Optimal. Leaf size=65 \[ \frac{1}{2} x^2 F^a \left (c+d x^n\right )^{b \log (F)} \left (\frac{d x^n}{c}+1\right )^{-b \log (F)} \text{Hypergeometric2F1}\left (\frac{2}{n},-b \log (F),\frac{n+2}{n},-\frac{d x^n}{c}\right ) \]
[Out]
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Rubi [A] time = 0.0673641, antiderivative size = 65, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 4, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.25 \[ \frac{1}{2} x^2 F^a \left (c+d x^n\right )^{b \log (F)} \left (\frac{d x^n}{c}+1\right )^{-b \log (F)} \text{Hypergeometric2F1}\left (\frac{2}{n},-b \log (F),\frac{n+2}{n},-\frac{d x^n}{c}\right ) \]
Antiderivative was successfully verified.
[In] Int[F^(a + b*Log[c + d*x^n])*x,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int F^{a + b \log{\left (c + d x^{n} \right )}} x\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(F**(a+b*ln(c+d*x**n))*x,x)
[Out]
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Mathematica [A] time = 0.239701, size = 0, normalized size = 0. \[ \int F^{a+b \log \left (c+d x^n\right )} x \, dx \]
Verification is Not applicable to the result.
[In] Integrate[F^(a + b*Log[c + d*x^n])*x,x]
[Out]
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Maple [F] time = 0.058, size = 0, normalized size = 0. \[ \int{F}^{a+b\ln \left ( c+d{x}^{n} \right ) }x\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(F^(a+b*ln(c+d*x^n))*x,x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int F^{b \log \left (d x^{n} + c\right ) + a} x\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(F^(b*log(d*x^n + c) + a)*x,x, algorithm="maxima")
[Out]
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Fricas [F] time = 0., size = 0, normalized size = 0. \[{\rm integral}\left (F^{b \log \left (d x^{n} + c\right ) + a} x, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(F^(b*log(d*x^n + c) + a)*x,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))*x,x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int F^{b \log \left (d x^{n} + c\right ) + a} x\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(F^(b*log(d*x^n + c) + a)*x,x, algorithm="giac")
[Out]