Integrand size = 61, antiderivative size = 233 \[ \int \frac {-9+7 x+x^2-6 x^4-8 x^5+5 x^6+5 x^7}{-12+48 x+24 x^2-144 x^3-87 x^4+42 x^5+21 x^6} \, dx=\frac {-182-570 x-285 x^2+285 x^3}{2394 (1+x)}+\sqrt {\frac {147447819270109}{193432722516432}+\frac {27432480848221}{13816623036888 \sqrt {7}}} \text {arctanh}\left (3 \sqrt {\frac {1}{53} \left (9-2 \sqrt {7}\right )}+\sqrt {\frac {7}{53} \left (9-2 \sqrt {7}\right )} x\right )-\frac {\sqrt {\frac {1}{53} \left (147447819270109-54864961696442 \sqrt {7}\right )} \text {arctanh}\left (\sqrt {\frac {81}{53}+\frac {18 \sqrt {7}}{53}}-\sqrt {\frac {63}{53}+\frac {14 \sqrt {7}}{53}} x\right )}{1910412}+\frac {1226 \log (1+x)}{9747}+\frac {13309 \log \left (2 \sqrt {7}-6 \sqrt {7} x+7 x^2\right )}{272916 \sqrt {7}}-\frac {13309 \log \left (-2 \sqrt {7}+6 \sqrt {7} x+7 x^2\right )}{272916 \sqrt {7}}+\frac {456517 \log \left (-4+24 x-36 x^2+7 x^4\right )}{1910412} \] Output:
(285*x^3-285*x^2-570*x-182)/(2394+2394*x)+1/101251836*(7814734421315777+29 07842969911426*7^(1/2))^(1/2)*arctanh(3/53*(477-106*7^(1/2))^(1/2)+1/53*(3 339-742*7^(1/2))^(1/2)*x)+1/101251836*(7814734421315777-2907842969911426*7 ^(1/2))^(1/2)*arctanh(-3/53*(477+106*7^(1/2))^(1/2)+1/53*(3339+742*7^(1/2) )^(1/2)*x)+1226/9747*ln(1+x)+13309/1910412*ln(2*7^(1/2)-6*7^(1/2)*x+7*x^2) *7^(1/2)-13309/1910412*ln(-2*7^(1/2)+6*7^(1/2)*x+7*x^2)*7^(1/2)+456517/191 0412*ln(7*x^4-36*x^2+24*x-4)
Result contains higher order function than in optimal. Order 9 vs. order 3 in optimal.
Time = 0.05 (sec) , antiderivative size = 129, normalized size of antiderivative = 0.55 \[ \int \frac {-9+7 x+x^2-6 x^4-8 x^5+5 x^6+5 x^7}{-12+48 x+24 x^2-144 x^3-87 x^4+42 x^5+21 x^6} \, dx=\frac {114 \left (-855-570 x+285 x^2-\frac {182}{1+x}\right )+34328 \log (1+x)+\text {RootSum}\left [-57+68 \text {$\#$1}+6 \text {$\#$1}^2-28 \text {$\#$1}^3+7 \text {$\#$1}^4\&,\frac {-2125483 \log (1+x-\text {$\#$1})+3661146 \log (1+x-\text {$\#$1}) \text {$\#$1}-2206771 \log (1+x-\text {$\#$1}) \text {$\#$1}^2+456517 \log (1+x-\text {$\#$1}) \text {$\#$1}^3}{17+3 \text {$\#$1}-21 \text {$\#$1}^2+7 \text {$\#$1}^3}\&\right ]}{272916} \] Input:
Integrate[(-9 + 7*x + x^2 - 6*x^4 - 8*x^5 + 5*x^6 + 5*x^7)/(-12 + 48*x + 2 4*x^2 - 144*x^3 - 87*x^4 + 42*x^5 + 21*x^6),x]
Output:
(114*(-855 - 570*x + 285*x^2 - 182/(1 + x)) + 34328*Log[1 + x] + RootSum[- 57 + 68*#1 + 6*#1^2 - 28*#1^3 + 7*#1^4 & , (-2125483*Log[1 + x - #1] + 366 1146*Log[1 + x - #1]*#1 - 2206771*Log[1 + x - #1]*#1^2 + 456517*Log[1 + x - #1]*#1^3)/(17 + 3*#1 - 21*#1^2 + 7*#1^3) & ])/272916
Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.
