Optimal. Leaf size=197 \[ \frac {a^7 d^3 (e x)^{1+m}}{e (1+m)}+\frac {a^6 b d^3 (e x)^{2+m}}{e^2 (2+m)}-\frac {3 a^5 b^2 d^3 (e x)^{3+m}}{e^3 (3+m)}-\frac {3 a^4 b^3 d^3 (e x)^{4+m}}{e^4 (4+m)}+\frac {3 a^3 b^4 d^3 (e x)^{5+m}}{e^5 (5+m)}+\frac {3 a^2 b^5 d^3 (e x)^{6+m}}{e^6 (6+m)}-\frac {a b^6 d^3 (e x)^{7+m}}{e^7 (7+m)}-\frac {b^7 d^3 (e x)^{8+m}}{e^8 (8+m)} \]
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Rubi [A]
time = 0.09, antiderivative size = 197, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 24, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.042, Rules used = {90}
\begin {gather*} \frac {a^7 d^3 (e x)^{m+1}}{e (m+1)}+\frac {a^6 b d^3 (e x)^{m+2}}{e^2 (m+2)}-\frac {3 a^5 b^2 d^3 (e x)^{m+3}}{e^3 (m+3)}-\frac {3 a^4 b^3 d^3 (e x)^{m+4}}{e^4 (m+4)}+\frac {3 a^3 b^4 d^3 (e x)^{m+5}}{e^5 (m+5)}+\frac {3 a^2 b^5 d^3 (e x)^{m+6}}{e^6 (m+6)}-\frac {a b^6 d^3 (e x)^{m+7}}{e^7 (m+7)}-\frac {b^7 d^3 (e x)^{m+8}}{e^8 (m+8)} \end {gather*}
Antiderivative was successfully verified.
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Rule 90
Rubi steps
\begin {align*} \int (e x)^m (a+b x)^4 (a d-b d x)^3 \, dx &=\int \left (a^7 d^3 (e x)^m+\frac {a^6 b d^3 (e x)^{1+m}}{e}-\frac {3 a^5 b^2 d^3 (e x)^{2+m}}{e^2}-\frac {3 a^4 b^3 d^3 (e x)^{3+m}}{e^3}+\frac {3 a^3 b^4 d^3 (e x)^{4+m}}{e^4}+\frac {3 a^2 b^5 d^3 (e x)^{5+m}}{e^5}-\frac {a b^6 d^3 (e x)^{6+m}}{e^6}-\frac {b^7 d^3 (e x)^{7+m}}{e^7}\right ) \, dx\\ &=\frac {a^7 d^3 (e x)^{1+m}}{e (1+m)}+\frac {a^6 b d^3 (e x)^{2+m}}{e^2 (2+m)}-\frac {3 a^5 b^2 d^3 (e x)^{3+m}}{e^3 (3+m)}-\frac {3 a^4 b^3 d^3 (e x)^{4+m}}{e^4 (4+m)}+\frac {3 a^3 b^4 d^3 (e x)^{5+m}}{e^5 (5+m)}+\frac {3 a^2 b^5 d^3 (e x)^{6+m}}{e^6 (6+m)}-\frac {a b^6 d^3 (e x)^{7+m}}{e^7 (7+m)}-\frac {b^7 d^3 (e x)^{8+m}}{e^8 (8+m)}\\ \end {align*}
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Mathematica [A]
time = 0.11, size = 122, normalized size = 0.62 \begin {gather*} d^3 x (e x)^m \left (\frac {a^7}{1+m}+\frac {a^6 b x}{2+m}-\frac {3 a^5 b^2 x^2}{3+m}-\frac {3 a^4 b^3 x^3}{4+m}+\frac {3 a^3 b^4 x^4}{5+m}+\frac {3 a^2 b^5 x^5}{6+m}-\frac {a b^6 x^6}{7+m}-\frac {b^7 x^7}{8+m}\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.06, size = 196, normalized size = 0.99
