Optimal. Leaf size=200 \[ -\frac {(b c-a d)^7}{15 b^8 (a+b x)^{15}}-\frac {d (b c-a d)^6}{2 b^8 (a+b x)^{14}}-\frac {21 d^2 (b c-a d)^5}{13 b^8 (a+b x)^{13}}-\frac {35 d^3 (b c-a d)^4}{12 b^8 (a+b x)^{12}}-\frac {35 d^4 (b c-a d)^3}{11 b^8 (a+b x)^{11}}-\frac {21 d^5 (b c-a d)^2}{10 b^8 (a+b x)^{10}}-\frac {7 d^6 (b c-a d)}{9 b^8 (a+b x)^9}-\frac {d^7}{8 b^8 (a+b x)^8} \]
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Rubi [A]
time = 0.10, antiderivative size = 200, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {45}
\begin {gather*} -\frac {7 d^6 (b c-a d)}{9 b^8 (a+b x)^9}-\frac {21 d^5 (b c-a d)^2}{10 b^8 (a+b x)^{10}}-\frac {35 d^4 (b c-a d)^3}{11 b^8 (a+b x)^{11}}-\frac {35 d^3 (b c-a d)^4}{12 b^8 (a+b x)^{12}}-\frac {21 d^2 (b c-a d)^5}{13 b^8 (a+b x)^{13}}-\frac {d (b c-a d)^6}{2 b^8 (a+b x)^{14}}-\frac {(b c-a d)^7}{15 b^8 (a+b x)^{15}}-\frac {d^7}{8 b^8 (a+b x)^8} \end {gather*}
Antiderivative was successfully verified.
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Rule 45
Rubi steps
\begin {align*} \int \frac {(c+d x)^7}{(a+b x)^{16}} \, dx &=\int \left (\frac {(b c-a d)^7}{b^7 (a+b x)^{16}}+\frac {7 d (b c-a d)^6}{b^7 (a+b x)^{15}}+\frac {21 d^2 (b c-a d)^5}{b^7 (a+b x)^{14}}+\frac {35 d^3 (b c-a d)^4}{b^7 (a+b x)^{13}}+\frac {35 d^4 (b c-a d)^3}{b^7 (a+b x)^{12}}+\frac {21 d^5 (b c-a d)^2}{b^7 (a+b x)^{11}}+\frac {7 d^6 (b c-a d)}{b^7 (a+b x)^{10}}+\frac {d^7}{b^7 (a+b x)^9}\right ) \, dx\\ &=-\frac {(b c-a d)^7}{15 b^8 (a+b x)^{15}}-\frac {d (b c-a d)^6}{2 b^8 (a+b x)^{14}}-\frac {21 d^2 (b c-a d)^5}{13 b^8 (a+b x)^{13}}-\frac {35 d^3 (b c-a d)^4}{12 b^8 (a+b x)^{12}}-\frac {35 d^4 (b c-a d)^3}{11 b^8 (a+b x)^{11}}-\frac {21 d^5 (b c-a d)^2}{10 b^8 (a+b x)^{10}}-\frac {7 d^6 (b c-a d)}{9 b^8 (a+b x)^9}-\frac {d^7}{8 b^8 (a+b x)^8}\\ \end {align*}
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Mathematica [A]
time = 0.08, size = 371, normalized size = 1.86 \begin {gather*} -\frac {a^7 d^7+a^6 b d^6 (8 c+15 d x)+3 a^5 b^2 d^5 \left (12 c^2+40 c d x+35 d^2 x^2\right )+5 a^4 b^3 d^4 \left (24 c^3+108 c^2 d x+168 c d^2 x^2+91 d^3 x^3\right )+5 a^3 b^4 d^3 \left (66 c^4+360 c^3 d x+756 c^2 d^2 x^2+728 c d^3 x^3+273 d^4 x^4\right )+3 a^2 b^5 d^2 \left (264 c^5+1650 c^4 d x+4200 c^3 d^2 x^2+5460 c^2 d^3 x^3+3640 c d^4 x^4+1001 d^5 x^5\right )+a b^6 d \left (1716 c^6+11880 c^5 d x+34650 c^4 d^2 x^2+54600 c^3 d^3 x^3+49140 c^2 d^4 x^4+24024 c d^5 x^5+5005 d^6 x^6\right )+b^7 \left (3432 c^7+25740 c^6 d x+83160 c^5 d^2 x^2+150150 c^4 d^3 x^3+163800 c^3 d^4 x^4+108108 c^2 d^5 x^5+40040 c d^6 x^6+6435 d^7 x^7\right )}{51480 b^8 (a+b x)^{15}} \end {gather*}
Antiderivative was successfully verified.
