Optimal. Leaf size=36 \[ \frac {x \left (a x^m\right )^r \left (b x^n\right )^s \left (c x^p\right )^t}{m r+n s+p t+1} \]
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Rubi [A] time = 0.02, antiderivative size = 36, normalized size of antiderivative = 1.00, number of steps used = 4, number of rules used = 2, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {15, 30} \[ \frac {x \left (a x^m\right )^r \left (b x^n\right )^s \left (c x^p\right )^t}{m r+n s+p t+1} \]
Antiderivative was successfully verified.
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Rule 15
Rule 30
Rubi steps
\begin {align*} \int \left (a x^m\right )^r \left (b x^n\right )^s \left (c x^p\right )^t \, dx &=\left (x^{-m r} \left (a x^m\right )^r\right ) \int x^{m r} \left (b x^n\right )^s \left (c x^p\right )^t \, dx\\ &=\left (x^{-m r-n s} \left (a x^m\right )^r \left (b x^n\right )^s\right ) \int x^{m r+n s} \left (c x^p\right )^t \, dx\\ &=\left (x^{-m r-n s-p t} \left (a x^m\right )^r \left (b x^n\right )^s \left (c x^p\right )^t\right ) \int x^{m r+n s+p t} \, dx\\ &=\frac {x \left (a x^m\right )^r \left (b x^n\right )^s \left (c x^p\right )^t}{1+m r+n s+p t}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 36, normalized size = 1.00 \[ \frac {x \left (a x^m\right )^r \left (b x^n\right )^s \left (c x^p\right )^t}{m r+n s+p t+1} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.48, size = 44, normalized size = 1.22 \[ \frac {x e^{\left (m r \log \relax (x) + n s \log \relax (x) + p t \log \relax (x) + r \log \relax (a) + s \log \relax (b) + t \log \relax (c)\right )}}{m r + n s + p t + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.24, size = 44, normalized size = 1.22 \[ \frac {x e^{\left (m r \log \relax (x) + n s \log \relax (x) + p t \log \relax (x) + r \log \relax (a) + s \log \relax (b) + t \log \relax (c)\right )}}{m r + n s + p t + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 37, normalized size = 1.03 \[ \frac {x \left (a \,x^{m}\right )^{r} \left (b \,x^{n}\right )^{s} \left (c \,x^{p}\right )^{t}}{m r +n s +p t +1} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.27, size = 44, normalized size = 1.22 \[ \frac {a^{r} b^{s} c^{t} x e^{\left (r \log \left (x^{m}\right ) + s \log \left (x^{n}\right ) + t \log \left (x^{p}\right )\right )}}{m r + n s + p t + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.10, size = 36, normalized size = 1.00 \[ \frac {x\,{\left (a\,x^m\right )}^r\,{\left (b\,x^n\right )}^s\,{\left (c\,x^p\right )}^t}{m\,r+n\,s+p\,t+1} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
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