Optimal. Leaf size=18 \[ \frac {(a+b x)^{n+1}}{b (n+1)} \]
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Rubi [A] time = 0.00, antiderivative size = 18, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 7, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {32} \begin {gather*} \frac {(a+b x)^{n+1}}{b (n+1)} \end {gather*}
Antiderivative was successfully verified.
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Rule 32
Rubi steps
\begin {align*} \int (a+b x)^n \, dx &=\frac {(a+b x)^{1+n}}{b (1+n)}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 17, normalized size = 0.94 \begin {gather*} \frac {(a+b x)^{n+1}}{b n+b} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.01, size = 0, normalized size = 0.00 \begin {gather*} \int (a+b x)^n \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 1.23, size = 20, normalized size = 1.11 \begin {gather*} \frac {{\left (b x + a\right )} {\left (b x + a\right )}^{n}}{b n + b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.14, size = 18, normalized size = 1.00 \begin {gather*} \frac {{\left (b x + a\right )}^{n + 1}}{b {\left (n + 1\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 19, normalized size = 1.06 \begin {gather*} \frac {\left (b x +a \right )^{n +1}}{\left (n +1\right ) b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.30, size = 18, normalized size = 1.00 \begin {gather*} \frac {{\left (b x + a\right )}^{n + 1}}{b {\left (n + 1\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.20, size = 18, normalized size = 1.00 \begin {gather*} \frac {{\left (a+b\,x\right )}^{n+1}}{b\,\left (n+1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.07, size = 20, normalized size = 1.11 \begin {gather*} \frac {\begin {cases} \frac {\left (a + b x\right )^{n + 1}}{n + 1} & \text {for}\: n \neq -1 \\\log {\left (a + b x \right )} & \text {otherwise} \end {cases}}{b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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