Optimal. Leaf size=25 \[ \text {Int}\left (\frac {\sin \left (a+b (c+d x)^{2/3}\right )}{(e+f x)^2},x\right ) \]
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Rubi [A] time = 0.01, 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 = {} \[ \int \frac {\sin \left (a+b (c+d x)^{2/3}\right )}{(e+f x)^2} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {\sin \left (a+b (c+d x)^{2/3}\right )}{(e+f x)^2} \, dx &=\int \frac {\sin \left (a+b (c+d x)^{2/3}\right )}{(e+f x)^2} \, dx\\ \end {align*}
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Mathematica [A] time = 21.10, size = 0, normalized size = 0.00 \[ \int \frac {\sin \left (a+b (c+d x)^{2/3}\right )}{(e+f x)^2} \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 0.63, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {\sin \left ({\left (d x + c\right )}^{\frac {2}{3}} b + a\right )}{f^{2} x^{2} + 2 \, e f x + e^{2}}, x\right ) \]
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 \[ \int \frac {\sin \left ({\left (d x + c\right )}^{\frac {2}{3}} b + a\right )}{{\left (f x + e\right )}^{2}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.07, size = 0, normalized size = 0.00 \[ \int \frac {\sin \left (a +b \left (d x +c \right )^{\frac {2}{3}}\right )}{\left (f x +e \right )^{2}}\, dx \]
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 \[ \int \frac {\sin \left ({\left (d x + c\right )}^{\frac {2}{3}} b + a\right )}{{\left (f x + e\right )}^{2}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [A] time = 0.00, size = -1, normalized size = -0.04 \[ \int \frac {\sin \left (a+b\,{\left (c+d\,x\right )}^{2/3}\right )}{{\left (e+f\,x\right )}^2} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\sin {\left (a + b \left (c + d x\right )^{\frac {2}{3}} \right )}}{\left (e + f x\right )^{2}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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