Integrand size = 15, antiderivative size = 258 \[ \int \frac {(c+d x)^{10}}{(a+b x)^4} \, dx=\frac {210 d^4 (b c-a d)^6 x}{b^{10}}-\frac {(b c-a d)^{10}}{3 b^{11} (a+b x)^3}-\frac {5 d (b c-a d)^9}{b^{11} (a+b x)^2}-\frac {45 d^2 (b c-a d)^8}{b^{11} (a+b x)}+\frac {126 d^5 (b c-a d)^5 (a+b x)^2}{b^{11}}+\frac {70 d^6 (b c-a d)^4 (a+b x)^3}{b^{11}}+\frac {30 d^7 (b c-a d)^3 (a+b x)^4}{b^{11}}+\frac {9 d^8 (b c-a d)^2 (a+b x)^5}{b^{11}}+\frac {5 d^9 (b c-a d) (a+b x)^6}{3 b^{11}}+\frac {d^{10} (a+b x)^7}{7 b^{11}}+\frac {120 d^3 (b c-a d)^7 \log (a+b x)}{b^{11}} \]
[Out]
Time = 0.31 (sec) , antiderivative size = 258, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {45} \[ \int \frac {(c+d x)^{10}}{(a+b x)^4} \, dx=\frac {5 d^9 (a+b x)^6 (b c-a d)}{3 b^{11}}+\frac {9 d^8 (a+b x)^5 (b c-a d)^2}{b^{11}}+\frac {30 d^7 (a+b x)^4 (b c-a d)^3}{b^{11}}+\frac {70 d^6 (a+b x)^3 (b c-a d)^4}{b^{11}}+\frac {126 d^5 (a+b x)^2 (b c-a d)^5}{b^{11}}+\frac {120 d^3 (b c-a d)^7 \log (a+b x)}{b^{11}}-\frac {45 d^2 (b c-a d)^8}{b^{11} (a+b x)}-\frac {5 d (b c-a d)^9}{b^{11} (a+b x)^2}-\frac {(b c-a d)^{10}}{3 b^{11} (a+b x)^3}+\frac {d^{10} (a+b x)^7}{7 b^{11}}+\frac {210 d^4 x (b c-a d)^6}{b^{10}} \]
[In]
[Out]
Rule 45
Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {210 d^4 (b c-a d)^6}{b^{10}}+\frac {(b c-a d)^{10}}{b^{10} (a+b x)^4}+\frac {10 d (b c-a d)^9}{b^{10} (a+b x)^3}+\frac {45 d^2 (b c-a d)^8}{b^{10} (a+b x)^2}+\frac {120 d^3 (b c-a d)^7}{b^{10} (a+b x)}+\frac {252 d^5 (b c-a d)^5 (a+b x)}{b^{10}}+\frac {210 d^6 (b c-a d)^4 (a+b x)^2}{b^{10}}+\frac {120 d^7 (b c-a d)^3 (a+b x)^3}{b^{10}}+\frac {45 d^8 (b c-a d)^2 (a+b x)^4}{b^{10}}+\frac {10 d^9 (b c-a d) (a+b x)^5}{b^{10}}+\frac {d^{10} (a+b x)^6}{b^{10}}\right ) \, dx \\ & = \frac {210 d^4 (b c-a d)^6 x}{b^{10}}-\frac {(b c-a d)^{10}}{3 b^{11} (a+b x)^3}-\frac {5 d (b c-a d)^9}{b^{11} (a+b x)^2}-\frac {45 d^2 (b c-a d)^8}{b^{11} (a+b x)}+\frac {126 d^5 (b c-a d)^5 (a+b x)^2}{b^{11}}+\frac {70 d^6 (b c-a d)^4 (a+b x)^3}{b^{11}}+\frac {30 d^7 (b c-a d)^3 (a+b x)^4}{b^{11}}+\frac {9 d^8 (b c-a d)^2 (a+b x)^5}{b^{11}}+\frac {5 d^9 (b c-a d) (a+b x)^6}{3 b^{11}}+\frac {d^{10} (a+b x)^7}{7 b^{11}}+\frac {120 d^3 (b c-a d)^7 \log (a+b x)}{b^{11}} \\ \end{align*}
