Optimal. Leaf size=537 \[ \frac {120960 \sin \left (a+b \sqrt [3]{c+d x}\right )}{b^9 d^3}-\frac {120960 \sqrt [3]{c+d x} \cos \left (a+b \sqrt [3]{c+d x}\right )}{b^8 d^3}-\frac {60480 (c+d x)^{2/3} \sin \left (a+b \sqrt [3]{c+d x}\right )}{b^7 d^3}+\frac {20160 (c+d x) \cos \left (a+b \sqrt [3]{c+d x}\right )}{b^6 d^3}-\frac {720 c \cos \left (a+b \sqrt [3]{c+d x}\right )}{b^6 d^3}+\frac {5040 (c+d x)^{4/3} \sin \left (a+b \sqrt [3]{c+d x}\right )}{b^5 d^3}-\frac {720 c \sqrt [3]{c+d x} \sin \left (a+b \sqrt [3]{c+d x}\right )}{b^5 d^3}-\frac {1008 (c+d x)^{5/3} \cos \left (a+b \sqrt [3]{c+d x}\right )}{b^4 d^3}+\frac {360 c (c+d x)^{2/3} \cos \left (a+b \sqrt [3]{c+d x}\right )}{b^4 d^3}-\frac {6 c^2 \sin \left (a+b \sqrt [3]{c+d x}\right )}{b^3 d^3}-\frac {168 (c+d x)^2 \sin \left (a+b \sqrt [3]{c+d x}\right )}{b^3 d^3}+\frac {120 c (c+d x) \sin \left (a+b \sqrt [3]{c+d x}\right )}{b^3 d^3}+\frac {6 c^2 \sqrt [3]{c+d x} \cos \left (a+b \sqrt [3]{c+d x}\right )}{b^2 d^3}+\frac {24 (c+d x)^{7/3} \cos \left (a+b \sqrt [3]{c+d x}\right )}{b^2 d^3}-\frac {30 c (c+d x)^{4/3} \cos \left (a+b \sqrt [3]{c+d x}\right )}{b^2 d^3}+\frac {3 c^2 (c+d x)^{2/3} \sin \left (a+b \sqrt [3]{c+d x}\right )}{b d^3}+\frac {3 (c+d x)^{8/3} \sin \left (a+b \sqrt [3]{c+d x}\right )}{b d^3}-\frac {6 c (c+d x)^{5/3} \sin \left (a+b \sqrt [3]{c+d x}\right )}{b d^3} \]
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Rubi [A] time = 0.51, antiderivative size = 537, normalized size of antiderivative = 1.00, number of steps used = 20, number of rules used = 4, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.222, Rules used = {3432, 3296, 2637, 2638} \[ -\frac {6 c^2 \sin \left (a+b \sqrt [3]{c+d x}\right )}{b^3 d^3}+\frac {6 c^2 \sqrt [3]{c+d x} \cos \left (a+b \sqrt [3]{c+d x}\right )}{b^2 d^3}-\frac {168 (c+d x)^2 \sin \left (a+b \sqrt [3]{c+d x}\right )}{b^3 d^3}+\frac {5040 (c+d x)^{4/3} \sin \left (a+b \sqrt [3]{c+d x}\right )}{b^5 d^3}+\frac {120 c (c+d x) \sin \left (a+b \sqrt [3]{c+d x}\right )}{b^3 d^3}-\frac {60480 (c+d x)^{2/3} \sin \left (a+b \sqrt [3]{c+d x}\right )}{b^7 d^3}-\frac {720 c \sqrt [3]{c+d x} \sin \left (a+b \sqrt [3]{c+d x}\right )}{b^5 d^3}+\frac {120960 \sin \left (a+b \sqrt [3]{c+d x}\right )}{b^9 d^3}+\frac {24 (c+d x)^{7/3} \cos \left (a+b \sqrt [3]{c+d x}\right )}{b^2 d^3}-\frac {1008 (c+d x)^{5/3} \cos \left (a+b \sqrt [3]{c+d x}\right )}{b^4 d^3}-\frac {30 c (c+d x)^{4/3} \cos \left (a+b \sqrt [3]{c+d x}\right )}{b^2 d^3}+\frac {20160 (c+d x) \cos \left (a+b \sqrt [3]{c+d x}\right )}{b^6 d^3}+\frac {360 c (c+d x)^{2/3} \cos \left (a+b \sqrt [3]{c+d x}\right )}{b^4 d^3}-\frac {120960 \sqrt [3]{c+d x} \cos \left (a+b \sqrt [3]{c+d x}\right )}{b^8 d^3}-\frac {720 c \cos \left (a+b \sqrt [3]{c+d x}\right )}{b^6 d^3}+\frac {3 c^2 (c+d x)^{2/3} \sin \left (a+b \sqrt [3]{c+d x}\right )}{b d^3}+\frac {3 (c+d x)^{8/3} \sin \left (a+b \sqrt [3]{c+d x}\right )}{b d^3}-\frac {6 c (c+d x)^{5/3} \sin \left (a+b \sqrt [3]{c+d x}\right )}{b d^3} \]
Antiderivative was successfully verified.