| \(\displaystyle \int \frac {5 x^7+5 x^6-8 x^5-6 x^4+x^2+7 x-9}{21 x^6+42 x^5-87 x^4-144 x^3+24 x^2+48 x-12} \, dx\) |
| \(\Big \downarrow \) 2462 |
| \(\displaystyle \int \left (\frac {456517 x^3-837220 x^2+617155 x-214591}{68229 \left (7 x^4-36 x^2+24 x-4\right )}+\frac {5 x}{21}+\frac {1226}{9747 (x+1)}+\frac {13}{171 (x+1)^2}-\frac {5}{21}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle \frac {12537391 \int \frac {x}{7 x^4-36 x^2+24 x-4}dx}{477603}-\frac {837220 \int \frac {x^2}{7 x^4-36 x^2+24 x-4}dx}{68229}-\frac {4241239 \sqrt {\frac {1}{742} \left (270+7 \sqrt {7}\right )} \text {arctanh}\left (\frac {2-3 x}{\sqrt {9-2 \sqrt {7}} x}\right )}{955206}+\frac {4241239 \sqrt {\frac {1}{742} \left (270-7 \sqrt {7}\right )} \text {arctanh}\left (\frac {2-3 x}{\sqrt {9+2 \sqrt {7}} x}\right )}{955206}+\frac {5 x^2}{42}-\frac {4241239 \log \left (-\frac {-\sqrt {7} x^2-6 x+2}{x^2}\right )}{1273608 \sqrt {7}}+\frac {4241239 \log \left (\frac {\sqrt {7} x^2-6 x+2}{x^2}\right )}{1273608 \sqrt {7}}+\frac {456517 \log \left (7 x^4-36 x^2+24 x-4\right )}{1910412}-\frac {5 x}{21}-\frac {13}{171 (x+1)}+\frac {1226 \log (x+1)}{9747}\) |
Input:
Int[(-9 + 7*x + x^2 - 6*x^4 - 8*x^5 + 5*x^6 + 5*x^7)/(-12 + 48*x + 24*x^2 - 144*x^3 - 87*x^4 + 42*x^5 + 21*x^6),x]
Output:
$Aborted
Result contains higher order function than in optimal. Order 9 vs. order 3.
Time = 0.07 (sec) , antiderivative size = 70, normalized size of antiderivative = 0.30
| method | result | size |
| risch | \(\frac {5 x^{2}}{42}-\frac {5 x}{21}-\frac {13}{171 \left (1+x \right )}+\frac {\left (\munderset {\textit {\_R} =\operatorname {RootOf}\left (444087 \textit {\_Z}^{4}-1354942456 \textit {\_Z}^{3}-177348969358 \textit {\_Z}^{2}+2046980307370824 \textit {\_Z} -961594993216030509\right )}{\sum }\textit {\_R} \ln \left (-6959558422351778579469 \textit {\_R}^{3}+20437113244618150785324361 \textit {\_R}^{2}+14202653843620853496116406745 \textit {\_R} +7985913953752581760050400284594 x -30758934757722092697299701470561\right )\right )}{3192}+\frac {1226 \ln \left (1+x \right )}{9747}\) | \(70\) |
| default | \(\frac {5 x^{2}}{42}-\frac {5 x}{21}+\frac {\left (\munderset {\textit {\_R} =\operatorname {RootOf}\left (7 \textit {\_Z}^{4}-36 \textit {\_Z}^{2}+24 \textit {\_Z} -4\right )}{\sum }\frac {\left (456517 \textit {\_R}^{3}-837220 \textit {\_R}^{2}+617155 \textit {\_R} -214591\right ) \ln \left (x -\textit {\_R} \right )}{7 \textit {\_R}^{3}-18 \textit {\_R} +6}\right )}{272916}-\frac {13}{171 \left (1+x \right )}+\frac {1226 \ln \left (1+x \right )}{9747}\) | \(78\) |
Input:
int((5*x^7+5*x^6-8*x^5-6*x^4+x^2+7*x-9)/(21*x^6+42*x^5-87*x^4-144*x^3+24*x ^2+48*x-12),x,method=_RETURNVERBOSE)
Output:
5/42*x^2-5/21*x-13/171/(1+x)+1/3192*sum(_R*ln(-6959558422351778579469*_R^3 +20437113244618150785324361*_R^2+14202653843620853496116406745*_R+79859139 53752581760050400284594*x-30758934757722092697299701470561),_R=RootOf(4440 87*_Z^4-1354942456*_Z^3-177348969358*_Z^2+2046980307370824*_Z-961594993216 030509))+1226/9747*ln(1+x)