method | result | size |
norman | \(\frac {a^{7} d^{3} x \,{\mathrm e}^{m \ln \left (e x \right )}}{1+m}+\frac {a^{6} b \,d^{3} x^{2} {\mathrm e}^{m \ln \left (e x \right )}}{2+m}-\frac {b^{7} d^{3} x^{8} {\mathrm e}^{m \ln \left (e x \right )}}{8+m}-\frac {a \,b^{6} d^{3} x^{7} {\mathrm e}^{m \ln \left (e x \right )}}{7+m}+\frac {3 a^{2} b^{5} d^{3} x^{6} {\mathrm e}^{m \ln \left (e x \right )}}{6+m}+\frac {3 a^{3} b^{4} d^{3} x^{5} {\mathrm e}^{m \ln \left (e x \right )}}{5+m}-\frac {3 a^{4} b^{3} d^{3} x^{4} {\mathrm e}^{m \ln \left (e x \right )}}{4+m}-\frac {3 a^{5} b^{2} d^{3} x^{3} {\mathrm e}^{m \ln \left (e x \right )}}{3+m}\) | \(196\) |
gosper | \(\frac {d^{3} \left (e x \right )^{m} \left (-b^{7} m^{7} x^{7}-a \,b^{6} m^{7} x^{6}-28 b^{7} m^{6} x^{7}+3 a^{2} b^{5} m^{7} x^{5}-29 a \,b^{6} m^{6} x^{6}-322 b^{7} m^{5} x^{7}+3 a^{3} b^{4} m^{7} x^{4}+90 a^{2} b^{5} m^{6} x^{5}-343 a \,b^{6} m^{5} x^{6}-1960 b^{7} m^{4} x^{7}-3 a^{4} b^{3} m^{7} x^{3}+93 a^{3} b^{4} m^{6} x^{4}+1098 a^{2} b^{5} m^{5} x^{5}-2135 a \,b^{6} m^{4} x^{6}-6769 b^{7} m^{3} x^{7}-3 a^{5} b^{2} m^{7} x^{2}-96 a^{4} b^{3} m^{6} x^{3}+1173 a^{3} b^{4} m^{5} x^{4}+7020 a^{2} b^{5} m^{4} x^{5}-7504 a \,b^{6} m^{3} x^{6}-13132 b^{7} m^{2} x^{7}+a^{6} b \,m^{7} x -99 a^{5} b^{2} m^{6} x^{2}-1254 a^{4} b^{3} m^{5} x^{3}+7743 a^{3} b^{4} m^{4} x^{4}+25227 a^{2} b^{5} m^{3} x^{5}-14756 a \,b^{6} m^{2} x^{6}-13068 m \,x^{7} b^{7}+a^{7} m^{7}+34 a^{6} b \,m^{6} x -1341 a^{5} b^{2} m^{5} x^{2}-8592 a^{4} b^{3} m^{4} x^{3}+28632 a^{3} b^{4} m^{3} x^{4}+50490 a^{2} b^{5} m^{2} x^{5}-14832 a \,b^{6} m \,x^{6}-5040 b^{7} x^{7}+35 a^{7} m^{6}+478 a^{6} b \,m^{5} x -9585 a^{5} b^{2} m^{4} x^{2}-32979 a^{4} b^{3} m^{3} x^{3}+58692 a^{3} b^{4} m^{2} x^{4}+51432 a^{2} b^{5} m \,x^{5}-5760 a \,b^{6} x^{6}+511 a^{7} m^{5}+3580 a^{6} b \,m^{4} x -38592 a^{5} b^{2} m^{3} x^{2}-69936 a^{4} b^{3} m^{2} x^{3}+60912 a^{3} b^{4} m \,x^{4}+20160 a^{2} b^{5} x^{5}+4025 a^{7} m^{4}+15289 a^{6} b \,m^{3} x -86076 a^{5} b^{2} m^{2} x^{2}-74628 a^{4} b^{3} m \,x^{3}+24192 a^{3} b^{4} x^{4}+18424 