Optimal. Leaf size=23 \[ \frac{\left (a+b x^n\right )^{p+1}}{b n (p+1)} \]
[Out]
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Rubi [A] time = 0.0284346, antiderivative size = 23, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067 \[ \frac{\left (a+b x^n\right )^{p+1}}{b n (p+1)} \]
Antiderivative was successfully verified.
[In] Int[x^(-1 + n)*(a + b*x^n)^p,x]
[Out]
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Rubi in Sympy [A] time = 3.00776, size = 15, normalized size = 0.65 \[ \frac{\left (a + b x^{n}\right )^{p + 1}}{b n \left (p + 1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**(-1+n)*(a+b*x**n)**p,x)
[Out]
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Mathematica [A] time = 0.0335867, size = 22, normalized size = 0.96 \[ \frac{\left (a+b x^n\right )^{p+1}}{b n p+b n} \]
Antiderivative was successfully verified.
[In] Integrate[x^(-1 + n)*(a + b*x^n)^p,x]
[Out]
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Maple [A] time = 0.069, size = 29, normalized size = 1.3 \[{\frac{ \left ( a+b{x}^{n} \right ) \left ( a+b{x}^{n} \right ) ^{p}}{b \left ( 1+p \right ) n}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^(-1+n)*(a+b*x^n)^p,x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: ValueError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^n + a)^p*x^(n - 1),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.237404, size = 36, normalized size = 1.57 \[ \frac{{\left (b x^{n} + a\right )}{\left (b x^{n} + a\right )}^{p}}{b n p + b n} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^n + a)^p*x^(n - 1),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(x**(-1+n)*(a+b*x**n)**p,x)
[Out]
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GIAC/XCAS [A] time = 0.215972, size = 31, normalized size = 1.35 \[ \frac{{\left (b x^{n} + a\right )}^{p + 1}}{b n{\left (p + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^n + a)^p*x^(n - 1),x, algorithm="giac")
[Out]