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Mathics [F(-1)]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Warning: Unable to verify antiderivative.
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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(463\) vs.
\(2(184)=368\).
time = 0.14, size = 464, normalized size = 2.32
method | result | size |
risch | \(\frac {-\frac {a^{7} d^{7}+8 a^{6} b c \,d^{6}+36 a^{5} b^{2} c^{2} d^{5}+120 a^{4} b^{3} c^{3} d^{4}+330 a^{3} b^{4} c^{4} d^{3}+792 a^{2} b^{5} c^{5} d^{2}+1716 a \,b^{6} c^{6} d +3432 b^{7} c^{7}}{51480 b^{8}}-\frac {d \left (a^{6} d^{6}+8 a^{5} b c \,d^{5}+36 a^{4} b^{2} c^{2} d^{4}+120 a^{3} b^{3} c^{3} d^{3}+330 a^{2} b^{4} c^{4} d^{2}+792 a \,b^{5} c^{5} d +1716 b^{6} c^{6}\right ) x}{3432 b^{7}}-\frac {7 d^{2} \left (a^{5} d^{5}+8 a^{4} b c \,d^{4}+36 a^{3} b^{2} c^{2} d^{3}+120 a^{2} b^{3} c^{3} d^{2}+330 a \,b^{4} c^{4} d +792 b^{5} c^{5}\right ) x^{2}}{3432 b^{6}}-\frac {7 d^{3} \left (a^{4} d^{4}+8 a^{3} b c \,d^{3}+36 a^{2} b^{2} c^{2} d^{2}+120 a \,b^{3} c^{3} d +330 b^{4} c^{4}\right ) x^{3}}{792 b^{5}}-\frac {7 d^{4} \left (a^{3} d^{3}+8 a^{2} b c \,d^{2}+36 a \,b^{2} c^{2} d +120 b^{3} c^{3}\right ) x^{4}}{264 b^{4}}-\frac {7 d^{5} \left (a^{2} d^{2}+8 a b c d +36 b^{2} c^{2}\right ) x^{5}}{120 b^{3}}-\frac {7 d^{6} \left (a d +8 b c \right ) x^{6}}{72 b^{2}}-\frac {d^{7} x^{7}}{8 b}}{\left (b x +a \right )^{15}}\) | \(438\) |
default | \(\frac {21 d^{2} \left (a^{5} d^{5}-5 a^{4} b c \,d^{4}+10 a^{3} b^{2} c^{2} d^{3}-10 a^{2} b^{3} c^{3} d^{2}+5 a \,b^{4} c^{4} d -b^{5} c^{5}\right )}{13 b^{8} \left (b x +a \right )^{13}}-\frac {35 d^{3} \left (a^{4} d^{4}-4 a^{3} b c \,d^{3}+6 a^{2} b^{2} c^{2} d^{2}-4 a \,b^{3} c^{3} d +b^{4} c^{4}\right )}{12 b^{8} \left (b x +a \right )^{12}}+\frac {7 d^{6} \left (a d -b c \right )}{9 b^{8} \left (b x +a \right )^{9}}-\frac {d^{7}}{8 b^{8} \left (b x +a \right )^{8}}-\frac {d \left (a^{6} d^{6}-6 a^{5} b c \,d^{5}+15 a^{4} b^{2} c^{2} d^{4}-20 a^{3} b^{3} c^{3} d^{3}+15 a^{2} b^{4} c^{4} d^{2}-6 a \,b^{5} c^{5} d +b^{6} c^{6}\right )}{2 b^{8} \left (b x +a \right )^{14}}-\frac {21 d^{5} \left (a^{2} d^{2}-2 a b c d +b^{2} c^{2}\right )}{10 b^{8} \left (b x +a \right )^{10}}-\frac {-a^{7} d^{7}+7 a^{6} b c \,d^{6}-21 a^{5} b^{2} c^{2} d^{5}+35 a^{4} b^{3} c^{3} d^{4}-35 a^{3} b^{4} c^{4} d^{3}+21 a^{2} b^{5} c^{5} d^{2}-7 a \,b^{6} c^{6} d +b^{7} c^{7}}{15 b^{8} \left (b x +a \right )^{15}}+\frac {35 d^{4} \left (a^{3} d^{3}-3 a^{2} b c \,d^{2}+3 a \,b^{2} c^{2} d -b^{3} c^{3}\right )}{11 b^{8} \left (b x +a \right )^{11}}\) | \(464\) |
norman | \(\frac {\frac {-a^{7} b^{7} d^{7}-8 a^{6} b^{8} c \,d^{6}-36 a^{5} b^{9} c^{2} d^{5}-120 a^{4} b^{10} c^{3} d^{4}-330 a^{3} b^{11} c^{4} d^{3}-792 a^{2} b^{12} c^{5} d^{2}-1716 a \,b^{13} c^{6} d -3432 b^{14} c^{7}}{51480 b^{15}}+\frac {\left (-a^{6} b^{7} d^{7}-8 a^{5} b^{8} c \,d^{6}-36 a^{4} b^{9} c^{2} d^{5}-120 a^{3} b^{10} c^{3} d^{4}-330 a^{2} b^{11} c^{4} d^{3}-792 a \,b^{12} c^{5} d^{2}-1716 b^{13} c^{6} d \right ) x}{3432 b^{14}}+\frac {7 \left (-a^{5} b^{7} d^{7}-8 a^{4} b^{8} c \,d^{6}-36 a^{3} b^{9} c^{2} d^{5}-120 a^{2} b^{10} c^{3} d^{4}-330 a \,b^{11} c^{4} d^{3}-792 b^{12} c^{5} d^{2}\right ) x^{2}}{3432 b^{13}}+\frac {7 \left (-a^{4} b^{7} d^{7}-8 a^{3} b^{8} c \,d^{6}-36 a^{2} b^{9} c^{2} d^{5}-120 a \,b^{10} c^{3} d^{4}-330 b^{11} c^{4} d^{3}\right ) x^{3}}{792 b^{12}}+\frac {7 \left (-a^{3} b^{7} d^{7}-8 a^{2} b^{8} c \,d^{6}-36 a \,b^{9} c^{2} d^{5}-120 b^{10} c^{3} d^{4}\right ) x^{4}}{264 b^{11}}+\frac {7 \left (-a^{2} b^{7} d^{7}-8 a \,b^{8} c \,d^{6}-36 b^{9} c^{2} d^{5}\right ) x^{5}}{120 b^{10}}+\frac {7 \left (-a \,b^{7} d^{7}-8 b^{8} c \,d^{6}\right ) x^{6}}{72 b^{9}}-\frac {d^{7} x^{7}}{8 b}}{\left (b x +a \right )^{15}}\) | \(492\) |
gosper | \(-\frac {6435 d^{7} x^{7} b^{7}+5005 a \,b^{6} d^{7} x^{6}+40040 b^{7} c \,d^{6} x^{6}+3003 a^{2} b^{5} d^{7} x^{5}+24024 a \,b^{6} c \,d^{6} x^{5}+108108 b^{7} c^{2} d^{5} x^{5}+1365 a^{3} b^{4} d^{7} x^{4}+10920 a^{2} b^{5} c \,d^{6} x^{4}+49140 a \,b^{6} c^{2} d^{5} x^{4}+163800 b^{7} c^{3} d^{4} x^{4}+455 a^{4} b^{3} d^{7} x^{3}+3640 a^{3} b^{4} c \,d^{6} x^{3}+16380 a^{2} b^{5} c^{2} d^{5} x^{3}+54600 a \,b^{6} c^{3} d^{4} x^{3}+150150 b^{7} c^{4} d^{3} x^{3}+105 a^{5} b^{2} d^{7} x^{2}+840 a^{4} b^{3} c \,d^{6} x^{2}+3780 a^{3} b^{4} c^{2} d^{5} x^{2}+12600 a^{2} b^{5} c^{3} d^{4} x^{2}+34650 a \,b^{6} c^{4} d^{3} x^{2}+83160 