Optimal. Leaf size=16 \[ a x+\frac{b x^{n+1}}{n+1} \]
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Rubi [A] time = 0.0035536, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 0, integrand size = 7, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., Rules used = {} \[ a x+\frac{b x^{n+1}}{n+1} \]
Antiderivative was successfully verified.
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Rubi steps
\begin{align*} \int \left (a+b x^n\right ) \, dx &=a x+\frac{b x^{1+n}}{1+n}\\ \end{align*}
Mathematica [A] time = 0.0059723, size = 16, normalized size = 1. \[ a x+\frac{b x^{n+1}}{n+1} \]
Antiderivative was successfully verified.
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Maple [A] time = 0., size = 17, normalized size = 1.1 \begin{align*} ax+{\frac{b{x}^{1+n}}{1+n}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F(-2)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: ValueError} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.61279, size = 45, normalized size = 2.81 \begin{align*} \frac{b x x^{n} +{\left (a n + a\right )} x}{n + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.054022, size = 17, normalized size = 1.06 \begin{align*} a x + b \left (\begin{cases} \frac{x^{n + 1}}{n + 1} & \text{for}\: n \neq -1 \\\log{\left (x \right )} & \text{otherwise} \end{cases}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.82322, size = 22, normalized size = 1.38 \begin{align*} a x + \frac{b x^{n + 1}}{n + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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