Time = 0.10 (sec) , antiderivative size = 427, normalized size of antiderivative = 1.66 \[ \int \frac {(c+d x)^{10}}{(a+b x)^4} \, dx=\frac {21 b d^4 \left (210 b^6 c^6-1008 a b^5 c^5 d+2100 a^2 b^4 c^4 d^2-2400 a^3 b^3 c^3 d^3+1575 a^4 b^2 c^2 d^4-560 a^5 b c d^5+84 a^6 d^6\right ) x+21 b^2 d^5 \left (126 b^5 c^5-420 a b^4 c^4 d+600 a^2 b^3 c^3 d^2-450 a^3 b^2 c^2 d^3+175 a^4 b c d^4-28 a^5 d^5\right ) x^2+35 b^3 d^6 \left (42 b^4 c^4-96 a b^3 c^3 d+90 a^2 b^2 c^2 d^2-40 a^3 b c d^3+7 a^4 d^4\right ) x^3+105 b^4 d^7 \left (6 b^3 c^3-9 a b^2 c^2 d+5 a^2 b c d^2-a^3 d^3\right ) x^4+21 b^5 d^8 \left (9 b^2 c^2-8 a b c d+2 a^2 d^2\right ) x^5+7 b^6 d^9 (5 b c-2 a d) x^6+3 b^7 d^{10} x^7-\frac {7 (b c-a d)^{10}}{(a+b x)^3}+\frac {105 d (-b c+a d)^9}{(a+b x)^2}-\frac {945 d^2 (b c-a d)^8}{a+b x}+2520 d^3 (b c-a d)^7 \log (a+b x)}{21 b^{11}} \]
[In]
[Out]
Leaf count of result is larger than twice the leaf count of optimal. \(840\) vs. \(2(252)=504\).
Time = 0.22 (sec) , antiderivative size = 841, normalized size of antiderivative = 3.26
method | result | size |
norman | \(\frac {-\frac {660 a^{10} d^{10}-4620 a^{9} b c \,d^{9}+13860 a^{8} b^{2} c^{2} d^{8}-23100 a^{7} b^{3} c^{3} d^{7}+23100 a^{6} b^{4} c^{4} d^{6}-13860 a^{5} b^{5} c^{5} d^{5}+4620 a^{4} b^{6} c^{6} d^{4}-660 a^{3} b^{7} c^{7} d^{3}+45 a^{2} b^{8} c^{8} d^{2}+5 a \,b^{9} c^{9} d +b^{10} c^{10}}{3 b^{11}}+\frac {d^{10} x^{10}}{7 b}-\frac {3 \left (120 a^{8} d^{10}-840 a^{7} b c \,d^{9}+2520 a^{6} b^{2} c^{2} d^{8}-4200 a^{5} b^{3} c^{3} d^{7}+4200 a^{4} b^{4} c^{4} d^{6}-2520 a^{3} b^{5} c^{5} d^{5}+840 a^{2} b^{6} c^{6} d^{4}-120 a \,b^{7} c^{7} d^{3}+15 b^{8} c^{8} d^{2}\right ) x^{2}}{b^{9}}-\frac {\left (540 a^{9} d^{10}-3780 a^{8} b c \,d^{9}+11340 a^{7} b^{2} c^{2} d^{8}-18900 a^{6} b^{3} c^{3} d^{7}+18900 a^{5} b^{4} c^{4} d^{6}-11340 a^{4} b^{5} c^{5} d^{5}+3780 