a^{7} m^{3}+36706 a^{6} b \,m^{2} x -96144 a^{5} b^{2} m \,x^{2}-30240 a^{4} b^{3} x^{3}+48860 a^{7} m^{2}+44712 a^{6} b m x -40320 a^{5} b^{2} x^{2}+69264 a^{7} m +20160 a^{6} b x +40320 a^{7}\right ) x}{\left (8+m \right ) \left (7+m \right ) \left (6+m \right ) \left (5+m \right ) \left (4+m \right ) \left (3+m \right ) \left (2+m \right ) \left (1+m \right )}\) | \(786\) |
risch | \(\frac {d^{3} \left (e x \right )^{m} \left (-b^{7} m^{7} x^{7}-a \,b^{6} m^{7} x^{6}-28 b^{7} m^{6} x^{7}+3 a^{2} b^{5} m^{7} x^{5}-29 a \,b^{6} m^{6} x^{6}-322 b^{7} m^{5} x^{7}+3 a^{3} b^{4} m^{7} x^{4}+90 a^{2} b^{5} m^{6} x^{5}-343 a \,b^{6} m^{5} x^{6}-1960 b^{7} m^{4} x^{7}-3 a^{4} b^{3} m^{7} x^{3}+93 a^{3} b^{4} m^{6} x^{4}+1098 a^{2} b^{5} m^{5} x^{5}-2135 a \,b^{6} m^{4} x^{6}-6769 b^{7} m^{3} x^{7}-3 a^{5} b^{2} m^{7} x^{2}-96 a^{4} b^{3} m^{6} x^{3}+1173 a^{3} b^{4} m^{5} x^{4}+7020 a^{2} b^{5} m^{4} x^{5}-7504 a \,b^{6} m^{3} x^{6}-13132 b^{7} m^{2} x^{7}+a^{6} b \,m^{7} x -99 a^{5} b^{2} m^{6} x^{2}-1254 a^{4} b^{3} m^{5} x^{3}+7743 a^{3} b^{4} m^{4} x^{4}+25227 a^{2} b^{5} m^{3} x^{5}-14756 a \,b^{6} m^{2} x^{6}-13068 m \,x^{7} b^{7}+a^{7} m^{7}+34 a^{6} b \,m^{6} x -1341 a^{5} b^{2} m^{5} x^{2}-8592 a^{4} b^{3} m^{4} x^{3}+28632 a^{3} b^{4} m^{3} x^{4}+50490 a^{2} b^{5} m^{2} x^{5}-14832 a \,b^{6} m \,x^{6}-5040 b^{7} x^{7}+35 a^{7} m^{6}+478 a^{6} b \,m^{5} x -9585 a^{5} b^{2} m^{4} x^{2}-32979 a^{4} b^{3} m^{3} x^{3}+58692 a^{3} b^{4} m^{2} x^{4}+51432 a^{2} b^{5} m \,x^{5}-5760 a \,b^{6} x^{6}+511 a^{7} m^{5}+3580 a^{6} b \,m^{4} x -38592 a^{5} b^{2} m^{3} x^{2}-69936 a^{4} b^{3} m^{2} x^{3}+60912 a^{3} b^{4} m \,x^{4}+20160 a^{2} b^{5} x^{5}+4025 a^{7} m^{4}+15289 a^{6} b \,m^{3} x -86076 a^{5} b^{2} m^{2} x^{2}-74628 a^{4} b^{3} m \,x^{3}+24192 a^{3} b^{4} x^{4}+18424 a^{7} m^{3}+36706 a^{6} b \,m^{2} x -96144 a^{5} b^{2} m \,x^{2}-30240 a^{4} b^{3} x^{3}+48860 a^{7} m^{2}+44712 a^{6} b m x -40320 a^{5} b^{2} x^{2}+69264 a^{7} m +20160 a^{6} b x +40320 a^{7}\right ) x}{\left (8+m \right ) \left (7+m \right ) \left (6+m \right ) \left (5+m \right ) \left (4+m \right ) \left (3+m \right ) \left (2+m \right ) \left (1+m \right )}\) | \(786\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.31, size = 197, normalized size = 1.00 \begin {gather*} -\frac {b^{7} d^{3} x^{8} e^{\left (m \log \left (x\right ) + m\right )}}{m + 8} - \frac {a b^{6} d^{3} x^{7} e^{\left (m \log \left (x\right ) + m\right )}}{m + 7} + \frac {3 \, a^{2} b^{5} d^{3} x^{6} e^{\left (m \log \left (x\right ) + m\right )}}{m + 6} + \frac {3 \, a^{3} b^{4} d^{3} x^{5} e^{\left (m \log \left (x\right ) + m\right )}}{m + 5} - \frac {3 \, a^{4} b^{3} d^{3} x^{4} e^{\left (m \log \left (x\right ) + m\right )}}{m + 4} - \frac {3 \, a^{5} b^{2} d^{3} x^{3} e^{\left (m \log \left (x\right ) + m\right )}}{m + 3} + \frac {a^{6} b d^{3} x^{2} e^{\left (m \log \left (x\right ) + m\right )}}{m + 2} + \frac {\left (x e\right )^{m + 1} a^{7} d^{3} e^{\left (-1\right )}}{m + 1} \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. 861 vs.
\(2 (197) = 394\).
time = 1.84, size = 861, normalized size = 4.37 \begin {gather*} -\frac {{\left ({\left (b^{7} d^{3} m^{7} + 28 \, b^{7} d^{3} m^{6} + 322 \, b^{7} d^{3} m^{5} + 1960 \, b^{7} d^{3} m^{4} + 6769 \, b^{7} d^{3} m^{3} + 13132 \, b^{7} d^{3} m^{2} + 13068 \, b^{7} d^{3} m + 5040 \, b^{7} d^{3}\right )} x^{8} + {\left (a b^{6} d^{3} m^{7} + 29 \, a b^{6} d^{3} m^{6} + 343 \, a b^{6} d^{3} m^{5} + 2135 \, a b^{6} d^{3} m^{4} + 7504 \, a b^{6} d^{3} m^{3} + 14756 \, a b^{6} d^{3} m^{2} + 14832 \, a b^{6} d^{3} m + 5760 \, a b^{6} d^{3}\right )} x^{7} - 3 \, {\left (a^{2} b^{5} d^{3} m^{7} + 30 \, a^{2} b^{5} d^{3} m^{6} + 366 \, a^{2} b^{5} d^{3} m^{5} + 2340 \, a^{2} b^{5} d^{3} m^{4} + 8409 \, a^{2} b^{5} d^{3} m^{3} + 16830 \, a^{2} b^{5} d^{3} m^{2} + 17144 \, a^{2} b^{5} d^{3} m + 6720 \, a^{2} b^{5} d^{3}\right )} x^{6} - 3 \, {\left (a^{3} b^{4} d^{3} m^{7} + 31 \, a^{3} b^{4} d^{3} m^{6} + 391 \, a^{3} b^{4} d^{3} m^{5} + 2581 \, a^{3} b^{4} d^{3} m^{4} + 9544 \, a^{3} b^{4} d^{3} m^{3} + 19564 \, a^{3} b^{4} d^{3} m^{2} + 20304 \, a^{3} b^{4} d^{3} m + 8064 \, a^{3} b^{4} d^{3}\right )} x^{5} + 3 \, {\left (a^{4} b^{3} d^{3} m^{7} + 32 \, a^{4} b^{3} d^{3} m^{6} + 418 \, a^{4} b^{3} d^{3} m^{5} + 2864 \, a^{4} b^{3} d^{3} m^{4} + 