Optimal. Leaf size=18 \[ \frac {(a+b x)^{1+n}}{b (1+n)} \]
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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 = 0.02, size = 17, normalized size = 0.94 \begin {gather*} \frac {(a+b x)^{1+n}}{b+b n} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.11, size = 19, normalized size = 1.06
method | result | size |
gosper | \(\frac {\left (b x +a \right )^{1+n}}{b \left (1+n \right )}\) | \(19\) |
default | \(\frac {\left (b x +a \right )^{1+n}}{b \left (1+n \right )}\) | \(19\) |
risch | \(\frac {\left (b x +a \right ) \left (b x +a \right )^{n}}{b \left (1+n \right )}\) | \(22\) |
norman | \(\frac {x \,{\mathrm e}^{n \ln \left (b x +a \right )}}{1+n}+\frac {a \,{\mathrm e}^{n \ln \left (b x +a \right )}}{b \left (1+n \right )}\) | \(37\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, 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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Fricas [A]
time = 1.25, 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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Sympy [A]
time = 0.01, 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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Giac [A]
time = 1.69, 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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