a^{3} b^{6} c^{6} d^{4}-540 a^{2} b^{7} c^{7} d^{3}+45 a \,b^{8} c^{8} d^{2}+5 b^{9} c^{9} d \right ) x}{b^{10}}+\frac {30 d^{4} \left (a^{6} d^{6}-7 a^{5} b c \,d^{5}+21 a^{4} b^{2} c^{2} d^{4}-35 a^{3} b^{3} c^{3} d^{3}+35 a^{2} b^{4} c^{4} d^{2}-21 a \,b^{5} c^{5} d +7 b^{6} c^{6}\right ) x^{4}}{b^{7}}-\frac {6 d^{5} \left (a^{5} d^{5}-7 a^{4} b c \,d^{4}+21 a^{3} b^{2} c^{2} d^{3}-35 a^{2} b^{3} c^{3} d^{2}+35 a \,b^{4} c^{4} d -21 b^{5} c^{5}\right ) x^{5}}{b^{6}}+\frac {2 d^{6} \left (a^{4} d^{4}-7 a^{3} b c \,d^{3}+21 a^{2} b^{2} c^{2} d^{2}-35 a \,b^{3} c^{3} d +35 b^{4} c^{4}\right ) x^{6}}{b^{5}}-\frac {6 d^{7} \left (a^{3} d^{3}-7 a^{2} b c \,d^{2}+21 a \,b^{2} c^{2} d -35 b^{3} c^{3}\right ) x^{7}}{7 b^{4}}+\frac {3 d^{8} \left (a^{2} d^{2}-7 a b c d +21 b^{2} c^{2}\right ) x^{8}}{7 b^{3}}-\frac {5 d^{9} \left (a d -7 b c \right ) x^{9}}{21 b^{2}}}{\left (b x +a \right )^{3}}-\frac {120 d^{3} \left (a^{7} d^{7}-7 a^{6} b c \,d^{6}+21 a^{5} b^{2} c^{2} d^{5}-35 a^{4} b^{3} c^{3} d^{4}+35 a^{3} b^{4} c^{4} d^{3}-21 a^{2} b^{5} c^{5} d^{2}+7 a \,b^{6} c^{6} d -b^{7} c^{7}\right ) \ln \left (b x +a \right )}{b^{11}}\) | \(841\) |
default | \(\frac {d^{4} \left (9 b^{6} c^{2} d^{4} x^{5}-1008 a \,b^{5} c^{5} d x +210 b^{6} c^{6} x +84 a^{6} d^{6} x +\frac {1}{7} d^{6} x^{7} b^{6}-160 a \,b^{5} c^{3} d^{3} x^{3}+175 a^{4} b^{2} c \,d^{5} x^{2}-450 a^{3} b^{3} c^{2} d^{4} x^{2}+600 a^{2} b^{4} c^{3} d^{3} x^{2}-420 a \,b^{5} c^{4} d^{2} x^{2}-560 a^{5} b c \,d^{5} x +1575 a^{4} b^{2} c^{2} d^{4} x -2400 a^{3} b^{3} c^{3} d^{3} x +2100 a^{2} b^{4} c^{4} d^{2} x +30 b^{6} c^{3} d^{3} x^{4}+\frac {35}{3} a^{4} b^{2} d^{6} x^{3}+70 b^{6} c^{4} d^{2} x^{3}-28 a^{5} b \,d^{6} x^{2}+126 b^{6} c^{5} d \,x^{2}-\frac {2}{3} a \,b^{5} d^{6} x^{6}+\frac {5}{3} b^{6} c \,d^{5} x^{6}+2 a^{2} b^{4} d^{6} x^{5}-5 a^{3} b^{3} d^{6} x^{4}+25 a^{2} b^{4} c \,d^{5} x^{4}-45 a \,b^{5} c^{2} d^{4} x^{4}-\frac {200}{3} a^{3} b^{3} c \,d^{5} x^{3}+150 a^{2} b^{4} c^{2} d^{4} x^{3}-8 a \,b^{5} c \,d^{5} x^{5}\right )}{b^{10}}-\frac {a^{10} d^{10}-10 a^{9} b c \,d^{9}+45 a^{8} b^{2} c^{2} d^{8}-120 a^{7} b^{3} c^{3} d^{7}+210 a^{6} b^{4} c^{4} d^{6}-252 a^{5} b^{5} c^{5} d^{5}+210 a^{4} b^{6} c^{6} d^{4}-120 a^{3} b^{7} c^{7} d^{3}+45 a^{2} b^{8} c^{8} d^{2}-10 a \,b^{9} c^{9} d +b^{10} c^{10}}{3 b^{11} \left (b x +a \right )^{3}}-\frac {120 d^{3} \left (a^{7} d^{7}-7 a^{6} b c \,d^{6}+21 a^{5} b^{2} c^{2} d^{5}-35 a^{4} b^{3} c^{3} d^{4}+35 a^{3} b^{4} c^{4} d^{3}-21 a^{2} b^{5} c^{5} d^{2}+7 a \,b^{6} c^{6} d -b^{7} c^{7}\right ) \ln \left (b x +a \right )}{b^{11}}+\frac {5 d \left (a^{9} d^{9}-9 a^{8} b c \,d^{8}+36 a^{7} b^{2} c^{2} d^{7}-84 a^{6} b^{3} c^{3} d^{6}+126 a^{5} b^{4} c^{4} d^{5}-126 a^{4} b^{5} c^{5} d^{4}+84 a^{3} b^{6} c^{6} d^{3}-36 a^{2} b^{7} c^{7} d^{2}+9 a \,b^{8} c^{8} d -b^{9} c^{9}\right )}{b^{11} \left (b x +a \right )^{2}}-\frac {45 d^{2} \left (a^{8} d^{8}-8 a^{7} b c \,d^{7}+28 a^{6} b^{2} c^{2} d^{6}-56 a^{5} b^{3} c^{3} d^{5}+70 a^{4} b^{4} c^{4} d^{4}-56 a^{3} b^{5} c^{5} d^{3}+28 a^{2} b^{6} c^{6} d^{2}-8 a \,b^{7} c^{7} d +b^{8} c^{8}\right )}{b^{11} \left (b x +a \right )}\) | \(896\) |
risch | \(\frac {9 d^{8} c^{2} x^{5}}{b^{4}}+\frac {210 d^{4} c^{6} x}{b^{4}}+\frac {84 d^{10} a^{6} x}{b^{10}}+\frac {30 d^{7} c^{3} x^{4}}{b^{4}}+\frac {35 d^{10} a^{4} x^{3}}{3 b^{8}}+\frac {70 d^{6} c^{4} x^{3}}{b^{4}}-\frac {28 d^{10} a^{5} x^{2}}{b^{9}}+\frac {126 d^{5} c^{5} x^{2}}{b^{4}}-\frac {2 d^{10} a \,x^{6}}{3 b^{5}}+\frac {5 d^{9} c \,x^{6}}{3 b^{4}}+\frac {2 d^{10} a^{2} x^{5}}{b^{6}}-\frac {5 d^{10} a^{3} x^{4}}{b^{7}}-\frac {120 d^{10} \ln \left (b x +a \right ) a^{7}}{b^{11}}+\frac {120 d^{3} \ln \left (b x +a \right ) c^{7}}{b^{4}}-\frac {1008 d^{5} a \,c^{5} x}{b^{5}}-\frac {160 d^{7} a \,c^{3} x^{3}}{b^{5}}+\frac {840 d^{9} \ln \left (b x +a \right ) a^{6} c}{b^{10}}-\frac {2520 d^{8} \ln \left (b x +a \right ) a^{5} c^{2}}{b^{9}}+\frac {4200 d^{7} \ln \left (b x +a \right ) a^{4} c^{3}}{b^{8}}-\frac {4200 d^{6} \ln \left (b x +a \right ) a^{3} c^{4}}{b^{7}}+\frac {2520 d^{5} \ln \left (b x +a \right ) a^{2} c^{5}}{b^{6}}-\frac {840 d^{4} \ln \left (b x +a \right ) a \,c^{6}}{b^{5}}+\frac {175 d^{9} a^{4} c \,x^{2}}{b^{8}}-\frac {450 d^{8} a^{3} c^{2} x^{2}}{b^{7}}+\frac {600 d^{7} a^{2} c^{3} x^{2}}{b^{6}}-\frac {420 d^{6} a \,c^{4} x^{2}}{b^{5}}-\frac {560 d^{9} a^{5} c x}{b^{9}}+\frac {1575 d^{8} a^{4} c^{2} x}{b^{8}}-\frac {2400 d^{7} a^{3} c^{3} x}{b^{7}}+\frac {2100 d^{6} a^{2} c^{4} x}{b^{6}}+\frac {25 d^{9} a^{2} c \,x^{4}}{b^{6}}-\frac {45 d^{8} a \,c^{2} x^{4}}{b^{5}}-\frac {200 d^{9} a^{3} c \,x^{3}}{3 b^{7}}+\frac {150 d^{8} a^{2} c^{2} x^{3}}{b^{6}}-\frac {8 d^{9} a c \,x^{5}}{b^{5}}+\frac {d^{10} x^{7}}{7 b^{4}}+\frac {\left (-45 a^{8} b \,d^{10}+360 a^{7} b^{2} c \,d^{9}-1260 a^{6} b^{3} c^{2} d^{8}+2520 a^{5} b^{4} c^{3} d^{7}-3150 a^{4} b^{5} c^{4} d^{6}+2520 a^{3} b^{6} c^{5} d^{5}-1260 a^{2} b^{7} c^{6} d^{4}+360 a \,b^{8} c^{7} d^{3}-45 b^{9} c^{8} d^{2}\right ) x^{2}-5 d \left (17 a^{9} d^{9}-135 a^{8} b c \,d^{8}+468 a^{7} b^{2} c^{2} d^{7}-924 a^{6} b^{3} c^{3} d^{6}+1134 a^{5} b^{4} c^{4} d^{5}-882 a^{4} b^{5} c^{5} d^{4}+420 a^{3} b^{6} c^{6} d^{3}-108 a^{2} b^{7} c^{7} d^{2}+9 a \,b^{8} c^{8} d +b^{9} c^{9}\right ) x -\frac {121 a^{10} d^{10}-955 a^{9} b c \,d^{9}+3285 a^{8} b^{2} c^{2} d^{8}-6420 a^{7} b^{3} c^{3} d^{7}+7770 a^{6} b^{4} c^{4} d^{6}-5922 a^{5} b^{5} c^{5} d^{5}+2730 a^{4} b^{6} c^{6} d^{4}-660 a^{3} b^{7} c^{7} d^{3}+45 a^{2} b^{8} c^{8} d^{2}+5 a \,b^{9} c^{9} d +b^{10} c^{10}}{3 b}}{b^{10} \left (b x +a \right )^{3}}\) | \(942\) |
parallelrisch | \(\text {Expression too large to display}\) | \(1499\) |
[In]
[Out]
Leaf count of result is larger than twice the leaf count of optimal. 1316 vs. \(2 (252) = 504\).
Time = 0.23 (sec) , antiderivative size = 1316, normalized size of antiderivative = 5.10 \[ \int \frac {(c+d x)^{10}}{(a+b x)^4} \, dx=\text {Too large to display} \]
[In]
[Out]
Timed out. \[ \int \frac {(c+d x)^{10}}{(a+b x)^4} \, dx=\text {Timed out} \]
[In]
[Out]
Leaf count of result is larger than twice the leaf count of optimal. 891 vs. \(2 (252) = 504\).
