Optimal. Leaf size=395 \[ \frac{1}{9} d^2 x^5 \left (1-c^2 x^2\right )^2 \left (a+b \sin ^{-1}(c x)\right )^2+\frac{4}{63} d^2 x^5 \left (1-c^2 x^2\right ) \left (a+b \sin ^{-1}(c x)\right )^2+\frac{16 b d^2 x^4 \sqrt{1-c^2 x^2} \left (a+b \sin ^{-1}(c x)\right )}{1575 c}+\frac{64 b d^2 x^2 \sqrt{1-c^2 x^2} \left (a+b \sin ^{-1}(c x)\right )}{4725 c^3}+\frac{2 b d^2 \left (1-c^2 x^2\right )^{9/2} \left (a+b \sin ^{-1}(c x)\right )}{81 c^5}-\frac{20 b d^2 \left (1-c^2 x^2\right )^{7/2} \left (a+b \sin ^{-1}(c x)\right )}{441 c^5}-\frac{2 b d^2 \left (1-c^2 x^2\right )^{5/2} \left (a+b \sin ^{-1}(c x)\right )}{315 c^5}+\frac{8 b d^2 \left (1-c^2 x^2\right )^{3/2} \left (a+b \sin ^{-1}(c x)\right )}{189 c^5}+\frac{128 b d^2 \sqrt{1-c^2 x^2} \left (a+b \sin ^{-1}(c x)\right )}{4725 c^5}+\frac{8}{315} d^2 x^5 \left (a+b \sin ^{-1}(c x)\right )^2-\frac{2}{729} b^2 c^4 d^2 x^9+\frac{212 b^2 c^2 d^2 x^7}{27783}-\frac{2104 b^2 d^2 x^3}{297675 c^2}-\frac{4208 b^2 d^2 x}{99225 c^4}-\frac{526 b^2 d^2 x^5}{165375} \]
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Rubi [A] time = 0.724235, antiderivative size = 395, normalized size of antiderivative = 1., number of steps used = 16, number of rules used = 11, integrand size = 27, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.407, Rules used = {4699, 4627, 4707, 4677, 8, 30, 266, 43, 4689, 12, 1153} \[ \frac{1}{9} d^2 x^5 \left (1-c^2 x^2\right )^2 \left (a+b \sin ^{-1}(c x)\right )^2+\frac{4}{63} d^2 x^5 \left (1-c^2 x^2\right ) \left (a+b \sin ^{-1}(c x)\right )^2+\frac{16 b d^2 x^4 \sqrt{1-c^2 x^2} \left (a+b \sin ^{-1}(c x)\right )}{1575 c}+\frac{64 b d^2 x^2 \sqrt{1-c^2 x^2} \left (a+b \sin ^{-1}(c x)\right )}{4725 c^3}+\frac{2 b d^2 \left (1-c^2 x^2\right )^{9/2} \left (a+b \sin ^{-1}(c x)\right )}{81 c^5}-\frac{20 b d^2 \left (1-c^2 x^2\right )^{7/2} \left (a+b \sin ^{-1}(c x)\right )}{441 c^5}-\frac{2 b d^2 \left (1-c^2 x^2\right )^{5/2} \left (a+b \sin ^{-1}(c x)\right )}{315 c^5}+\frac{8 b d^2 \left (1-c^2 x^2\right )^{3/2} \left (a+b \sin ^{-1}(c x)\right )}{189 c^5}+\frac{128 b d^2 \sqrt{1-c^2 x^2} \left (a+b \sin ^{-1}(c x)\right )}{4725 c^5}+\frac{8}{315} d^2 x^5 \left (a+b \sin ^{-1}(c x)\right )^2-\frac{2}{729} b^2 c^4 d^2 x^9+\frac{212 b^2 c^2 d^2 x^7}{27783}-\frac{2104 b^2 d^2 x^3}{297675 c^2}-\frac{4208 b^2 d^2 x}{99225 c^4}-\frac{526 b^2 d^2 x^5}{165375} \]
Antiderivative was successfully verified.