Time = 0.09 (sec) , antiderivative size = 253, normalized size of antiderivative = 1.09 \[ \int \frac {-9+7 x+x^2-6 x^4-8 x^5+5 x^6+5 x^7}{-12+48 x+24 x^2-144 x^3-87 x^4+42 x^5+21 x^6} \, dx=\frac {454860 \, x^{3} - 454860 \, x^{2} - {\left (26618 \, \sqrt {7} {\left (x + 1\right )} + {\left (x + 1\right )} \sqrt {\frac {54864961696442}{53} \, \sqrt {7} + \frac {147447819270109}{53}} - 913034 \, x - 913034\right )} \log \left (\sqrt {\frac {54864961696442}{53} \, \sqrt {7} + \frac {147447819270109}{53}} {\left (13611035 \, \sqrt {7} - 51143176\right )} + 24883066697517 \, x + 10664171441793 \, \sqrt {7}\right ) - {\left (26618 \, \sqrt {7} {\left (x + 1\right )} - {\left (x + 1\right )} \sqrt {\frac {54864961696442}{53} \, \sqrt {7} + \frac {147447819270109}{53}} - 913034 \, x - 913034\right )} \log \left (-\sqrt {\frac {54864961696442}{53} \, \sqrt {7} + \frac {147447819270109}{53}} {\left (13611035 \, \sqrt {7} - 51143176\right )} + 24883066697517 \, x + 10664171441793 \, \sqrt {7}\right ) + {\left (26618 \, \sqrt {7} {\left (x + 1\right )} + {\left (x + 1\right )} \sqrt {-\frac {54864961696442}{53} \, \sqrt {7} + \frac {147447819270109}{53}} + 913034 \, x + 913034\right )} \log \left ({\left (13611035 \, \sqrt {7} + 51143176\right )} \sqrt {-\frac {54864961696442}{53} \, \sqrt {7} + \frac {147447819270109}{53}} + 24883066697517 \, x - 10664171441793 \, \sqrt {7}\right ) + {\left (26618 \, \sqrt {7} {\left (x + 1\right )} - {\left (x + 1\right )} \sqrt {-\frac {54864961696442}{53} \, \sqrt {7} + \frac {147447819270109}{53}} + 913034 \, x + 913034\right )} \log \left (-{\left (13611035 \, \sqrt {7} + 51143176\right )} \sqrt {-\frac {54864961696442}{53} \, \sqrt {7} + \frac {147447819270109}{53}} + 24883066697517 \, x - 10664171441793 \, \sqrt {7}\right ) + 480592 \, {\left (x + 1\right )} \log \left (x + 1\right ) - 909720 \, x - 290472}{3820824 \, {\left (x + 1\right )}} \] Input:
integrate((5*x^7+5*x^6-8*x^5-6*x^4+x^2+7*x-9)/(21*x^6+42*x^5-87*x^4-144*x^ 3+24*x^2+48*x-12),x, algorithm="fricas")
Output:
1/3820824*(454860*x^3 - 454860*x^2 - (26618*sqrt(7)*(x + 1) + (x + 1)*sqrt (54864961696442/53*sqrt(7) + 147447819270109/53) - 913034*x - 913034)*log( sqrt(54864961696442/53*sqrt(7) + 147447819270109/53)*(13611035*sqrt(7) - 5 1143176) + 24883066697517*x + 10664171441793*sqrt(7)) - (26618*sqrt(7)*(x + 1) - (x + 1)*sqrt(54864961696442/53*sqrt(7) + 147447819270109/53) - 9130 34*x - 913034)*log(-sqrt(54864961696442/53*sqrt(7) + 147447819270109/53)*( 13611035*sqrt(7) - 51143176) + 24883066697517*x + 10664171441793*sqrt(7)) + (26618*sqrt(7)*(x + 1) + (x + 1)*sqrt(-54864961696442/53*sqrt(7) + 14744 7819270109/53) + 913034*x + 913034)*log((13611035*sqrt(7) + 51143176)*sqrt (-54864961696442/53*sqrt(7) + 147447819270109/53) + 24883066697517*x - 106 64171441793*sqrt(7)) + (26618*sqrt(7)*(x + 1) - (x + 1)*sqrt(-548649616964 42/53*sqrt(7) + 147447819270109/53) + 913034*x + 913034)*log(-(13611035*sq rt(7) + 51143176)*sqrt(-54864961696442/53*sqrt(7) + 147447819270109/53) + 24883066697517*x - 10664171441793*sqrt(7)) + 480592*(x + 1)*log(x + 1) - 9 09720*x - 290472)/(x + 1)