10993 \, a^{4} b^{3} d^{3} m^{3} + 23312 \, a^{4} b^{3} d^{3} m^{2} + 24876 \, a^{4} b^{3} d^{3} m + 10080 \, a^{4} b^{3} d^{3}\right )} x^{4} + 3 \, {\left (a^{5} b^{2} d^{3} m^{7} + 33 \, a^{5} b^{2} d^{3} m^{6} + 447 \, a^{5} b^{2} d^{3} m^{5} + 3195 \, a^{5} b^{2} d^{3} m^{4} + 12864 \, a^{5} b^{2} d^{3} m^{3} + 28692 \, a^{5} b^{2} d^{3} m^{2} + 32048 \, a^{5} b^{2} d^{3} m + 13440 \, a^{5} b^{2} d^{3}\right )} x^{3} - {\left (a^{6} b d^{3} m^{7} + 34 \, a^{6} b d^{3} m^{6} + 478 \, a^{6} b d^{3} m^{5} + 3580 \, a^{6} b d^{3} m^{4} + 15289 \, a^{6} b d^{3} m^{3} + 36706 \, a^{6} b d^{3} m^{2} + 44712 \, a^{6} b d^{3} m + 20160 \, a^{6} b d^{3}\right )} x^{2} - {\left (a^{7} d^{3} m^{7} + 35 \, a^{7} d^{3} m^{6} + 511 \, a^{7} d^{3} m^{5} + 4025 \, a^{7} d^{3} m^{4} + 18424 \, a^{7} d^{3} m^{3} + 48860 \, a^{7} d^{3} m^{2} + 69264 \, a^{7} d^{3} m + 40320 \, a^{7} d^{3}\right )} x\right )} \left (x e\right )^{m}}{m^{8} + 36 \, m^{7} + 546 \, m^{6} + 4536 \, m^{5} + 22449 \, m^{4} + 67284 \, m^{3} + 118124 \, m^{2} + 109584 \, m + 40320} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 4779 vs.
\(2 (184) = 368\).
time = 0.73, size = 4779, normalized size = 24.26 \begin {gather*} \text {Too large to display} \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. 1313 vs.
\(2 (197) = 394\).
time = 1.29, size = 1313, normalized size = 6.66 \begin {gather*} -\frac {b^{7} d^{3} m^{7} x^{8} x^{m} e^{m} + a b^{6} d^{3} m^{7} x^{7} x^{m} e^{m} + 28 \, b^{7} d^{3} m^{6} x^{8} x^{m} e^{m} - 3 \, a^{2} b^{5} d^{3} m^{7} x^{6} x^{m} e^{m} + 29 \, a b^{6} d^{3} m^{6} x^{7} x^{m} e^{m} + 322 \, b^{7} d^{3} m^{5} x^{8} x^{m} e^{m} - 3 \, a^{3} b^{4} d^{3} m^{7} x^{5} x^{m} e^{m} - 90 \, a^{2} b^{5} d^{3} m^{6} x^{6} x^{m} e^{m} + 343 \, a b^{6} d^{3} m^{5} x^{7} x^{m} e^{m} + 1960 \, b^{7} d^{3} m^{4} x^{8} x^{m} e^{m} + 3 \, a^{4} b^{3} d^{3} m^{7} x^{4} x^{m} e^{m} - 93 \, a^{3} b^{4} d^{3} m^{6} x^{5} x^{m} e^{m} - 1098 \, a^{2} b^{5} d^{3} m^{5} x^{6} x^{m} e^{m} + 2135 \, a b^{6} d^{3} m^{4} x^{7} x^{m} e^{m} + 6769 \, b^{7} d^{3} m^{3} x^{8} x^{m} e^{m} + 3 \, a^{5} b^{2} d^{3} m^{7} x^{3} x^{m} e^{m} + 96 \, a^{4} b^{3} d^{3} m^{6} x^{4} x^{m} e^{m} - 1173 \, a^{3} b^{4} d^{3} m^{5} x^{5} x^{m} e^{m} - 7020 \, a^{2} b^{5} d^{3} m^{4} x^{6} x^{m} e^{m} + 7504 \, a b^{6} d^{3} m^{3} x^{7} x^{m} e^{m} + 13132 \, b^{7} d^{3} m^{2} x^{8} x^{m} e^{m} - a^{6} b d^{3} m^{7} x^{2} x^{m} e^{m} + 99 \, a^{5} b^{2} d^{3} m^{6} x^{3} x^{m} e^{m} + 1254 \, a^{4} b^{3} d^{3} m^{5} x^{4} x^{m} e^{m} - 7743 \, a^{3} b^{4} d^{3} m^{4} x^{5} x^{m} e^{m} - 25227 \, a^{2} b^{5} d^{3} m^{3} x^{6} x^{m} e^{m} + 14756 \, a b^{6} d^{3} m^{2} x^{7} x^{m} e^{m} + 13068 \, b^{7} d^{3} m x^{8} x^{m} e^{m} - a^{7} d^{3} m^{7} x x^{m} e^{m} - 34 \, a^{6} b d^{3} m^{6} x^{2} x^{m} e^{m} + 1341 \, a^{5} b^{2} d^{3} m^{5} x^{3} x^{m} e^{m} + 8592 \, a^{4} b^{3} d^{3} m^{4} x^{4} x^{m} e^{m} - 28632 \, a^{3} b^{4} d^{3} m^{3} x^{5} x^{m} e^{m} - 50490 \, a^{2} b^{5} d^{3} m^{2} x^{6} x^{m} e^{m} + 14832 \, a b^{6} d^{3} m x^{7} x^{m} e^{m} + 5040 \, b^{7} d^{3} x^{8} x^{m} e^{m} - 35 \, a^{7} d^{3} m^{6} x x^{m} e^{m} - 478 \, a^{6} b d^{3} m^{5} x^{2} x^{m} e^{m} + 9585 \, a^{5} b^{2} d^{3} m^{4} x^{3} x^{m} e^{m} + 32979 \, a^{4} b^{3} d^{3} m^{3} x^{4} x^{m} e^{m} - 58692 \, a^{3} b^{4} d^{3} m^{2} x^{5} x^{m} e^{m} - 51432 \, a^{2} b^{5} d^{3} m x^{6} x^{m} e^{m} + 5760 \, a b^{6} d^{3} x^{7} x^{m} e^{m} - 511 \, a^{7} d^{3} m^{5} x x^{m} e^{m} - 3580 \, a^{6} b d^{3} m^{4} x^{2} x^{m} e^{m} + 38592 \, a^{5} b^{2} d^{3} m^{3} x^{3} x^{m} e^{m} + 69936 \, a^{4} b^{3} d^{3} m^{2} x^{4} x^{m} e^{m} - 60912 \, a^{3} b^{4} d^{3} m x^{5} x^{m} e^{m} - 20160 \, a^{2} b^{5} d^{3} x^{6} x^{m} e^{m} - 4025 \, a^{7} d^{3} m^{4} x x^{m} e^{m} - 15289 \, a^{6} b d^{3} m^{3} x^{2} x^{m} e^{m} + 86076 \, a^{5} b^{2} d^{3} m^{2} x^{3} x^{m} e^{m} + 74628 \, a^{4} b^{3} d^{3} m x^{4} x^{m} e^{m} - 24192 \, a^{3} b^{4} d^{3} x^{5} x^{m} e^{m} - 18424 \, a^{7} d^{3} m^{3} x x^{m} e^{m} - 36706 \, a^{6} b d^{3} m^{2} x^{2} x^{m} e^{m} + 96144 \, a^{5} b^{2} d^{3} m x^{3} x^{m} e^{m} + 30240 \, a^{4} b^{3} d^{3} x^{4} x^{m} e^{m} - 48860 \, a^{7} d^{3} m^{2} x x^{m} e^{m} - 44712 \, a^{6} b d^{3} m x^{2} x^{m} e^{m} + 40320 \, a^{5} b^{2} d^{3} x^{3} x^{m} e^{m} - 69264 \, a^{7} d^{3} m x