right )\right ) \log \left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )}{\left (16 x^3-7 x^4+17 x^5-7 x^6+x^7+e^{4+x} \left (16 x^2-7 x^3+x^4\right )\right ) \log ^2\left (\frac {16-7 x+x^2}{e^{4+x}+x+x^3}\right )} \, dx=\frac {3}{x\,\ln \left (\frac {x^2-7\,x+16}{x+{\mathrm {e}}^4\,{\mathrm {e}}^x+x^3}\right )} \]

[In]

int((48*x + exp(x + 4)*(69*x - 27*x^2 + 3*x^3) - log((x^2 - 7*x + 16)/(x + exp(x + 4) + x^3))*(48*x + exp(x +
4)*(3*x^2 - 21*x + 48) - 21*x^2 + 51*x^3 - 21*x^4 + 3*x^5) + 141*x^3 - 42*x^4 + 3*x^5)/(log((x^2 - 7*x + 16)/(
x + exp(x + 4) + x^3))^2*(exp(x + 4)*(16*x^2 - 7*x^3 + x^4) + 16*x^3 - 7*x^4 + 17*x^5 - 7*x^6 + x^7)),x)

[Out]

3/(x*log((x^2 - 7*x + 16)/(x + exp(4)*exp(x) + x^3)))