Optimal. Leaf size=18 \[ \frac{(d+e x)^{m+1}}{e (m+1)} \]
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Rubi [A] time = 0.0031172, antiderivative size = 18, normalized size of antiderivative = 1., 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} \[ \frac{(d+e x)^{m+1}}{e (m+1)} \]
Antiderivative was successfully verified.
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Rule 32
Rubi steps
\begin{align*} \int (d+e x)^m \, dx &=\frac{(d+e x)^{1+m}}{e (1+m)}\\ \end{align*}
Mathematica [A] time = 0.0092179, size = 17, normalized size = 0.94 \[ \frac{(d+e x)^{m+1}}{e m+e} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.043, size = 19, normalized size = 1.1 \begin{align*}{\frac{ \left ( ex+d \right ) ^{1+m}}{e \left ( 1+m \right ) }} \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 = 1.9878, size = 45, normalized size = 2.5 \begin{align*} \frac{{\left (e x + d\right )}{\left (e x + d\right )}^{m}}{e m + e} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.06186, size = 20, normalized size = 1.11 \begin{align*} \frac{\begin{cases} \frac{\left (d + e x\right )^{m + 1}}{m + 1} & \text{for}\: m \neq -1 \\\log{\left (d + e x \right )} & \text{otherwise} \end{cases}}{e} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.23295, size = 24, normalized size = 1.33 \begin{align*} \frac{{\left (x e + d\right )}^{m + 1} e^{\left (-1\right )}}{m + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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