Optimal. Leaf size=518 \[ \frac {f^5 F^{a+b (c+d x)^2}}{b^3 d^6 \log ^3(F)}+\frac {15 f^4 (d e-c f) F^a \sqrt {\pi } \text {erfi}\left (\sqrt {b} (c+d x) \sqrt {\log (F)}\right )}{8 b^{5/2} d^6 \log ^{\frac {5}{2}}(F)}-\frac {5 f^3 (d e-c f)^2 F^{a+b (c+d x)^2}}{b^2 d^6 \log ^2(F)}-\frac {15 f^4 (d e-c f) F^{a+b (c+d x)^2} (c+d x)}{4 b^2 d^6 \log ^2(F)}-\frac {f^5 F^{a+b (c+d x)^2} (c+d x)^2}{b^2 d^6 \log ^2(F)}-\frac {5 f^2 (d e-c f)^3 F^a \sqrt {\pi } \text {erfi}\left (\sqrt {b} (c+d x) \sqrt {\log (F)}\right )}{2 b^{3/2} d^6 \log ^{\frac {3}{2}}(F)}+\frac {5 f (d e-c f)^4 F^{a+b (c+d x)^2}}{2 b d^6 \log (F)}+\frac {5 f^2 (d e-c f)^3 F^{a+b (c+d x)^2} (c+d x)}{b d^6 \log (F)}+\frac {5 f^3 (d e-c f)^2 F^{a+b (c+d x)^2} (c+d x)^2}{b d^6 \log (F)}+\frac {5 f^4 (d e-c f) F^{a+b (c+d x)^2} (c+d x)^3}{2 b d^6 \log (F)}+\frac {f^5 F^{a+b (c+d x)^2} (c+d x)^4}{2 b d^6 \log (F)}+\frac {(d e-c f)^5 F^a \sqrt {\pi } \text {erfi}\left (\sqrt {b} (c+d x) \sqrt {\log (F)}\right )}{2 \sqrt {b} d^6 \sqrt {\log (F)}} \]
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Rubi [A]
time = 0.63, antiderivative size = 518, normalized size of antiderivative = 1.00, number of steps
used = 14, number of rules used = 4, integrand size = 21, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.190, Rules used = {2258, 2235,
2240, 2243} \begin {gather*} \frac {15 \sqrt {\pi } f^4 F^a (d e-c f) \text {Erfi}\left (\sqrt {b} \sqrt {\log (F)} (c+d x)\right )}{8 b^{5/2} d^6 \log ^{\frac {5}{2}}(F)}-\frac {5 \sqrt {\pi } f^2 F^a (d e-c f)^3 \text {Erfi}\left (\sqrt {b} \sqrt {\log (F)} (c+d x)\right )}{2 b^{3/2} d^6 \log ^{\frac {3}{2}}(F)}+\frac {f^5 F^{a+b (c+d x)^2}}{b^3 d^6 \log ^3(F)}-\frac {15 f^4 (c+d x) (d e-c f) F^{a+b (c+d x)^2}}{4 b^2 d^6 \log ^2(F)}-\frac {5 f^3 (d e-c f)^2 F^{a+b (c+d x)^2}}{b^2 d^6 \log ^2(F)}-\frac {f^5 (c+d x)^2 F^{a+b (c+d x)^2}}{b^2 d^6 \log ^2(F)}+\frac {\sqrt {\pi } F^a (d e-c f)^5 \text {Erfi}\left (\sqrt {b} \sqrt {\log (F)} (c+d x)\right )}{2 \sqrt {b} d^6 \sqrt {\log (F)}}+\frac {5 f^4 (c+d x)^3 (d e-c f) F^{a+b (c+d x)^2}}{2 b d^6 \log (F)}+\frac {5 f^3 (c+d x)^2 (d e-c f)^2 F^{a+b (c+d x)^2}}{b d^6 \log (F)}+\frac {5 f^2 (c+d x) (d e-c f)^3 F^{a+b (c+d x)^2}}{b d^6 \log (F)}+\frac {5 f (d e-c f)^4 F^{a+b (c+d x)^2}}{2 b d^6 \log (F)}+\frac {f^5 (c+d x)^4 F^{a+b (c+d x)^2}}{2 b d^6 \log (F)} \end {gather*}
Antiderivative was successfully verified.