Time = 0.55 (sec) , antiderivative size = 80, normalized size of antiderivative = 0.34 \[ \int \frac {-9+7 x+x^2-6 x^4-8 x^5+5 x^6+5 x^7}{-12+48 x+24 x^2-144 x^3-87 x^4+42 x^5+21 x^6} \, dx=\frac {5 x^{2}}{42} - \frac {5 x}{21} + \frac {1226 \log {\left (x + 1 \right )}}{9747} + \operatorname {RootSum} {\left (106688654585856 t^{4} - 101978389008384 t^{3} - 4181702014336 t^{2} + 15120814828224 t - 2225311647577, \left ( t \mapsto t \log {\left (- \frac {459131128881657673048455371656096361628665221541419008 t^{4}}{643874660611987289835864594285862394112626071202699} + \frac {420611320451790090945706975678868870815870194599673600 t^{3}}{643874660611987289835864594285862394112626071202699} + \frac {34784709157616888004683859460114529110782934404083232 t^{2}}{643874660611987289835864594285862394112626071202699} - \frac {61416748387941039117552316594189231141973353111718092 t}{643874660611987289835864594285862394112626071202699} + x + \frac {7096576781057043747679005044196835327775046553423155}{643874660611987289835864594285862394112626071202699} \right )} \right )\right )} - \frac {13}{171 x + 171} \] Input:
integrate((5*x**7+5*x**6-8*x**5-6*x**4+x**2+7*x-9)/(21*x**6+42*x**5-87*x** 4-144*x**3+24*x**2+48*x-12),x)
Output:
5*x**2/42 - 5*x/21 + 1226*log(x + 1)/9747 + RootSum(106688654585856*_t**4 - 101978389008384*_t**3 - 4181702014336*_t**2 + 15120814828224*_t - 222531 1647577, Lambda(_t, _t*log(-4591311288816576730484553716560963616286652215 41419008*_t**4/643874660611987289835864594285862394112626071202699 + 42061 1320451790090945706975678868870815870194599673600*_t**3/643874660611987289 835864594285862394112626071202699 + 34784709157616888004683859460114529110 782934404083232*_t**2/643874660611987289835864594285862394112626071202699 - 61416748387941039117552316594189231141973353111718092*_t/643874660611987 289835864594285862394112626071202699 + x + 7096576781057043747679005044196 835327775046553423155/643874660611987289835864594285862394112626071202699) )) - 13/(171*x + 171)
\[ \int \frac {-9+7 x+x^2-6 x^4-8 x^5+5 x^6+5 x^7}{-12+48 x+24 x^2-144 x^3-87 x^4+42 x^5+21 x^6} \, dx=\int { \frac {5 \, x^{7} + 5 \, x^{6} - 8 \, x^{5} - 6 \, x^{4} + x^{2} + 7 \, x - 9}{3 \, {\left (7 \, x^{6} + 14 \, x^{5} - 29 \, x^{4} - 48 \, x^{3} + 8 \, x^{2} + 16 \, x - 4\right )}} \,d x } \] Input:
integrate((5*x^7+5*x^6-8*x^5-6*x^4+x^2+7*x-9)/(21*x^6+42*x^5-87*x^4-144*x^ 3+24*x^2+48*x-12),x, algorithm="maxima")
Output:
5/42*x^2 - 5/21*x - 13/171/(x + 1) + 1/68229*integrate((456517*x^3 - 83722 0*x^2 + 617155*x - 214591)/(7*x^4 - 36*x^2 + 24*x - 4), x) + 1226/9747*log (x + 1)
