Optimal. Leaf size=22 \[ \frac{(b x)^{p+1} (c x)^m}{b (m+p+1)} \]
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Rubi [A] time = 0.0071705, antiderivative size = 22, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.182, Rules used = {20, 32} \[ \frac{(b x)^{p+1} (c x)^m}{b (m+p+1)} \]
Antiderivative was successfully verified.
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Rule 20
Rule 32
Rubi steps
\begin{align*} \int (b x)^p (c x)^m \, dx &=\left ((b x)^{-m} (c x)^m\right ) \int (b x)^{m+p} \, dx\\ &=\frac{(b x)^{1+p} (c x)^m}{b (1+m+p)}\\ \end{align*}
Mathematica [A] time = 0.0039337, size = 18, normalized size = 0.82 \[ \frac{x (b x)^p (c x)^m}{m+p+1} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 19, normalized size = 0.9 \begin{align*}{\frac{x \left ( bx \right ) ^{p} \left ( cx \right ) ^{m}}{1+m+p}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.06032, size = 32, normalized size = 1.45 \begin{align*} \frac{b^{p} c^{m} x e^{\left (m \log \left (x\right ) + p \log \left (x\right )\right )}}{m + p + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.38174, size = 69, normalized size = 3.14 \begin{align*} \frac{\left (b x\right )^{p} x e^{\left (m \log \left (b x\right ) + m \log \left (\frac{c}{b}\right )\right )}}{m + p + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-2)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: TypeError} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.18008, size = 35, normalized size = 1.59 \begin{align*} \frac{x e^{\left (p \log \left (b\right ) + m \log \left (c\right ) + m \log \left (x\right ) + p \log \left (x\right )\right )}}{m + p + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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