Time = 0.26 (sec) , antiderivative size = 891, normalized size of antiderivative = 3.45 \[ \int \frac {(c+d x)^{10}}{(a+b x)^4} \, dx=-\frac {b^{10} c^{10} + 5 \, a b^{9} c^{9} d + 45 \, a^{2} b^{8} c^{8} d^{2} - 660 \, a^{3} b^{7} c^{7} d^{3} + 2730 \, a^{4} b^{6} c^{6} d^{4} - 5922 \, a^{5} b^{5} c^{5} d^{5} + 7770 \, a^{6} b^{4} c^{4} d^{6} - 6420 \, a^{7} b^{3} c^{3} d^{7} + 3285 \, a^{8} b^{2} c^{2} d^{8} - 955 \, a^{9} b c d^{9} + 121 \, a^{10} d^{10} + 135 \, {\left (b^{10} c^{8} d^{2} - 8 \, a b^{9} c^{7} d^{3} + 28 \, a^{2} b^{8} c^{6} d^{4} - 56 \, a^{3} b^{7} c^{5} d^{5} + 70 \, a^{4} b^{6} c^{4} d^{6} - 56 \, a^{5} b^{5} c^{3} d^{7} + 28 \, a^{6} b^{4} c^{2} d^{8} - 8 \, a^{7} b^{3} c d^{9} + a^{8} b^{2} d^{10}\right )} x^{2} + 15 \, {\left (b^{10} c^{9} d + 9 \, a b^{9} c^{8} d^{2} - 108 \, a^{2} b^{8} c^{7} d^{3} + 420 \, a^{3} b^{7} c^{6} d^{4} - 882 \, a^{4} b^{6} c^{5} d^{5} + 1134 \, a^{5} b^{5} c^{4} d^{6} - 924 \, a^{6} b^{4} c^{3} d^{7} + 468 \, a^{7} b^{3} c^{2} d^{8} - 135 \, a^{8} b^{2} c d^{9} + 17 \, a^{9} b d^{10}\right )} x}{3 \, {\left (b^{14} x^{3} + 3 \, a b^{13} x^{2} + 3 \, a^{2} b^{12} x + a^{3} b^{11}\right )}} + \frac {3 \, b^{6} d^{10} x^{7} + 7 \, {\left (5 \, b^{6} c d^{9} - 2 \, a b^{5} d^{10}\right )} x^{6} + 21 \, {\left (9 \, b^{6} c^{2} d^{8} - 8 \, a b^{5} c d^{9} + 2 \, a^{2} b^{4} d^{10}\right )} x^{5} + 105 \, {\left (6 \, b^{6} c^{3} d^{7} - 9 \, a b^{5} c^{2} d^{8} + 5 \, a^{2} b^{4} c d^{9} - a^{3} b^{3} d^{10}\right )} x^{4} + 35 \, {\left (42 \, b^{6} c^{4} d^{6} - 96 \, a b^{5} c^{3} d^{7} + 90 \, a^{2} b^{4} c^{2} d^{8} - 40 \, a^{3} b^{3} c d^{9} + 7 \, a^{4} b^{2} d^{10}\right )} x^{3} + 21 \, {\left (126 \, b^{6} c^{5} d^{5} - 420 \, a b^{5} c^{4} d^{6} + 600 \, a^{2} b^{4} c^{3} d^{7} - 450 \, a^{3} b^{3} c^{2} d^{8} + 175 \, a^{4} b^{2} c d^{9} - 28 \, a^{5} b d^{10}\right )} x^{2} + 21 \, {\left (210 \, b^{6} c^{6} d^{4} - 1008 \, a b^{5} c^{5} d^{5} + 2100 \, a^{2} b^{4} c^{4} d^{6} - 2400 \, a^{3} b^{3} c^{3} d^{7} + 1575 \, a^{4} b^{2} c^{2} d^{8} - 560 \, a^{5} b c d^{9} + 84 \, a^{6} d^{10}\right )} x}{21 \, b^{10}} + \frac {120 \, {\left (b^{7} c^{7} d^{3} - 7 \, a b^{6} c^{6} d^{4} + 21 \, a^{2} b^{5} c^{5} d^{5} - 35 \, a^{3} b^{4} c^{4} d^{6} + 35 \, a^{4} b^{3} c^{3} d^{7} - 21 \, a^{5} b^{2} c^{2} d^{8} + 7 \, a^{6} b c d^{9} - a^{7} d^{10}\right )} \log \left (b x + a\right )}{b^{11}} \]
[In]
[Out]
Leaf count of result is larger than twice the leaf count of optimal. 907 vs. \(2 (252) = 504\).