Time = 0.15 (sec) , antiderivative size = 66, normalized size of antiderivative = 0.28 \[ \int \frac {-9+7 x+x^2-6 x^4-8 x^5+5 x^6+5 x^7}{-12+48 x+24 x^2-144 x^3-87 x^4+42 x^5+21 x^6} \, dx=\frac {5}{42} \, x^{2} - \frac {5}{21} \, x - \frac {13}{171 \, {\left (x + 1\right )}} + 0.596528807208595 \, \log \left (x + 2.56275423511000\right ) - \frac {13759974409}{21724250058} \, \log \left (x - 0.294967397054000\right ) + 0.0728202222081972 \, \log \left (x - 0.406029874333000\right ) - 0.0359566512100309 \, \log \left (x - 1.86175696372000\right ) + \frac {456517}{1910412} \, \log \left ({\left | 7 \, x^{4} - 36 \, x^{2} + 24 \, x - 4 \right |}\right ) + \frac {1226}{9747} \, \log \left ({\left | x + 1 \right |}\right ) \] Input:
integrate((5*x^7+5*x^6-8*x^5-6*x^4+x^2+7*x-9)/(21*x^6+42*x^5-87*x^4-144*x^ 3+24*x^2+48*x-12),x, algorithm="giac")
Output:
5/42*x^2 - 5/21*x - 13/171/(x + 1) + 0.596528807208595*log(x + 2.562754235 11000) - 13759974409/21724250058*log(x - 0.294967397054000) + 0.0728202222 081972*log(x - 0.406029874333000) - 0.0359566512100309*log(x - 1.861756963 72000) + 456517/1910412*log(abs(7*x^4 - 36*x^2 + 24*x - 4)) + 1226/9747*lo g(abs(x + 1))
Time = 0.10 (sec) , antiderivative size = 166, normalized size of antiderivative = 0.71 \[ \int \frac {-9+7 x+x^2-6 x^4-8 x^5+5 x^6+5 x^7}{-12+48 x+24 x^2-144 x^3-87 x^4+42 x^5+21 x^6} \, dx=\frac {1226\,\ln \left (x+1\right )}{9747}-\frac {5\,x}{21}-\frac {13}{171\,\left (x+1\right )}+\left (\sum _{k=1}^4\ln \left (-\frac {58710137727601\,x}{3539939466861}-\mathrm {root}\left (z^4-\frac {456517\,z^3}{477603}-\frac {4667078141\,z^2}{119072159136}+\frac {11250606271\,z}{79381439424}-\frac {2225311647577}{106688654585856},z,k\right )\,\left (\frac {2244714273\,x}{6067327}-\mathrm {root}\left (z^4-\frac {456517\,z^3}{477603}-\frac {4667078141\,z^2}{119072159136}+\frac {11250606271\,z}{79381439424}-\frac {2225311647577}{106688654585856},z,k\right )\,\left (\frac {8839526135207188\,x}{1179979822287}+\mathrm {root}\left (z^4-\frac {456517\,z^3}{477603}-\frac {4667078141\,z^2}{119072159136}+\frac {11250606271\,z}{79381439424}-\frac {2225311647577}{106688654585856},z,k\right )\,\left (-\frac {493930129216\,x}{15647317}+\mathrm {root}\left (z^4-\frac {456517\,z^3}{477603}-\frac {4667078141\,z^2}{119072159136}+\frac {11250606271\,z}{79381439424}-\frac {2225311647577}{106688654585856},z,k\right )\,\left (\frac {465882880\,x}{16807}-\frac {160128512}{16807}\right )+\frac {1455193577408}{140825853}\right )-\frac {779319434401232}{393326607429}\right )+\frac {61696879052062}{3539939466861}\right )+\frac {17559825878003}{1179979822287}\right )\,\mathrm {root}\left (z^4-\frac {456517\,z^3}{477603}-\frac {4667078141\,z^2}{119072159136}+\frac {11250606271\,z}{79381439424}-\frac {2225311647577}{106688654585856},z,k\right )\right )+\frac {5\,x^2}{42} \] Input:
