Optimal. Leaf size=65 \[ -\frac {1}{2 b d \left (a+b F^{c+d x}\right )^2 x \log (F)}-\frac {\text {Int}\left (\frac {1}{\left (a+b F^{c+d x}\right )^2 x^2},x\right )}{2 b d \log (F)} \]
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Rubi [A]
time = 0.08, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps
used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {}
\begin {gather*} \int \frac {F^{c+d x}}{\left (a+b F^{c+d x}\right )^3 x} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {F^{c+d x}}{\left (a+b F^{c+d x}\right )^3 x} \, dx &=-\frac {1}{2 b d \left (a+b F^{c+d x}\right )^2 x \log (F)}-\frac {\int \frac {1}{\left (a+b F^{c+d x}\right )^2 x^2} \, dx}{2 b d \log (F)}\\ \end {align*}
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Mathematica [A]
time = 0.73, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {F^{c+d x}}{\left (a+b F^{c+d x}\right )^3 x} \, dx \end {gather*}
Verification is not applicable to the result.
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Maple [A]
time = 0.01, size = 0, normalized size = 0.00 \[\int \frac {F^{d x +c}}{\left (a +b \,F^{d x +c}\right )^{3} x}\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
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 [A]
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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Sympy [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \frac {- F^{c + d x} b - a d x \log {\left (F \right )} - a}{4 F^{c + d x} a^{2} b^{2} d^{2} x^{2} \log {\left (F \right )}^{2} + 2 F^{2 c + 2 d x} a b^{3} d^{2} x^{2} \log {\left (F \right )}^{2} + 2 a^{3} b d^{2} x^{2} \log {\left (F \right )}^{2}} - \frac {\int \frac {d x \log {\left (F \right )}}{a x^{3} + b x^{3} e^{c \log {\left (F \right )}} e^{d x \log {\left (F \right )}}}\, dx + \int \frac {2}{a x^{3} + b x^{3} e^{c \log {\left (F \right )}} e^{d x \log {\left (F \right )}}}\, dx}{2 a b d^{2} \log {\left (F \right )}^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
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 [A]
time = 0.00, size = -1, normalized size = -0.02 \begin {gather*} \int \frac {F^{c+d\,x}}{x\,{\left (a+F^{c+d\,x}\,b\right )}^3} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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