x^{m} e^{m} - 20160 \, a^{6} b d^{3} x^{2} x^{m} e^{m} - 40320 \, a^{7} d^{3} x x^{m} e^{m}}{m^{8} + 36 \, m^{7} + 546 \, m^{6} + 4536 \, m^{5} + 22449 \, m^{4} + 67284 \, m^{3} + 118124 \, m^{2} + 109584 \, m + 40320} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.89, size = 723, normalized size = 3.67 \begin {gather*} \frac {a^7\,d^3\,x\,{\left (e\,x\right )}^m\,\left (m^7+35\,m^6+511\,m^5+4025\,m^4+18424\,m^3+48860\,m^2+69264\,m+40320\right )}{m^8+36\,m^7+546\,m^6+4536\,m^5+22449\,m^4+67284\,m^3+118124\,m^2+109584\,m+40320}-\frac {b^7\,d^3\,x^8\,{\left (e\,x\right )}^m\,\left (m^7+28\,m^6+322\,m^5+1960\,m^4+6769\,m^3+13132\,m^2+13068\,m+5040\right )}{m^8+36\,m^7+546\,m^6+4536\,m^5+22449\,m^4+67284\,m^3+118124\,m^2+109584\,m+40320}-\frac {a\,b^6\,d^3\,x^7\,{\left (e\,x\right )}^m\,\left (m^7+29\,m^6+343\,m^5+2135\,m^4+7504\,m^3+14756\,m^2+14832\,m+5760\right )}{m^8+36\,m^7+546\,m^6+4536\,m^5+22449\,m^4+67284\,m^3+118124\,m^2+109584\,m+40320}+\frac {a^6\,b\,d^3\,x^2\,{\left (e\,x\right )}^m\,\left (m^7+34\,m^6+478\,m^5+3580\,m^4+15289\,m^3+36706\,m^2+44712\,m+20160\right )}{m^8+36\,m^7+546\,m^6+4536\,m^5+22449\,m^4+67284\,m^3+118124\,m^2+109584\,m+40320}+\frac {3\,a^2\,b^5\,d^3\,x^6\,{\left (e\,x\right )}^m\,\left (m^7+30\,m^6+366\,m^5+2340\,m^4+8409\,m^3+16830\,m^2+17144\,m+6720\right )}{m^8+36\,m^7+546\,m^6+4536\,m^5+22449\,m^4+67284\,m^3+118124\,m^2+109584\,m+40320}+\frac {3\,a^3\,b^4\,d^3\,x^5\,{\left (e\,x\right )}^m\,\left (m^7+31\,m^6+391\,m^5+2581\,m^4+9544\,m^3+19564\,m^2+20304\,m+8064\right )}{m^8+36\,m^7+546\,m^6+4536\,m^5+22449\,m^4+67284\,m^3+118124\,m^2+109584\,m+40320}-\frac {3\,a^4\,b^3\,d^3\,x^4\,{\left (e\,x\right )}^m\,\left (m^7+32\,m^6+418\,m^5+2864\,m^4+10993\,m^3+23312\,m^2+24876\,m+10080\right )}{m^8+36\,m^7+546\,m^6+4536\,m^5+22449\,m^4+67284\,m^3+118124\,m^2+109584\,m+40320}-\frac {3\,a^5\,b^2\,d^3\,x^3\,{\left (e\,x\right )}^m\,\left (m^7+33\,m^6+447\,m^5+3195\,m^4+12864\,m^3+28692\,m^2+32048\,m+13440\right )}{m^8+36\,m^7+546\,m^6+4536\,m^5+22449\,m^4+67284\,m^3+118124\,m^2+109584\,m+40320} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
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