b^{7} c^{5} d^{2} x^{2}+15 a^{6} b \,d^{7} x +120 a^{5} b^{2} c \,d^{6} x +540 a^{4} b^{3} c^{2} d^{5} x +1800 a^{3} b^{4} c^{3} d^{4} x +4950 a^{2} b^{5} c^{4} d^{3} x +11880 a \,b^{6} c^{5} d^{2} x +25740 b^{7} c^{6} d x +a^{7} d^{7}+8 a^{6} b c \,d^{6}+36 a^{5} b^{2} c^{2} d^{5}+120 a^{4} b^{3} c^{3} d^{4}+330 a^{3} b^{4} c^{4} d^{3}+792 a^{2} b^{5} c^{5} d^{2}+1716 a \,b^{6} c^{6} d +3432 b^{7} c^{7}}{51480 b^{8} \left (b x +a \right )^{15}}\) | \(497\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 614 vs.
\(2 (184) = 368\).
time = 0.29, size = 614, normalized size = 3.07 \begin {gather*} -\frac {6435 \, b^{7} d^{7} x^{7} + 3432 \, b^{7} c^{7} + 1716 \, a b^{6} c^{6} d + 792 \, a^{2} b^{5} c^{5} d^{2} + 330 \, a^{3} b^{4} c^{4} d^{3} + 120 \, a^{4} b^{3} c^{3} d^{4} + 36 \, a^{5} b^{2} c^{2} d^{5} + 8 \, a^{6} b c d^{6} + a^{7} d^{7} + 5005 \, {\left (8 \, b^{7} c d^{6} + a b^{6} d^{7}\right )} x^{6} + 3003 \, {\left (36 \, b^{7} c^{2} d^{5} + 8 \, a b^{6} c d^{6} + a^{2} b^{5} d^{7}\right )} x^{5} + 1365 \, {\left (120 \, b^{7} c^{3} d^{4} + 36 \, a b^{6} c^{2} d^{5} + 8 \, a^{2} b^{5} c d^{6} + a^{3} b^{4} d^{7}\right )} x^{4} + 455 \, {\left (330 \, b^{7} c^{4} d^{3} + 120 \, a b^{6} c^{3} d^{4} + 36 \, a^{2} b^{5} c^{2} d^{5} + 8 \, a^{3} b^{4} c d^{6} + a^{4} b^{3} d^{7}\right )} x^{3} + 105 \, {\left (792 \, b^{7} c^{5} d^{2} + 330 \, a b^{6} c^{4} d^{3} + 120 \, a^{2} b^{5} c^{3} d^{4} + 36 \, a^{3} b^{4} c^{2} d^{5} + 8 \, a^{4} b^{3} c d^{6} + a^{5} b^{2} d^{7}\right )} x^{2} + 15 \, {\left (1716 \, b^{7} c^{6} d + 792 \, a b^{6} c^{5} d^{2} + 330 \, a^{2} b^{5} c^{4} d^{3} + 120 \, a^{3} b^{4} c^{3} d^{4} + 36 \, a^{4} b^{3} c^{2} d^{5} + 8 \, a^{5} b^{2} c d^{6} + a^{6} b d^{7}\right )} x}{51480 \, {\left (b^{23} x^{15} + 15 \, a b^{22} x^{14} + 105 \, a^{2} b^{21} x^{13} + 455 \, a^{3} b^{20} x^{12} + 1365 \, a^{4} b^{19} x^{11} + 3003 \, a^{5} b^{18} x^{10} + 5005 \, a^{6} b^{17} x^{9} + 6435 \, a^{7} b^{16} x^{8} + 6435 \, a^{8} b^{15} x^{7} + 5005 \, a^{9} b^{14} x^{6} + 3003 \, a^{10} b^{13} x^{5} + 1365 \, a^{11} b^{12} x^{4} + 455 \, a^{12} b^{11} x^{3} + 105 \, a^{13} b^{10} x^{2} + 15 \, a^{14} b^{9} x + a^{15} b^{8}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 614 vs.