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Rule 2235
Rule 2240
Rule 2243
Rule 2258
Rubi steps
\begin {align*} \int F^{a+b (c+d x)^2} (e+f x)^5 \, dx &=\int \left (\frac {(d e-c f)^5 F^{a+b (c+d x)^2}}{d^5}+\frac {5 f (d e-c f)^4 F^{a+b (c+d x)^2} (c+d x)}{d^5}+\frac {10 f^2 (d e-c f)^3 F^{a+b (c+d x)^2} (c+d x)^2}{d^5}+\frac {10 f^3 (d e-c f)^2 F^{a+b (c+d x)^2} (c+d x)^3}{d^5}+\frac {5 f^4 (d e-c f) F^{a+b (c+d x)^2} (c+d x)^4}{d^5}+\frac {f^5 F^{a+b (c+d x)^2} (c+d x)^5}{d^5}\right ) \, dx\\ &=\frac {f^5 \int F^{a+b (c+d x)^2} (c+d x)^5 \, dx}{d^5}+\frac {\left (5 f^4 (d e-c f)\right ) \int F^{a+b (c+d x)^2} (c+d x)^4 \, dx}{d^5}+\frac {\left (10 f^3 (d e-c f)^2\right ) \int F^{a+b (c+d x)^2} (c+d x)^3 \, dx}{d^5}+\frac {\left (10 f^2 (d e-c f)^3\right ) \int F^{a+b (c+d x)^2} (c+d x)^2 \, dx}{d^5}+\frac {\left (5 f (d e-c f)^4\right ) \int F^{a+b (c+d x)^2} (c+d x) \, dx}{d^5}+\frac {(d e-c f)^5 \int F^{a+b (c+d x)^2} \, dx}{d^5}\\ &=\frac {5 f (d e-c f)^4 F^{a+b (c+d x)^2}}{2 b d^6 \log (F)}+\frac {5 f^2 (d e-c f)^3 F^{a+b (c+d x)^2} (c+d x)}{b d^6 \log (F)}+\frac {5 f^3 (d e-c f)^2 F^{a+b (c+d x)^2} (c+d x)^2}{b d^6 \log (F)}+\frac {5 f^4 (d e-c f) F^{a+b (c+d x)^2} (c+d x)^3}{2 b d^6 \log (F)}+\frac {f^5 F^{a+b (c+d x)^2} (c+d x)^4}{2 b d^6 \log (F)}+\frac {(d e-c f)^5 F^a \sqrt {\pi } \text {erfi}\left (\sqrt {b} (c+d x) \sqrt {\log (F)}\right )}{2 \sqrt {b} d^6 \sqrt {\log (F)}}-\frac {\left (2 f^5\right ) \int F^{a+b (c+d x)^2} (c+d x)^3 \, dx}{b d^5 \log (F)}-\frac {\left (15 f^4 (d e-c f)\right ) \int F^{a+b (c+d x)^2} (c+d x)^2 \, dx}{2 b d^5 \log (F)}-\frac {\left (10 f^3 (d e-c f)^2\right ) \int F^{a+b (c+d x)^2} (c+d x) \, dx}{b d^5 \log (F)}-\frac {\left (5 f^2 (d e-c f)^3\right ) \int F^{a+b (c+d x)^2} \, dx}{b d^5 \log (F)}\\ &=-\frac {5 f^3 (d e-c f)^2 F^{a+b (c+d x)^2}}{b^2 d^6 \log ^2(F)}-\frac {15 f^4 (d e-c f) F^{a+b (c+d x)^2} (c+d x)}{4 b^2 d^6 \log ^2(F)}-\frac {f^5 F^{a+b (c+d x)^2} (c+d x)^2}{b^2 d^6 \log ^2(F)}-\frac {5 f^2 (d e-c f)^3 F^a \sqrt {\pi } \text {erfi}\left (\sqrt {b} (c+d x) \sqrt {\log (F)}\right )}{2 b^{3/2} d^6 \log ^{\frac {3}{2}}(F)}+\frac {5 f (d e-c f)^4 F^{a+b (c+d x)^2}}{2 b d^6 \log (F)}+\frac {5 f^2 (d e-c f)^3 F^{a+b (c+d x)^2} (c+d x)}{b d^6 \log (F)}+\frac {5 f^3 (d e-c f)^2 F^{a+b (c+d x)^2} (c+d x)^2}{b d^6 \log (F)}+\frac {5 f^4 (d e-c f) F^{a+b (c+d x)^2} (c+d x)^3}{2 b d^6 \log (F)}+\frac {f^5 F^{a+b (c+d x)^2} (c+d x)^4}{2 b d^6 \log (F)}+\frac {(d e-c f)^5 F^a \sqrt {\pi } \text {erfi}\left (\sqrt {b} (c+d x) \sqrt {\log (F)}\right )}{2 \sqrt {b} d^6 \sqrt {\log (F)}}+\frac {\left (2 f^5\right ) \int F^{a+b (c+d x)^2} (c+d x) \, dx}{b^2 d^5 \log ^2(F)}+\frac {\left (15 f^4 (d e-c f)\right ) \int F^{a+b (c+d x)^2} \, dx}{4 b^2 d^5 \log ^2(F)}\\ &=\frac {f^5 F^{a+b (c+d x)^2}}{b^3 d^6 \log ^3(F)}+\frac {15 f^4 (d e-c f) F^a \sqrt {\pi } \text {erfi}\left (\sqrt {b} (c+d x) \sqrt {\log (F)}\right )}{8 b^{5/2} d^6 \log ^{\frac {5}{2}}(F)}-\frac {5 f^3 (d e-c f)^2 F^{a+b (c+d x)^2}}{b^2 d^6 \log ^2(F)}-\frac {15 f^4 (d e-c f) F^{a+b (c+d x)^2} (c+d x)}{4 b^2 d^6 \log ^2(F)}-\frac {f^5 F^{a+b (c+d x)^2} (c+d x)^2}{b^2 d^6 \log ^2(F)}-\frac {5 f^2 (d e-c f)^3 F^a \sqrt {\pi } \text {erfi}\left (\sqrt {b} (c+d x) \sqrt {\log (F)}\right )}{2 b^{3/2} d^6 \log ^{\frac {3}{2}}(F)}+\frac {5 f (d e-c f)^4 F^{a+b (c+d x)^2}}{2 b d^6 \log (F)}+\frac {5 f^2 (d e-c f)^3 F^{a+b (c+d x)^2} (c+d x)}{b d^6 \log (F)}+\frac {5 f^3 (d e-c f)^2 F^{a+b (c+d x)^2} (c+d x)^2}{b d^6 \log (F)}+\frac {5 f^4 (d e-c f) F^{a+b (c+d x)^2} (c+d x)^3}{2 b d^6 \log (F)}+\frac {f^5 F^{a+b (c+d x)^2} (c+d x)^4}{2 b d^6 \log (F)}+\frac {(d e-c f)^5 F^a \sqrt {\pi } \text {erfi}\left (\sqrt {b} (c+d x) \sqrt {\log (F)}\right )}{2 \sqrt {b} d^6 \sqrt {\log (F)}}\\ \end {align*}
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Mathematica [A]
time = 1.36, size = 412, normalized size = 0.80 \begin {gather*} \frac {F^a \left (-40 f^3 (d e-c f)^2 F^{b (c+d x)^2}+\frac {15 f^4 (-d e+c f) \left (-\sqrt {\pi } \text {erfi}\left (\sqrt {b} (c+d x) \sqrt {\log (F)}\right )+2 \sqrt {b} F^{b (c+d x)^2} (c+d x) \sqrt {\log (F)}\right )}{\sqrt {b} \sqrt {\log (F)}}+20 \sqrt {b} f^2 (-d e+c f)^3 \sqrt {\pi } \text {erfi}\left (\sqrt {b} (c+d x) \sqrt {\log (F)}\right ) \sqrt {\log (F)}+20 b f (d e-c f)^4 F^{b (c+d x)^2} \log (F)+40 b f^2 (d e-c f)^3 F^{b (c+d x)^2} (c+d x) \log (F)+40 b f^3 (d e-c f)^2 F^{b (c+d x)^2} (c+d x)^2 \log (F)+20 b f^4 (d e-c f) F^{b (c+d x)^2} (c+d x)^3 \log (F)+4 b f^5 F^{b (c+d x)^2} (c+d x)^4 \log (F)+4 b^{3/2} (d e-c f)^5 \sqrt {\pi } \text {erfi}\left (\sqrt {b} (c+d x) \sqrt {\log (F)}\right ) \log ^{\frac {3}{2}}(F)+\frac {8 f^5 F^{b (c+d x)^2} \left (1-b (c+d x)^2 \log (F)\right )}{b \log (F)}\right )}{8 b^2 d^6 \log ^2(F)} \end {gather*}
Antiderivative was successfully verified.