int((7*x + x^2 - 6*x^4 - 8*x^5 + 5*x^6 + 5*x^7 - 9)/(48*x + 24*x^2 - 144*x ^3 - 87*x^4 + 42*x^5 + 21*x^6 - 12),x)
Output:
(1226*log(x + 1))/9747 - (5*x)/21 - 13/(171*(x + 1)) + symsum(log(17559825 878003/1179979822287 - root(z^4 - (456517*z^3)/477603 - (4667078141*z^2)/1 19072159136 + (11250606271*z)/79381439424 - 2225311647577/106688654585856, z, k)*((2244714273*x)/6067327 - root(z^4 - (456517*z^3)/477603 - (4667078 141*z^2)/119072159136 + (11250606271*z)/79381439424 - 2225311647577/106688 654585856, z, k)*((8839526135207188*x)/1179979822287 + root(z^4 - (456517* z^3)/477603 - (4667078141*z^2)/119072159136 + (11250606271*z)/79381439424 - 2225311647577/106688654585856, z, k)*(root(z^4 - (456517*z^3)/477603 - ( 4667078141*z^2)/119072159136 + (11250606271*z)/79381439424 - 2225311647577 /106688654585856, z, k)*((465882880*x)/16807 - 160128512/16807) - (4939301 29216*x)/15647317 + 1455193577408/140825853) - 779319434401232/39332660742 9) + 61696879052062/3539939466861) - (58710137727601*x)/3539939466861)*roo t(z^4 - (456517*z^3)/477603 - (4667078141*z^2)/119072159136 + (11250606271 *z)/79381439424 - 2225311647577/106688654585856, z, k), k, 1, 4) + (5*x^2) /42
\[ \int \frac {-9+7 x+x^2-6 x^4-8 x^5+5 x^6+5 x^7}{-12+48 x+24 x^2-144 x^3-87 x^4+42 x^5+21 x^6} \, dx=\frac {-242454 \left (\int \frac {x^{2}}{7 x^{6}+14 x^{5}-29 x^{4}-48 x^{3}+8 x^{2}+16 x -4}d x \right ) x -242454 \left (\int \frac {x^{2}}{7 x^{6}+14 x^{5}-29 x^{4}-48 x^{3}+8 x^{2}+16 x -4}d x \right )+396750 \left (\int \frac {x}{7 x^{6}+14 x^{5}-29 x^{4}-48 x^{3}+8 x^{2}+16 x -4}d x \right ) x +396750 \left (\int \frac {x}{7 x^{6}+14 x^{5}-29 x^{4}-48 x^{3}+8 x^{2}+16 x -4}d x \right )-123842 \left (\int \frac {1}{7 x^{6}+14 x^{5}-29 x^{4}-48 x^{3}+8 x^{2}+16 x -4}d x \right ) x -123842 \left (\int \frac {1}{7 x^{6}+14 x^{5}-29 x^{4}-48 x^{3}+8 x^{2}+16 x -4}d x \right )+1882 \,\mathrm {log}\left (7 x^{4}-36 x^{2}+24 x -4\right ) x +1882 \,\mathrm {log}\left (7 x^{4}-36 x^{2}+24 x -4\right )+422 \,\mathrm {log}\left (x +1\right ) x +422 \,\mathrm {log}\left (x +1\right )+875 x^{3}-875 x^{2}-14578 x}{7350 x +7350} \] Input:
int((5*x^7+5*x^6-8*x^5-6*x^4+x^2+7*x-9)/(21*x^6+42*x^5-87*x^4-144*x^3+24*x ^2+48*x-12),x)
Output:
( - 242454*int(x**2/(7*x**6 + 14*x**5 - 29*x**4 - 48*x**3 + 8*x**2 + 16*x - 4),x)*x - 242454*int(x**2/(7*x**6 + 14*x**5 - 29*x**4 - 48*x**3 + 8*x**2 + 16*x - 4),x) + 396750*int(x/(7*x**6 + 14*x**5 - 29*x**4 - 48*x**3 + 8*x **2 + 16*x - 4),x)*x + 396750*int(x/(7*x**6 + 14*x**5 - 29*x**4 - 48*x**3 + 8*x**2 + 16*x - 4),x) - 123842*int(1/(7*x**6 + 14*x**5 - 29*x**4 - 48*x* *3 + 8*x**2 + 16*x - 4),x)*x - 123842*int(1/(7*x**6 + 14*x**5 - 29*x**4 - 48*x**3 + 8*x**2 + 16*x - 4),x) + 1882*log(7*x**4 - 36*x**2 + 24*x - 4)*x + 1882*log(7*x**4 - 36*x**2 + 24*x - 4) + 422*log(x + 1)*x + 422*log(x + 1 ) + 875*x**3 - 875*x**2 - 14578*x)/(7350*(x + 1))