\(2 (184) = 368\).
time = 0.30, size = 614, normalized size = 3.07 \begin {gather*} -\frac {6435 \, b^{7} d^{7} x^{7} + 3432 \, b^{7} c^{7} + 1716 \, a b^{6} c^{6} d + 792 \, a^{2} b^{5} c^{5} d^{2} + 330 \, a^{3} b^{4} c^{4} d^{3} + 120 \, a^{4} b^{3} c^{3} d^{4} + 36 \, a^{5} b^{2} c^{2} d^{5} + 8 \, a^{6} b c d^{6} + a^{7} d^{7} + 5005 \, {\left (8 \, b^{7} c d^{6} + a b^{6} d^{7}\right )} x^{6} + 3003 \, {\left (36 \, b^{7} c^{2} d^{5} + 8 \, a b^{6} c d^{6} + a^{2} b^{5} d^{7}\right )} x^{5} + 1365 \, {\left (120 \, b^{7} c^{3} d^{4} + 36 \, a b^{6} c^{2} d^{5} + 8 \, a^{2} b^{5} c d^{6} + a^{3} b^{4} d^{7}\right )} x^{4} + 455 \, {\left (330 \, b^{7} c^{4} d^{3} + 120 \, a b^{6} c^{3} d^{4} + 36 \, a^{2} b^{5} c^{2} d^{5} + 8 \, a^{3} b^{4} c d^{6} + a^{4} b^{3} d^{7}\right )} x^{3} + 105 \, {\left (792 \, b^{7} c^{5} d^{2} + 330 \, a b^{6} c^{4} d^{3} + 120 \, a^{2} b^{5} c^{3} d^{4} + 36 \, a^{3} b^{4} c^{2} d^{5} + 8 \, a^{4} b^{3} c d^{6} + a^{5} b^{2} d^{7}\right )} x^{2} + 15 \, {\left (1716 \, b^{7} c^{6} d + 792 \, a b^{6} c^{5} d^{2} + 330 \, a^{2} b^{5} c^{4} d^{3} + 120 \, a^{3} b^{4} c^{3} d^{4} + 36 \, a^{4} b^{3} c^{2} d^{5} + 8 \, a^{5} b^{2} c d^{6} + a^{6} b d^{7}\right )} x}{51480 \, {\left (b^{23} x^{15} + 15 \, a b^{22} x^{14} + 105 \, a^{2} b^{21} x^{13} + 455 \, a^{3} b^{20} x^{12} + 1365 \, a^{4} b^{19} x^{11} + 3003 \, a^{5} b^{18} x^{10} + 5005 \, a^{6} b^{17} x^{9} + 6435 \, a^{7} b^{16} x^{8} + 6435 \, a^{8} b^{15} x^{7} + 5005 \, a^{9} b^{14} x^{6} + 3003 \, a^{10} b^{13} x^{5} + 1365 \, a^{11} b^{12} x^{4} + 455 \, a^{12} b^{11} x^{3} + 105 \, a^{13} b^{10} x^{2} + 15 \, a^{14} b^{9} x + a^{15} b^{8}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 496 vs.
\(2 (184) = 368\).
