Optimal. Leaf size=16 \[ a x+\frac {b x^{n+1}}{n+1} \]
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Rubi [A] time = 0.00, antiderivative size = 16, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 0, integrand size = 7, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, 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*}
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Mathematica [A] time = 0.01, size = 16, normalized size = 1.00 \[ a x+\frac {b x^{n+1}}{n+1} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.77, size = 20, normalized size = 1.25 \[ \frac {b x x^{n} + {\left (a n + a\right )} x}{n + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 16, normalized size = 1.00 \[ a x + \frac {b x^{n + 1}}{n + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 17, normalized size = 1.06 \[ a x +\frac {b \,x^{n +1}}{n +1} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.52, size = 16, normalized size = 1.00 \[ a x + \frac {b x^{n + 1}}{n + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.28, size = 15, normalized size = 0.94 \[ a\,x+\frac {b\,x\,x^n}{n+1} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.06, size = 17, normalized size = 1.06 \[ a x + b \left (\begin {cases} \frac {x^{n + 1}}{n + 1} & \text {for}\: n \neq -1 \\\log {\relax (x )} & \text {otherwise} \end {cases}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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