Optimal. Leaf size=77 \[ \frac{F^a (d x)^{m+1} \left (c+d x^n\right )^{b \log (F)} \left (\frac{d x^n}{c}+1\right )^{-b \log (F)} \text{Hypergeometric2F1}\left (\frac{m+1}{n},-b \log (F),\frac{m+n+1}{n},-\frac{d x^n}{c}\right )}{d (m+1)} \]
[Out]
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Rubi [A] time = 0.10707, antiderivative size = 77, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 4, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.2 \[ \frac{F^a (d x)^{m+1} \left (c+d x^n\right )^{b \log (F)} \left (\frac{d x^n}{c}+1\right )^{-b \log (F)} \text{Hypergeometric2F1}\left (\frac{m+1}{n},-b \log (F),\frac{m+n+1}{n},-\frac{d x^n}{c}\right )}{d (m+1)} \]
Antiderivative was successfully verified.
[In] Int[F^(a + b*Log[c + d*x^n])*(d*x)^m,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int F^{a + b \log{\left (c + d x^{n} \right )}} \left (d x\right )^{m}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(F**(a+b*ln(c+d*x**n))*(d*x)**m,x)
[Out]
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Mathematica [A] time = 0.286473, size = 0, normalized size = 0. \[ \int F^{a+b \log \left (c+d x^n\right )} (d x)^m \, dx \]
Verification is Not applicable to the result.
[In] Integrate[F^(a + b*Log[c + d*x^n])*(d*x)^m,x]
[Out]
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Maple [F] time = 0.108, size = 0, normalized size = 0. \[ \int{F}^{a+b\ln \left ( c+d{x}^{n} \right ) } \left ( dx \right ) ^{m}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(F^(a+b*ln(c+d*x^n))*(d*x)^m,x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \left (d x\right )^{m} F^{b \log \left (d x^{n} + c\right ) + a}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((d*x)^m*F^(b*log(d*x^n + c) + a),x, algorithm="maxima")
[Out]
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Fricas [F] time = 0., size = 0, normalized size = 0. \[{\rm integral}\left (\left (d x\right )^{m} F^{b \log \left (d x^{n} + c\right ) + a}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((d*x)^m*F^(b*log(d*x^n + c) + a),x, algorithm="fricas")
[Out]
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(F**(a+b*ln(c+d*x**n))*(d*x)**m,x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \left (d x\right )^{m} F^{b \log \left (d x^{n} + c\right ) + a}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((d*x)^m*F^(b*log(d*x^n + c) + a),x, algorithm="giac")
[Out]