time = 0.00, size = 534, normalized size = 2.67 \begin {gather*} \frac {-6435 x^{7} d^{7} b^{7}-5005 x^{6} d^{7} b^{6} a-40040 x^{6} d^{6} c b^{7}-3003 x^{5} d^{7} b^{5} a^{2}-24024 x^{5} d^{6} c b^{6} a-108108 x^{5} d^{5} c^{2} b^{7}-1365 x^{4} d^{7} b^{4} a^{3}-10920 x^{4} d^{6} c b^{5} a^{2}-49140 x^{4} d^{5} c^{2} b^{6} a-163800 x^{4} d^{4} c^{3} b^{7}-455 x^{3} d^{7} b^{3} a^{4}-3640 x^{3} d^{6} c b^{4} a^{3}-16380 x^{3} d^{5} c^{2} b^{5} a^{2}-54600 x^{3} d^{4} c^{3} b^{6} a-150150 x^{3} d^{3} c^{4} b^{7}-105 x^{2} d^{7} b^{2} a^{5}-840 x^{2} d^{6} c b^{3} a^{4}-3780 x^{2} d^{5} c^{2} b^{4} a^{3}-12600 x^{2} d^{4} c^{3} b^{5} a^{2}-34650 x^{2} d^{3} c^{4} b^{6} a-83160 x^{2} d^{2} c^{5} b^{7}-15 x d^{7} b a^{6}-120 x d^{6} c b^{2} a^{5}-540 x d^{5} c^{2} b^{3} a^{4}-1800 x d^{4} c^{3} b^{4} a^{3}-4950 x d^{3} c^{4} b^{5} a^{2}-11880 x d^{2} c^{5} b^{6} a-25740 x d c^{6} b^{7}-d^{7} a^{7}-8 d^{6} c b a^{6}-36 d^{5} c^{2} b^{2} a^{5}-120 d^{4} c^{3} b^{3} a^{4}-330 d^{3} c^{4} b^{4} a^{3}-792 d^{2} c^{5} b^{5} a^{2}-1716 d c^{6} b^{6} a-3432 c^{7} b^{7}}{51480 b^{8} \left (x b+a\right )^{15}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 2.20, size = 592, normalized size = 2.96 \begin {gather*} -\frac {\frac {a^7\,d^7+8\,a^6\,b\,c\,d^6+36\,a^5\,b^2\,c^2\,d^5+120\,a^4\,b^3\,c^3\,d^4+330\,a^3\,b^4\,c^4\,d^3+792\,a^2\,b^5\,c^5\,d^2+1716\,a\,b^6\,c^6\,d+3432\,b^7\,c^7}{51480\,b^8}+\frac {d^7\,x^7}{8\,b}+\frac {7\,d^2\,x^2\,\left (a^5\,d^5+8\,a^4\,b\,c\,d^4+36\,a^3\,b^2\,c^2\,d^3+120\,a^2\,b^3\,c^3\,d^2+330\,a\,b^4\,c^4\,d+792\,b^5\,c^5\right )}{3432\,b^6}+\frac {7\,d^4\,x^4\,\left (a^3\,d^3+8\,a^2\,b\,c\,d^2+36\,a\,b^2\,c^2\,d+120\,b^3\,c^3\right )}{264\,b^4}+\frac {7\,d^6\,x^6\,\left (a\,d+8\,b\,c\right )}{72\,b^2}+\frac {7\,d^3\,x^3\,\left (a^4\,d^4+8\,a^3\,b\,c\,d^3+36\,a^2\,b^2\,c^2\,d^2+120\,a\,b^3\,c^3\,d+330\,b^4\,c^4\right )}{792\,b^5}+\frac {d\,x\,\left (a^6\,d^6+8\,a^5\,b\,c\,d^5+36\,a^4\,b^2\,c^2\,d^4+120\,a^3\,b^3\,c^3\,d^3+330\,a^2\,b^4\,c^4\,d^2+792\,a\,b^5\,c^5\,d+1716\,b^6\,c^6\right )}{3432\,b^7}+\frac {7\,d^5\,x^5\,\left (a^2\,d^2+8\,a\,b\,c\,d+36\,b^2\,c^2\right )}{120\,b^3}}{a^{15}+15\,a^{14}\,b\,x+105\,a^{13}\,b^2\,x^2+455\,a^{12}\,b^3\,x^3+1365\,a^{11}\,b^4\,x^4+3003\,a^{10}\,b^5\,x^5+5005\,a^9\,b^6\,x^6+6435\,a^8\,b^7\,x^7+6435\,a^7\,b^8\,x^8+5005\,a^6\,b^9\,x^9+3003\,a^5\,b^{10}\,x^{10}+1365\,a^4\,b^{11}\,x^{11}+455\,a^3\,b^{12}\,x^{12}+105\,a^2\,b^{13}\,x^{13}+15\,a\,b^{14}\,x^{14}+b^{15}\,x^{15}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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