Optimal. Leaf size=19 \[ \frac{\log \left (a+b x^{m+1}\right )}{b (m+1)} \]
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Rubi [A] time = 0.0242368, antiderivative size = 19, 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 \[ \frac{\log \left (a+b x^{m+1}\right )}{b (m+1)} \]
Antiderivative was successfully verified.
[In] Int[x^m/(a + b*x^(1 + m)),x]
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Rubi in Sympy [A] time = 2.79787, size = 14, normalized size = 0.74 \[ \frac{\log{\left (a + b x^{m + 1} \right )}}{b \left (m + 1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**m/(a+b*x**(1+m)),x)
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Mathematica [A] time = 0.0101044, size = 19, normalized size = 1. \[ \frac{\log \left (a+b x^{m+1}\right )}{b (m+1)} \]
Antiderivative was successfully verified.
[In] Integrate[x^m/(a + b*x^(1 + m)),x]
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Maple [A] time = 0.022, size = 21, normalized size = 1.1 \[{\frac{\ln \left ( a+bx{{\rm e}^{m\ln \left ( x \right ) }} \right ) }{b \left ( 1+m \right ) }} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^m/(a+b*x^(1+m)),x)
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Maxima [A] time = 1.40971, size = 26, normalized size = 1.37 \[ \frac{\log \left (b x^{m + 1} + a\right )}{b{\left (m + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^m/(b*x^(m + 1) + a),x, algorithm="maxima")
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Fricas [A] time = 0.229625, size = 24, normalized size = 1.26 \[ \frac{\log \left (b x^{m + 1} + a\right )}{b m + b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^m/(b*x^(m + 1) + a),x, algorithm="fricas")
[Out]
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Sympy [A] time = 2.60728, size = 37, normalized size = 1.95 \[ \begin{cases} \frac{\log{\left (x \right )}}{a} & \text{for}\: b = 0 \wedge m = -1 \\\frac{x x^{m}}{a \left (m + 1\right )} & \text{for}\: b = 0 \\\frac{\log{\left (x \right )}}{a + b} & \text{for}\: m = -1 \\\frac{\log{\left (\frac{a}{b} + x x^{m} \right )}}{b m + b} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**m/(a+b*x**(1+m)),x)
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GIAC/XCAS [A] time = 0.21729, size = 26, normalized size = 1.37 \[ \frac{{\rm ln}\left ({\left | b x^{m + 1} + a \right |}\right )}{b m + b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^m/(b*x^(m + 1) + a),x, algorithm="giac")
[Out]