Optimal. Leaf size=18 \[ \frac{(4 x+3)^{p+1}}{4 (p+1)} \]
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Rubi [A] time = 0.0018257, 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} \[ \frac{(4 x+3)^{p+1}}{4 (p+1)} \]
Antiderivative was successfully verified.
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Rule 32
Rubi steps
\begin{align*} \int (3+4 x)^p \, dx &=\frac{(3+4 x)^{1+p}}{4 (1+p)}\\ \end{align*}
Mathematica [A] time = 0.0072413, size = 17, normalized size = 0.94 \[ \frac{(4 x+3)^{p+1}}{4 p+4} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.044, size = 17, normalized size = 0.9 \begin{align*}{\frac{ \left ( 4\,x+3 \right ) ^{1+p}}{4\,p+4}} \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 = 1.95592, size = 47, normalized size = 2.61 \begin{align*} \frac{{\left (4 \, x + 3\right )}^{p}{\left (4 \, x + 3\right )}}{4 \,{\left (p + 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.062529, size = 20, normalized size = 1.11 \begin{align*} \frac{\begin{cases} \frac{\left (4 x + 3\right )^{p + 1}}{p + 1} & \text{for}\: p \neq -1 \\\log{\left (4 x + 3 \right )} & \text{otherwise} \end{cases}}{4} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.28638, size = 22, normalized size = 1.22 \begin{align*} \frac{{\left (4 \, x + 3\right )}^{p + 1}}{4 \,{\left (p + 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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