Optimal. Leaf size=37 \[ \text {Int}\left (\frac {\left (a+b \log \left (c (d+e x)^n\right )\right )^3 \left (f+g \log \left (h (i+j x)^m\right )\right )}{x},x\right ) \]
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Rubi [A] time = 0.04, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \frac {\left (a+b \log \left (c (d+e x)^n\right )\right )^3 \left (f+g \log \left (h (i+j x)^m\right )\right )}{x} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {\left (a+b \log \left (c (d+e x)^n\right )\right )^3 \left (f+g \log \left (h (399+j x)^m\right )\right )}{x} \, dx &=\int \frac {\left (a+b \log \left (c (d+e x)^n\right )\right )^3 \left (f+g \log \left (h (399+j x)^m\right )\right )}{x} \, dx\\ \end {align*}
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Mathematica [A] time = 1.38, size = 0, normalized size = 0.00 \[ \int \frac {\left (a+b \log \left (c (d+e x)^n\right )\right )^3 \left (f+g \log \left (h (i+j x)^m\right )\right )}{x} \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 0.44, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {b^{3} f \log \left ({\left (e x + d\right )}^{n} c\right )^{3} + 3 \, a b^{2} f \log \left ({\left (e x + d\right )}^{n} c\right )^{2} + 3 \, a^{2} b f \log \left ({\left (e x + d\right )}^{n} c\right ) + a^{3} f + {\left (b^{3} g \log \left ({\left (e x + d\right )}^{n} c\right )^{3} + 3 \, a b^{2} g \log \left ({\left (e x + d\right )}^{n} c\right )^{2} + 3 \, a^{2} b g \log \left ({\left (e x + d\right )}^{n} c\right ) + a^{3} g\right )} \log \left ({\left (j x + i\right )}^{m} h\right )}{x}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {{\left (b \log \left ({\left (e x + d\right )}^{n} c\right ) + a\right )}^{3} {\left (g \log \left ({\left (j x + i\right )}^{m} h\right ) + f\right )}}{x}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 2.28, size = 0, normalized size = 0.00 \[ \int \frac {\left (b \ln \left (c \left (e x +d \right )^{n}\right )+a \right )^{3} \left (g \ln \left (h \left (j x +i \right )^{m}\right )+f \right )}{x}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.00, size = 0, normalized size = 0.00 \[ a^{3} f \log \relax (x) + \int \frac {{\left (g \log \relax (h) + f\right )} b^{3} \log \left ({\left (e x + d\right )}^{n}\right )^{3} + {\left (g \log \relax (h) + f\right )} b^{3} \log \relax (c)^{3} + 3 \, {\left (g \log \relax (h) + f\right )} a b^{2} \log \relax (c)^{2} + 3 \, {\left (g \log \relax (h) + f\right )} a^{2} b \log \relax (c) + a^{3} g \log \relax (h) + 3 \, {\left ({\left (g \log \relax (h) + f\right )} b^{3} \log \relax (c) + {\left (g \log \relax (h) + f\right )} a b^{2}\right )} \log \left ({\left (e x + d\right )}^{n}\right )^{2} + 3 \, {\left ({\left (g \log \relax (h) + f\right )} b^{3} \log \relax (c)^{2} + 2 \, {\left (g \log \relax (h) + f\right )} a b^{2} \log \relax (c) + {\left (g \log \relax (h) + f\right )} a^{2} b\right )} \log \left ({\left (e x + d\right )}^{n}\right ) + {\left (b^{3} g \log \left ({\left (e x + d\right )}^{n}\right )^{3} + b^{3} g \log \relax (c)^{3} + 3 \, a b^{2} g \log \relax (c)^{2} + 3 \, a^{2} b g \log \relax (c) + a^{3} g + 3 \, {\left (b^{3} g \log \relax (c) + a b^{2} g\right )} \log \left ({\left (e x + d\right )}^{n}\right )^{2} + 3 \, {\left (b^{3} g \log \relax (c)^{2} + 2 \, a b^{2} g \log \relax (c) + a^{2} b g\right )} \log \left ({\left (e x + d\right )}^{n}\right )\right )} \log \left ({\left (j x + i\right )}^{m}\right )}{x}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [A] time = 0.00, size = -1, normalized size = -0.03 \[ \int \frac {{\left (a+b\,\ln \left (c\,{\left (d+e\,x\right )}^n\right )\right )}^3\,\left (f+g\,\ln \left (h\,{\left (i+j\,x\right )}^m\right )\right )}{x} \,d x \]
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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