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Rule 2637
Rule 2638
Rule 3296
Rule 3432
Rubi steps
\begin {align*} \int x^2 \cos \left (a+b \sqrt [3]{c+d x}\right ) \, dx &=\frac {3 \operatorname {Subst}\left (\int \left (\frac {c^2 x^2 \cos (a+b x)}{d^2}-\frac {2 c x^5 \cos (a+b x)}{d^2}+\frac {x^8 \cos (a+b x)}{d^2}\right ) \, dx,x,\sqrt [3]{c+d x}\right )}{d}\\ &=\frac {3 \operatorname {Subst}\left (\int x^8 \cos (a+b x) \, dx,x,\sqrt [3]{c+d x}\right )}{d^3}-\frac {(6 c) \operatorname {Subst}\left (\int x^5 \cos (a+b x) \, dx,x,\sqrt [3]{c+d x}\right )}{d^3}+\frac {\left (3 c^2\right ) \operatorname {Subst}\left (\int x^2 \cos (a+b x) \, dx,x,\sqrt [3]{c+d x}\right )}{d^3}\\ &=\frac {3 c^2 (c+d x)^{2/3} \sin \left (a+b \sqrt [3]{c+d x}\right )}{b d^3}-\frac {6 c (c+d x)^{5/3} \sin \left (a+b \sqrt [3]{c+d x}\right )}{b d^3}+\frac {3 (c+d x)^{8/3} \sin \left (a+b \sqrt [3]{c+d x}\right )}{b d^3}-\frac {24 \operatorname {Subst}\left (\int x^7 \sin (a+b x) \, dx,x,\sqrt [3]{c+d x}\right )}{b d^3}+\frac {(30 c) \operatorname {Subst}\left (\int x^4 \sin (a+b x) \, dx,x,\sqrt [3]{c+d x}\right )}{b d^3}-\frac {\left (6 c^2\right ) \operatorname {Subst}\left (\int x \sin (a+b x) \, dx,x,\sqrt [3]{c+d x}\right )}{b d^3}\\ &=\frac {6 c^2 \sqrt [3]{c+d x} \cos \left (a+b \sqrt [3]{c+d x}\right )}{b^2 d^3}-\frac {30 c (c+d x)^{4/3} \cos \left (a+b \sqrt [3]{c+d x}\right )}{b^2 d^3}+\frac {24 (c+d x)^{7/3} \cos \left (a+b \sqrt [3]{c+d x}\right )}{b^2 d^3}+\frac {3 c^2 (c+d x)^{2/3} \sin \left (a+b \sqrt [3]{c+d x}\right )}{b d^3}-\frac {6 c (c+d x)^{5/3} \sin \left (a+b \sqrt [3]{c+d x}\right )}{b d^3}+\frac {3 (c+d x)^{8/3} \sin \left (a+b \sqrt [3]{c+d x}\right )}{b d^3}-\frac {168 \operatorname {Subst}\left (\int x^6 \cos (a+b x) \, dx,x,\sqrt [3]{c+d x}\right )}{b^2 d^3}+\frac {(120 c) \operatorname {Subst}\left (\int x^3 \cos (a+b x) \, dx,x,\sqrt [3]{c+d x}\right )}{b^2 d^3}-\frac {\left (6 c^2\right ) \operatorname {Subst}\left (\int \cos (a+b x) \, dx,x,\sqrt [3]{c+d x}\right )}{b^2 d^3}\\ &=\frac {6 c^2 \sqrt [3]{c+d x} \cos \left (a+b \sqrt [3]{c+d x}\right )}{b^2 d^3}-\frac {30 c (c+d x)^{4/3} \cos \left (a+b \sqrt [3]{c+d x}\right )}{b^2 d^3}+\frac {24 (c+d x)^{7/3} \cos \left (a+b \sqrt [3]{c+d x}\right )}{b^2 d^3}-\frac {6 c^2 \sin \left (a+b \sqrt [3]{c+d x}\right )}{b^3 d^3}+\frac {3 c^2 (c+d x)^{2/3} \sin \left (a+b \sqrt [3]{c+d x}\right )}{b d^3}+\frac {120 c (c+d x) \sin \left (a+b \sqrt [3]{c+d x}\right )}{b^3 d^3}-\frac {6 c (c+d x)^{5/3} \sin \left (a+b \sqrt [3]{c+d x}\right )}{b d^3}-\frac {168 (c+d x)^2 \sin \left (a+b \sqrt [3]{c+d x}\right )}{b^3 d^3}+\frac {3 (c+d x)^{8/3} \sin \left (a+b \sqrt [3]{c+d x}\right )}{b d^3}+\frac {1008 \operatorname {Subst}\left (\int x^5 \sin (a+b x) \, dx,x,\sqrt [3]{c+d x}\right )}{b^3 d^3}-\frac {(360 c) \operatorname {Subst}\left (\int x^2 \sin (a+b x) \, dx,x,\sqrt [3]{c+d x}\right )}{b^3 d^3}\\ &=\frac {6 c^2 \sqrt [3]{c+d x} \cos \left (a+b \sqrt [3]{c+d x}\right )}{b^2 d^3}+\frac {360 c (c+d x)^{2/3} \cos \left (a+b \sqrt [3]{c+d x}\right )}{b^4 d^3}-\frac {30 c (c+d x)^{4/3} \cos \left (a+b \sqrt [3]{c+d x}\right )}{b^2 d^3}-\frac {1008 (c+d x)^{5/3} \cos \left (a+b \sqrt [3]{c+d x}\right )}{b^4 d^3}+\frac {24 (c+d x)^{7/3} \cos \left (a+b \sqrt [3]{c+d x}\right )}{b^2 d^3}-\frac {6 c^2 \sin \left (a+b \sqrt [3]{c+d x}\right )}{b^3 d^3}+\frac {3 c^2 (c+d x)^{2/3} \sin \left (a+b \sqrt [3]{c+d x}\right )}{b d^3}+\frac {120 c (c+d x) \sin \left (a+b \sqrt [3]{c+d x}\right )}{b^3 d^3}-\frac {6 c (c+d x)^{5/3} \sin \left (a+b \sqrt [3]{c+d x}\right )}{b d^3}-\frac {168 (c+d x)^2 \sin \left (a+b \sqrt [3]{c+d x}\right )}{b^3 d^3}+\frac {3 (c+d x)^{8/3} \sin \left (a+b \sqrt [3]{c+d x}\right )}{b d^3}+\frac {5040 \operatorname {Subst}\left (\int x^4 \cos (a+b x) \, dx,x,\sqrt [3]{c+d x}\right )}{b^4 d^3}-\frac {(720 c) \operatorname {Subst}\left (\int x \cos (a+b x) \, dx,x,\sqrt [3]{c+d x}\right )}{b^4 d^3}\\ &=\frac {6 c^2 \sqrt [3]{c+d x} \cos \left (a+b \sqrt [3]{c+d x}\right )}{b^2 d^3}+\frac {360 c (c+d x)^{2/3} \cos \left (a+b \sqrt [3]{c+d x}\right )}{b^4 d^3}-\frac {30 c (c+d x)^{4/3} \cos \left (a+b \sqrt [3]{c+d x}\right )}{b^2 d^3}-\frac {1008 (c+d x)^{5/3} \cos \left (a+b \sqrt [3]{c+d x}\right )}{b^4 d^3}+\frac {24 (c+d x)^{7/3} \cos \left (a+b \sqrt [3]{c+d x}\right )}{b^2 d^3}-\frac {6 c^2 \sin \left (a+b \sqrt [3]{c+d x}\right )}{b^3 d^3}-\frac {720 c \sqrt [3]{c+d x} \sin \left (a+b \sqrt [3]{c+d x}\right )}{b^5 d^3}+\frac {3 c^2 (c+d x)^{2/3} \sin \left (a+b \sqrt [3]{c+d x}\right )}{b d^3}+\frac {120 c (c+d x) \sin \left (a+b \sqrt [3]{c+d x}\right )}{b^3 d^3}+\frac {5040 (c+d x)^{4/3} \sin \left (a+b \sqrt [3]{c+d x}\right )}{b^5 d^3}-\frac {6 c (c+d x)^{5/3} \sin \left (a+b \sqrt [3]{c+d x}\right )}{b d^3}-\frac {168 (c+d x)^2 \sin \left (a+b \sqrt [3]{c+d x}\right )}{b^3 d^3}+\frac {3 (c+d x)^{8/3} \sin \left (a+b \sqrt [3]{c+d x}\right )}{b d^3}-\frac {20160 \operatorname {Subst}\left (\int x^3 \sin (a+b x) \, dx,x,\sqrt [3]{c+d x}\right )}{b^5 d^3}+\frac {(720 c) \operatorname {Subst}\left (\int \sin (a+b x) \, dx,x,\sqrt [3]{c+d x}\right )}{b^5 d^3}\\ &=-\frac {720 c \cos \left (a+b \sqrt [3]{c+d x}\right )}{b^6 d^3}+\frac {6 c^2 \sqrt [3]{c+d x} \cos \left (a+b \sqrt [3]{c+d x}\right )}{b^2 d^3}+\frac {360 c (c+d x)^{2/3} \cos \left (a+b \sqrt [3]{c+d x}\right )}{b^4 d^3}+\frac {20160 (c+d x) \cos \left (a+b \sqrt [3]{c+d x}\right )}{b^6 d^3}-\frac {30 c (c+d x)^{4/3} \cos \left (a+b \sqrt [3]{c+d x}\right )}{b^2 d^3}-\frac {1008 (c+d x)^{5/3} \cos \left (a+b \sqrt [3]{c+d x}\right )}{b^4 d^3}+\frac {24 (c+d x)^{7/3} \cos \left (a+b \sqrt [3]{c+d x}\right )}{b^2 d^3}-\frac {6 c^2 \sin \left (a+b \sqrt [3]{c+d x}\right )}{b^3 d^3}-\frac {720 c \sqrt [3]{c+d x} \sin \left (a+b \sqrt [3]{c+d x}\right )}{b^5 d^3}+\frac {3 c^2 (c+d x)^{2/3} \sin \left (a+b \sqrt [3]{c+d x}\right )}{b d^3}+\frac {120 c (c+d x) \sin \left (a+b \sqrt [3]{c+d x}\right )}{b^3 d^3}+\frac {5040 (c+d x)^{4/3} \sin \left (a+b \sqrt [3]{c+d x}\right )}{b^5 d^3}-\frac {6 c (c+d x)^{5/3} \sin \left (a+b \sqrt [3]{c+d x}\right )}{b d^3}-\frac {168 (c+d x)^2 \sin \left (a+b \sqrt [3]{c+d x}\right )}{b^3 d^3}+\frac {3 (c+d x)^{8/3} \sin \left (a+b \sqrt [3]{c+d x}\right )}{b d^3}-\frac {60480 \operatorname {Subst}\left (\int x^2 \cos (a+b x) \, dx,x,\sqrt [3]{c+d x}\right )}{b^6 d^3}\\ &=-\frac {720 c \cos \left (a+b \sqrt [3]{c+d x}\right )}{b^6 d^3}+\frac {6 c^2 \sqrt [3]{c+d x} \cos \left (a+b \sqrt [3]{c+d x}\right )}{b^2 d^3}+\frac {360 c (c+d x)^{2/3} \cos \left (a+b \sqrt [3]{c+d x}\right )}{b^4 d^3}+\frac {20160 (c+d x) \cos \left (a+b \sqrt [3]{c+d x}\right )}{b^6 d^3}-\frac {30 c (c+d x)^{4/3} \cos \left (a+b \sqrt [3]{c+d x}\right )}{b^2 d^3}-\frac {1008 (c+d x)^{5/3} \cos \left (a+b \sqrt [3]{c+d x}\right )}{b^4 d^3}+\frac {24 (c+d x)^{7/3} \cos \left (a+b \sqrt [3]{c+d x}\right )}{b^2 d^3}-\frac {6 c^2 \sin \left (a+b \sqrt [3]{c+d x}\right )}{b^3 d^3}-\frac {720 c \sqrt [3]{c+d x} \sin \left (a+b \sqrt [3]{c+d x}\right )}{b^5 d^3}-\frac {60480 (c+d x)^{2/3} \sin \left (a+b \sqrt [3]{c+d x}\right )}{b^7 d^3}+\frac {3 c^2 (c+d x)^{2/3} \sin \left (a+b \sqrt [3]{c+d x}\right )}{b d^3}+\frac {120 c (c+d x) \sin \left (a+b \sqrt [3]{c+d x}\right )}{b^3 d^3}+\frac {5040 (c+d x)^{4/3} \sin \left (a+b \sqrt [3]{c+d x}\right )}{b^5 d^3}-\frac {6 c (c+d x)^{5/3} \sin \left (a+b \sqrt [3]{c+d x}\right )}{b d^3}-\frac {168 (c+d x)^2 \sin \left (a+b \sqrt [3]{c+d x}\right )}{b^3 d^3}+\frac {3 (c+d x)^{8/3} \sin \left (a+b \sqrt [3]{c+d x}\right )}{b d^3}+\frac {120960 \operatorname {Subst}\left (\int x \sin (a+b x) \, dx,x,\sqrt [3]{c+d x}\right )}{b^7 d^3}\\ &=-\frac {720 c \cos \left (a+b \sqrt [3]{c+d x}\right )}{b^6 d^3}-\frac {120960 \sqrt [3]{c+d x} \cos \left (a+b \sqrt [3]{c+d x}\right )}{b^8 d^3}+\frac {6 c^2 \sqrt [3]{c+d x} \cos \left (a+b \sqrt [3]{c+d x}\right )}{b^2 d^3}+\frac {360 c (c+d x)^{2/3} \cos \left (a+b \sqrt [3]{c+d x}\right )}{b^4 d^3}+\frac {20160 (c+d x) \cos \left (a+b \sqrt [3]{c+d x}\right )}{b^6 d^3}-\frac {30 c (c+d x)^{4/3} \cos \left (a+b \sqrt [3]{c+d x}\right )}{b^2 d^3}-\frac {1008 (c+d x)^{5/3} \cos \left (a+b \sqrt [3]{c+d x}\right )}{b^4 d^3}+\frac {24 (c+d x)^{7/3} \cos \left (a+b \sqrt [3]{c+d x}\right )}{b^2 d^3}-\frac {6 c^2 \sin \left (a+b \sqrt [3]{c+d x}\right )}{b^3 d^3}-\frac {720 c \sqrt [3]{c+d x} \sin \left (a+b \sqrt [3]{c+d x}\right )}{b^5 d^3}-\frac {60480 (c+d x)^{2/3} \sin \left (a+b \sqrt [3]{c+d x}\right )}{b^7 d^3}+\frac {3 c^2 (c+d x)^{2/3} \sin \left (a+b \sqrt [3]{c+d x}\right )}{b d^3}+\frac {120 c (c+d x) \sin \left (a+b \sqrt [3]{c+d x}\right )}{b^3 d^3}+\frac {5040 (c+d x)^{4/3} \sin \left (a+b \sqrt [3]{c+d x}\right )}{b^5 d^3}-\frac {6 c (c+d x)^{5/3} \sin \left (a+b \sqrt [3]{c+d x}\right )}{b d^3}-\frac {168 (c+d x)^2 \sin \left (a+b \sqrt [3]{c+d x}\right )}{b^3 d^3}+\frac {3 (c+d x)^{8/3} \sin \left (a+b \sqrt [3]{c+d x}\right )}{b d^3}+\frac {120960 \operatorname {Subst}\left (\int \cos (a+b x) \, dx,x,\sqrt [3]{c+d x}\right )}{b^8 d^3}\\ &=-\frac {720 c \cos \left (a+b \sqrt [3]{c+d x}\right )}{b^6 d^3}-\frac {120960 \sqrt [3]{c+d x} \cos \left (a+b \sqrt [3]{c+d x}\right )}{b^8 d^3}+\frac {6 c^2 \sqrt [3]{c+d x} \cos \left (a+b \sqrt [3]{c+d x}\right )}{b^2 d^3}+\frac {360 c (c+d x)^{2/3} \cos \left (a+b \sqrt [3]{c+d x}\right )}{b^4 d^3}+\frac {20160 (c+d x) \cos \left (a+b \sqrt [3]{c+d x}\right )}{b^6 d^3}-\frac {30 c (c+d x)^{4/3} \cos \left (a+b \sqrt [3]{c+d x}\right )}{b^2 d^3}-\frac {1008 (c+d x)^{5/3} \cos \left (a+b \sqrt [3]{c+d x}\right )}{b^4 d^3}+\frac {24 (c+d x)^{7/3} \cos \left (a+b \sqrt [3]{c+d x}\right )}{b^2 d^3}+\frac {120960 \sin \left (a+b \sqrt [3]{c+d x}\right )}{b^9 d^3}-\frac {6 c^2 \sin \left (a+b \sqrt [3]{c+d x}\right )}{b^3 d^3}-\frac {720 c \sqrt [3]{c+d x} \sin \left (a+b \sqrt [3]{c+d x}\right )}{b^5 d^3}-\frac {60480 (c+d x)^{2/3} \sin \left (a+b \sqrt [3]{c+d x}\right )}{b^7 d^3}+\frac {3 c^2 (c+d x)^{2/3} \sin \left (a+b \sqrt [3]{c+d x}\right )}{b d^3}+\frac {120 c (c+d x) \sin \left (a+b \sqrt [3]{c+d x}\right )}{b^3 d^3}+\frac {5040 (c+d x)^{4/3} \sin \left (a+b \sqrt [3]{c+d x}\right )}{b^5 d^3}-\frac {6 c (c+d x)^{5/3} \sin \left (a+b \sqrt [3]{c+d x}\right )}{b d^3}-\frac {168 (c+d x)^2 \sin \left (a+b \sqrt [3]{c+d x}\right )}{b^3 d^3}+\frac {3 (c+d x)^{8/3} \sin \left (a+b \sqrt [3]{c+d x}\right )}{b d^3}\\ \end {align*}
