Optimal. Leaf size=32 \[ -\frac {b^4 F^a \Gamma \left (-4,-b (c+d x)^n \log (F)\right ) \log ^4(F)}{d n} \]
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Rubi [A]
time = 0.03, antiderivative size = 32, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 1, integrand size = 25, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.040, Rules used = {2250}
\begin {gather*} -\frac {b^4 F^a \log ^4(F) \text {Gamma}\left (-4,-b \log (F) (c+d x)^n\right )}{d n} \end {gather*}
Antiderivative was successfully verified.
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Rule 2250
Rubi steps
\begin {align*} \int F^{a+b (c+d x)^n} (c+d x)^{-1-4 n} \, dx &=-\frac {b^4 F^a \Gamma \left (-4,-b (c+d x)^n \log (F)\right ) \log ^4(F)}{d n}\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 32, normalized size = 1.00 \begin {gather*} -\frac {b^4 F^a \Gamma \left (-4,-b (c+d x)^n \log (F)\right ) \log ^4(F)}{d n} \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. \(174\) vs.
\(2(34)=68\).
time = 0.10, size = 175, normalized size = 5.47
method | result | size |
risch | \(-\frac {F^{b \left (d x +c \right )^{n}} F^{a} \left (d x +c \right )^{-4 n}}{4 n d}-\frac {\ln \left (F \right ) b \,F^{b \left (d x +c \right )^{n}} F^{a} \left (d x +c \right )^{-3 n}}{12 n d}-\frac {\ln \left (F \right )^{2} b^{2} F^{b \left (d x +c \right )^{n}} F^{a} \left (d x +c \right )^{-2 n}}{24 n d}-\frac {\ln \left (F \right )^{3} b^{3} F^{b \left (d x +c \right )^{n}} F^{a} \left (d x +c \right )^{-n}}{24 n d}-\frac {\ln \left (F \right )^{4} b^{4} F^{a} \expIntegral \left (1, -b \left (d x +c \right )^{n} \ln \left (F \right )\right )}{24 n d}\) | \(175\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \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. 119 vs.
\(2 (36) = 72\).
time = 0.11, size = 119, normalized size = 3.72 \begin {gather*} \frac {{\left (d x + c\right )}^{4 \, n} F^{a} b^{4} {\rm Ei}\left ({\left (d x + c\right )}^{n} b \log \left (F\right )\right ) \log \left (F\right )^{4} - {\left ({\left (d x + c\right )}^{3 \, n} b^{3} \log \left (F\right )^{3} + {\left (d x + c\right )}^{2 \, n} b^{2} \log \left (F\right )^{2} + 2 \, {\left (d x + c\right )}^{n} b \log \left (F\right ) + 6\right )} e^{\left ({\left (d x + c\right )}^{n} b \log \left (F\right ) + a \log \left (F\right )\right )}}{24 \, {\left (d x + c\right )}^{4 \, n} d n} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] Timed out
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 [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [F]
time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int \frac {F^{a+b\,{\left (c+d\,x\right )}^n}}{{\left (c+d\,x\right )}^{4\,n+1}} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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