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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(1656\) vs.
\(2(474)=948\).
time = 0.10, size = 1657, normalized size = 3.20
method | result | size |
risch | \(\text {Expression too large to display}\) | \(1657\) |
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. 1456 vs.
\(2 (474) = 948\).
time = 0.71, size = 1456, normalized size = 2.81 \begin {gather*} \text {Too large to display} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.39, size = 525, normalized size = 1.01 \begin {gather*} \frac {\sqrt {\pi } {\left (15 \, c f^{5} - 15 \, d f^{4} e + 4 \, {\left (b^{2} c^{5} f^{5} - 5 \, b^{2} c^{4} d f^{4} e + 10 \, b^{2} c^{3} d^{2} f^{3} e^{2} - 10 \, b^{2} c^{2} d^{3} f^{2} e^{3} + 5 \, b^{2} c d^{4} f e^{4} - b^{2} d^{5} e^{5}\right )} \log \left (F\right )^{2} - 20 \, {\left (b c^{3} f^{5} - 3 \, b c^{2} d f^{4} e + 3 \, b c d^{2} f^{3} e^{2} - b d^{3} f^{2} e^{3}\right )} \log \left (F\right )\right )} \sqrt {-b d^{2} \log \left (F\right )} F^{a} \operatorname {erf}\left (\frac {\sqrt {-b d^{2} \log \left (F\right )} {\left (d x + c\right )}}{d}\right ) + 2 \, {\left (4 \, d f^{5} + 2 \, {\left (b^{2} d^{5} f^{5} x^{4} - b^{2} c d^{4} f^{5} x^{3} + b^{2} c^{2} d^{3} f^{5} x^{2} - b^{2} c^{3} d^{2} f^{5} x + b^{2} c^{4} d f^{5} + 5 \, b^{2} d^{5} f e^{4} + 10 \, {\left (b^{2} d^{5} f^{2} x - b^{2} c d^{4} f^{2}\right )} e^{3} + 10 \, {\left (b^{2} d^{5} f^{3} x^{2} - b^{2} c d^{4} f^{3} x + b^{2} c^{2} d^{3} f^{3}\right )} e^{2} + 5 \, {\left (b^{2} d^{5} f^{4} x^{3} - b^{2} c d^{4} f^{4} x^{2} + b^{2} c^{2} d^{3} f^{4} x - b^{2} c^{3} d^{2} f^{4}\right )} e\right )} \log \left (F\right )^{2} - {\left (4 \, b d^{3} f^{5} x^{2} - 7 \, b c d^{2} f^{5} x + 9 \, b c^{2} d f^{5} + 20 \, b d^{3} f^{3} e^{2} + 5 \, {\left (3 \, b d^{3} f^{4} x - 5 \, b c d^{2} f^{4}\right )} e\right )} \log \left (F\right )\right )} F^{b d^{2} x^{2} + 2 \, b c d x + b c^{2} + a}}{8 \, b^{3} d^{7} \log \left (F\right )^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int F^{a + b \left (c + d x\right )^{2}} \left (e + f x\right )^{5}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 3.45, size = 942, normalized size = 1.82 \begin {gather*} -\frac {\sqrt {\pi } \operatorname {erf}\left (-\sqrt {-b \log \left (F\right )} d {\left (x + \frac {c}{d}\right )}\right ) e^{\left (a \log \left (F\right ) + 5\right )}}{2 \, \sqrt {-b \log \left (F\right )} d} + \frac {5 \, {\left (\frac {\sqrt {\pi } c f \operatorname {erf}\left (-\sqrt {-b \log \left (F\right )} d {\left (x + \frac {c}{d}\right )}\right ) e^{\left (a \log \left (F\right ) + 4\right )}}{\sqrt {-b \log \left (F\right )} d} + \frac {f e^{\left (b d^{2} x^{2} \log \left (F\right ) + 2 \, b c d x \log \left (F\right ) + b c^{2} \log \left (F\right ) + a \log \left (F\right ) + 4\right )}}{b d \log \left (F\right )}\right )}}{2 \, d} - \frac {5 \, {\left (\frac {\sqrt {\pi } {\left (2 \, b c^{2} f^{2} \log \left (F\right ) - f^{2}\right )} \operatorname {erf}\left (-\sqrt {-b \log \left (F\right )} d {\left (x + \frac {c}{d}\right )}\right ) e^{\left (a \log \left (F\right ) + 3\right )}}{\sqrt {-b \log \left (F\right )} b d \log \left (F\right )} - \frac {2 \, {\left (d f^{2} {\left (x + \frac {c}{d}\right )} - 2 \, c f^{2}\right )} e^{\left (b d^{2} x^{2} \log \left (F\right ) + 2 \, b c d x \log \left (F\right ) + b c^{2} \log \left (F\right ) + a \log \left (F\right ) + 3\right )}}{b d \log \left (F\right )}\right )}}{2 \, d^{2}} + \frac {5 \, {\left (\frac {\sqrt {\pi } {\left (2 \, b c^{3} f^{3} \log \left (F\right ) - 3 \, c f^{3}\right )} \operatorname {erf}\left (-\sqrt {-b \log \left (F\right )} d {\left (x + \frac {c}{d}\right )}\right ) e^{\left (a \log \left (F\right ) + 2\right )}}{\sqrt {-b \log \left (F\right )} b d \log \left (F\right )} + \frac {2 \, {\left (b d^{2} f^{3} {\left (x + \frac {c}{d}\right )}^{2} \log \left (F\right ) - 3 \, b c d f^{3} {\left (x + \frac {c}{d}\right )} \log \left (F\right ) + 3 \, b c^{2} f^{3} \log \left (F\right ) - f^{3}\right )} e^{\left (b d^{2} x^{2} \log \left (F\right ) + 2 \, b c d x \log \left (F\right ) + b c^{2} \log \left (F\right ) + a \log \left (F\right ) + 2\right )}}{b^{2} d \log \left (F\right )^{2}}\right )}}{2 \, d^{3}} - \frac {5 \, {\left (\frac {\sqrt {\pi } {\left (4 \, b^{2} c^{4} f^{4} \log \left (F\right )^{2} - 12 \, b c^{2} f^{4} \log \left (F\right ) + 3 \, f^{4}\right )} \operatorname {erf}\left (-\sqrt {-b \log \left (F\right )} d {\left (x + \frac {c}{d}\right )}\right ) e^{\left (a \log \left (F\right ) + 1\right )}}{\sqrt {-b \log \left (F\right )} b^{2} d \log \left (F\right )^{2}} - \frac {2 \, {\left (2 \, b d^{3} f^{4} {\left (x + \frac {c}{d}\right )}^{3} \log \left (F\right ) - 8 \, b c d^{2} f^{4} {\left (x + \frac {c}{d}\right )}^{2} \log \left (F\right ) + 12 \, b c^{2} d f^{4} {\left (x + \frac {c}{d}\right )} \log \left (F\right ) - 8 \, b c^{3} f^{4} \log \left (F\right ) - 3 \, d f^{4} {\left (x + \frac {c}{d}\right )} + 8 \, c f^{4}\right )} e^{\left (b d^{2} x^{2} \log \left (F\right ) + 2 \, b c d x \log \left (F\right ) + b c^{2} \log \left (F\right ) + a \log \left (F\right ) + 1\right )}}{b^{2} d \log \left (F\right )^{2}}\right )}}{8 \, d^{4}} + \frac {\frac {\sqrt {\pi } {\left (4 \, b^{2} c^{5} f^{5} \log \left (F\right )^{2} - 20 \, b c^{3} f^{5} \log \left (F\right ) + 15 \, c f^{5}\right )} F^{a} \operatorname {erf}\left (-\sqrt {-b \log \left (F\right )} d {\left (x + \frac {c}{d}\right )}\right )}{\sqrt {-b \log \left (F\right )} b^{2} d \log \left (F\right )^{2}} + \frac {2 \, {\left (2 \, b^{2} d^{4} f^{5} {\left (x + \frac {c}{d}\right )}^{4} \log \left (F\right )^{2} - 10 \, b^{2} c d^{3} f^{5} {\left (x + \frac {c}{d}\right )}^{3} \log \left (F\right )^{2} + 20 \, b^{2} c^{2} d^{2} f^{5} {\left (x + \frac {c}{d}\right )}^{2} \log \left (F\right )^{2} - 20 \, b^{2} c^{3} d f^{5} {\left (x + \frac {c}{d}\right )} \log \left (F\right )^{2} + 10 \, b^{2} c^{4} f^{5} \log \left (F\right )^{2} - 4 \, b d^{2} f^{5} {\left (x + \frac {c}{d}\right )}^{2} \log \left (F\right ) + 15 \, b c d f^{5} {\left (x + \frac {c}{d}\right )} \log \left (F\right ) - 20 \, b c^{2} f^{5} \log \left (F\right ) + 4 \, f^{5}\right )} e^{\left (b d^{2} x^{2} \log \left (F\right ) + 2 \, b c d x \log \left (F\right ) + b c^{2} \log \left (F\right ) + a \log \left (F\right )\right )}}{b^{3} d \log \left (F\right )^{3}}}{8 \, d^{5}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 4.11, size = 716, normalized size = 1.38 \begin {gather*} \frac {F^{b\,d^2\,x^2}\,F^a\,F^{b\,c^2}\,F^{2\,b\,c\,d\,x}\,\left (f^5+\frac {{\ln \left (F\right )}^2\,\left (2\,F^a\,b^2\,c^4\,f^5+10\,F^a\,b^2\,d^4\,e^4\,f+20\,F^a\,b^2\,c^2\,d^2\,e^2\,f^3-10\,F^a\,b^2\,c^3\,d\,e\,f^4-20\,F^a\,b^2\,c\,d^3\,e^3\,f^2\right )}{4\,F^a}-\frac {\ln \left (F\right )\,\left (9\,F^a\,b\,c^2\,f^5+20\,F^a\,b\,d^2\,e^2\,f^3-25\,F^a\,b\,c\,d\,e\,f^4\right )}{4\,F^a}\right )}{b^3\,d^6\,{\ln \left (F\right )}^3}-\mathrm {erfi}\left (\frac {b\,x\,\ln \left (F\right )\,d^2+b\,c\,\ln \left (F\right )\,d}{\sqrt {b\,d^2\,\ln \left (F\right )}}\right )\,\left (\frac {\frac {F^a\,\sqrt {\pi }\,\left (15\,c\,f^5-15\,d\,e\,f^4\right )}{8\,\sqrt {b\,d^2\,\ln \left (F\right )}}-\frac {F^a\,\sqrt {\pi }\,\ln \left (F\right )\,\left (20\,b\,c^3\,f^5-60\,b\,c^2\,d\,e\,f^4+60\,b\,c\,d^2\,e^2\,f^3-20\,b\,d^3\,e^3\,f^2\right )}{8\,\sqrt {b\,d^2\,\ln \left (F\right )}}}{b^2\,d^5\,{\ln \left (F\right )}^2}+\frac {F^a\,\sqrt {\pi }\,\left (4\,b^2\,c^5\,f^5-20\,b^2\,c^4\,d\,e\,f^4+40\,b^2\,c^3\,d^2\,e^2\,f^3-40\,b^2\,c^2\,d^3\,e^3\,f^2+20\,b^2\,c\,d^4\,e^4\,f-4\,b^2\,d^5\,e^5\right )}{8\,b^2\,d^5\,\sqrt {b\,d^2\,\ln \left (F\right )}}\right )-\frac {F^{b\,d^2\,x^2}\,F^a\,F^{b\,c^2}\,F^{2\,b\,c\,d\,x}\,x\,\left (\ln \left (F\right )\,\left (\frac {b\,c^3\,f^5}{2}-\frac {5\,b\,c^2\,d\,e\,f^4}{2}+5\,b\,c\,d^2\,e^2\,f^3-5\,b\,d^3\,e^3\,f^2\right )-\frac {7\,c\,f^5}{4}+\frac {15\,d\,e\,f^4}{4}\right )}{b^2\,d^5\,{\ln \left (F\right )}^2}+\frac {F^{b\,d^2\,x^2}\,F^a\,F^{b\,c^2}\,F^{2\,b\,c\,d\,x}\,f^5\,x^4}{2\,b\,d^2\,\ln \left (F\right )}-\frac {F^{b\,d^2\,x^2}\,F^a\,F^{b\,c^2}\,F^{2\,b\,c\,d\,x}\,x^2\,\left (f^5-\frac {b\,f^3\,\left (\ln \left (F\right )\,c^2\,f^2-5\,\ln \left (F\right )\,c\,d\,e\,f+10\,\ln \left (F\right )\,d^2\,e^2\right )}{2}\right )}{b^2\,d^4\,{\ln \left (F\right )}^2}-\frac {F^{b\,d^2\,x^2}\,F^a\,F^{b\,c^2}\,F^{2\,b\,c\,d\,x}\,f^4\,x^3\,\left (c\,f-5\,d\,e\right )}{2\,b\,d^3\,\ln \left (F\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
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