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Mathematica [C] time = 1.10, size = 382, normalized size = 0.71 \[ \frac {3 e^{-i \left (a+b \sqrt [3]{c+d x}\right )} \left (-i b^8 d^2 x^2 (c+d x)^{2/3} \left (-1+e^{2 i \left (a+b \sqrt [3]{c+d x}\right )}\right )+2 b^7 d x \sqrt [3]{c+d x} (3 c+4 d x) \left (1+e^{2 i \left (a+b \sqrt [3]{c+d x}\right )}\right )+2 i b^6 \left (9 c^2+36 c d x+28 d^2 x^2\right ) \left (-1+e^{2 i \left (a+b \sqrt [3]{c+d x}\right )}\right )-24 b^5 (c+d x)^{2/3} (9 c+14 d x) \left (1+e^{2 i \left (a+b \sqrt [3]{c+d x}\right )}\right )-240 i b^4 \sqrt [3]{c+d x} (6 c+7 d x) \left (-1+e^{2 i \left (a+b \sqrt [3]{c+d x}\right )}\right )+240 b^3 (27 c+28 d x) \left (1+e^{2 i \left (a+b \sqrt [3]{c+d x}\right )}\right )+20160 i b^2 (c+d x)^{2/3} \left (-1+e^{2 i \left (a+b \sqrt [3]{c+d x}\right )}\right )-40320 b \sqrt [3]{c+d x} \left (1+e^{2 i \left (a+b \sqrt [3]{c+d x}\right )}\right )-40320 i \left (-1+e^{2 i \left (a+b \sqrt [3]{c+d x}\right )}\right )\right )}{2 b^9 d^3} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.95, size = 182, normalized size = 0.34 \[ \frac {3 \, {\left (2 \, {\left (3360 \, b^{3} d x + 3240 \, b^{3} c - 12 \, {\left (14 \, b^{5} d x + 9 \, b^{5} c\right )} {\left (d x + c\right )}^{\frac {2}{3}} + {\left (4 \, b^{7} d^{2} x^{2} + 3 \, b^{7} c d x - 20160 \, b\right )} {\left (d x + c\right )}^{\frac {1}{3}}\right )} \cos \left ({\left (d x + c\right )}^{\frac {1}{3}} b + a\right ) - {\left (56 \, b^{6} d^{2} x^{2} + 72 \, b^{6} c d x + 18 \, b^{6} c^{2} - {\left (b^{8} d^{2} x^{2} - 20160 \, b^{2}\right )} {\left (d x + c\right )}^{\frac {2}{3}} - 240 \, {\left (7 \, b^{4} d x + 6 \, b^{4} c\right )} {\left (d x + c\right )}^{\frac {1}{3}} - 40320\right )} \sin \left ({\left (d x + c\right )}^{\frac {1}{3}} b + a\right )\right )}}{b^{9} d^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.50, size = 1104, normalized size = 2.06 \[ \text {result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.05, size = 1809, normalized size = 3.37 \[ \text {result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.75, size = 1349, normalized size = 2.51 \[ \text {result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.00 \[ \int x^2\,\cos \left (a+b\,{\left (c+d\,x\right )}^{1/3}\right ) \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int x^{2} \cos {\left (a + b \sqrt [3]{c + d x} \right )}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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