Time = 0.40 (sec) , antiderivative size = 907, normalized size of antiderivative = 3.52 \[ \int \frac {(c+d x)^{10}}{(a+b x)^4} \, dx=\frac {120 \, {\left (b^{7} c^{7} d^{3} - 7 \, a b^{6} c^{6} d^{4} + 21 \, a^{2} b^{5} c^{5} d^{5} - 35 \, a^{3} b^{4} c^{4} d^{6} + 35 \, a^{4} b^{3} c^{3} d^{7} - 21 \, a^{5} b^{2} c^{2} d^{8} + 7 \, a^{6} b c d^{9} - a^{7} d^{10}\right )} \log \left ({\left | b x + a \right |}\right )}{b^{11}} - \frac {b^{10} c^{10} + 5 \, a b^{9} c^{9} d + 45 \, a^{2} b^{8} c^{8} d^{2} - 660 \, a^{3} b^{7} c^{7} d^{3} + 2730 \, a^{4} b^{6} c^{6} d^{4} - 5922 \, a^{5} b^{5} c^{5} d^{5} + 7770 \, a^{6} b^{4} c^{4} d^{6} - 6420 \, a^{7} b^{3} c^{3} d^{7} + 3285 \, a^{8} b^{2} c^{2} d^{8} - 955 \, a^{9} b c d^{9} + 121 \, a^{10} d^{10} + 135 \, {\left (b^{10} c^{8} d^{2} - 8 \, a b^{9} c^{7} d^{3} + 28 \, a^{2} b^{8} c^{6} d^{4} - 56 \, a^{3} b^{7} c^{5} d^{5} + 70 \, a^{4} b^{6} c^{4} d^{6} - 56 \, a^{5} b^{5} c^{3} d^{7} + 28 \, a^{6} b^{4} c^{2} d^{8} - 8 \, a^{7} b^{3} c d^{9} + a^{8} b^{2} d^{10}\right )} x^{2} + 15 \, {\left (b^{10} c^{9} d + 9 \, a b^{9} c^{8} d^{2} - 108 \, a^{2} b^{8} c^{7} d^{3} + 420 \, a^{3} b^{7} c^{6} d^{4} - 882 \, a^{4} b^{6} c^{5} d^{5} + 1134 \, a^{5} b^{5} c^{4} d^{6} - 924 \, a^{6} b^{4} c^{3} d^{7} + 468 \, a^{7} b^{3} c^{2} d^{8} - 135 \, a^{8} b^{2} c d^{9} + 17 \, a^{9} b d^{10}\right )} x}{3 \, {\left (b x + a\right )}^{3} b^{11}} + \frac {3 \, b^{24} d^{10} x^{7} + 35 \, b^{24} c d^{9} x^{6} - 14 \, a b^{23} d^{10} x^{6} + 189 \, b^{24} c^{2} d^{8} x^{5} - 168 \, a b^{23} c d^{9} x^{5} + 42 \, a^{2} b^{22} d^{10} x^{5} + 630 \, b^{24} c^{3} d^{7} x^{4} - 945 \, a b^{23} c^{2} d^{8} x^{4} + 525 \, a^{2} b^{22} c d^{9} x^{4} - 105 \, a^{3} b^{21} d^{10} x^{4} + 1470 \, b^{24} c^{4} d^{6} x^{3} - 3360 \, a b^{23} c^{3} d^{7} x^{3} + 3150 \, a^{2} b^{22} c^{2} d^{8} x^{3} - 1400 \, a^{3} b^{21} c d^{9} x^{3} + 245 \, a^{4} b^{20} d^{10} x^{3} + 2646 \, b^{24} c^{5} d^{5} x^{2} - 8820 \, a b^{23} c^{4} d^{6} x^{2} + 12600 \, a^{2} b^{22} c^{3} d^{7} x^{2} - 9450 \, a^{3} b^{21} c^{2} d^{8} x^{2} + 3675 \, a^{4} b^{20} c d^{9} x^{2} - 588 \, a^{5} b^{19} d^{10} x^{2} + 4410 \, b^{24} c^{6} d^{4} x - 21168 \, a b^{23} c^{5} d^{5} x + 44100 \, a^{2} b^{22} c^{4} d^{6} x - 50400 \, a^{3} b^{21} c^{3} d^{7} x + 33075 \, a^{4} b^{20} c^{2} d^{8} x - 11760 \, a^{5} b^{19} c d^{9} x + 1764 \, a^{6} b^{18} d^{10} x}{21 \, b^{28}} \]
[In]
[Out]
Time = 0.42 (sec) , antiderivative size = 2219, normalized size of antiderivative = 8.60 \[ \int \frac {(c+d x)^{10}}{(a+b x)^4} \, dx=\text {Too large to display} \]
[In]
[Out]