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Rule 4699
Rule 4627
Rule 4707
Rule 4677
Rule 8
Rule 30
Rule 266
Rule 43
Rule 4689
Rule 12
Rule 1153
Rubi steps
\begin{align*} \int x^4 \left (d-c^2 d x^2\right )^2 \left (a+b \sin ^{-1}(c x)\right )^2 \, dx &=\frac{1}{9} d^2 x^5 \left (1-c^2 x^2\right )^2 \left (a+b \sin ^{-1}(c x)\right )^2+\frac{1}{9} (4 d) \int x^4 \left (d-c^2 d x^2\right ) \left (a+b \sin ^{-1}(c x)\right )^2 \, dx-\frac{1}{9} \left (2 b c d^2\right ) \int x^5 \left (1-c^2 x^2\right )^{3/2} \left (a+b \sin ^{-1}(c x)\right ) \, dx\\ &=\frac{2 b d^2 \left (1-c^2 x^2\right )^{5/2} \left (a+b \sin ^{-1}(c x)\right )}{45 c^5}-\frac{4 b d^2 \left (1-c^2 x^2\right )^{7/2} \left (a+b \sin ^{-1}(c x)\right )}{63 c^5}+\frac{2 b d^2 \left (1-c^2 x^2\right )^{9/2} \left (a+b \sin ^{-1}(c x)\right )}{81 c^5}+\frac{4}{63} d^2 x^5 \left (1-c^2 x^2\right ) \left (a+b \sin ^{-1}(c x)\right )^2+\frac{1}{9} d^2 x^5 \left (1-c^2 x^2\right )^2 \left (a+b \sin ^{-1}(c x)\right )^2+\frac{1}{63} \left (8 d^2\right ) \int x^4 \left (a+b \sin ^{-1}(c x)\right )^2 \, dx-\frac{1}{63} \left (8 b c d^2\right ) \int x^5 \sqrt{1-c^2 x^2} \left (a+b \sin ^{-1}(c x)\right ) \, dx+\frac{1}{9} \left (2 b^2 c^2 d^2\right ) \int \frac{\left (1-c^2 x^2\right )^2 \left (-8-20 c^2 x^2-35 c^4 x^4\right )}{315 c^6} \, dx\\ &=\frac{8 b d^2 \left (1-c^2 x^2\right )^{3/2} \left (a+b \sin ^{-1}(c x)\right )}{189 c^5}-\frac{2 b d^2 \left (1-c^2 x^2\right )^{5/2} \left (a+b \sin ^{-1}(c x)\right )}{315 c^5}-\frac{20 b d^2 \left (1-c^2 x^2\right )^{7/2} \left (a+b \sin ^{-1}(c x)\right )}{441 c^5}+\frac{2 b d^2 \left (1-c^2 x^2\right )^{9/2} \left (a+b \sin ^{-1}(c x)\right )}{81 c^5}+\frac{8}{315} d^2 x^5 \left (a+b \sin ^{-1}(c x)\right )^2+\frac{4}{63} d^2 x^5 \left (1-c^2 x^2\right ) \left (a+b \sin ^{-1}(c x)\right )^2+\frac{1}{9} d^2 x^5 \left (1-c^2 x^2\right )^2 \left (a+b \sin ^{-1}(c x)\right )^2+\frac{\left (2 b^2 d^2\right ) \int \left (1-c^2 x^2\right )^2 \left (-8-20 c^2 x^2-35 c^4 x^4\right ) \, dx}{2835 c^4}-\frac{1}{315} \left (16 b c d^2\right ) \int \frac{x^5 \left (a+b \sin ^{-1}(c x)\right )}{\sqrt{1-c^2 x^2}} \, dx+\frac{1}{63} \left (8 b^2 c^2 d^2\right ) \int \frac{-8-4 c^2 x^2-3 c^4 x^4+15 c^6 x^6}{105 c^6} \, dx\\ &=\frac{16 b d^2 x^4 \sqrt{1-c^2 x^2} \left (a+b \sin ^{-1}(c x)\right )}{1575 c}+\frac{8 b d^2 \left (1-c^2 x^2\right )^{3/2} \left (a+b \sin ^{-1}(c x)\right )}{189 c^5}-\frac{2 b d^2 \left (1-c^2 x^2\right )^{5/2} \left (a+b \sin ^{-1}(c x)\right )}{315 c^5}-\frac{20 b d^2 \left (1-c^2 x^2\right )^{7/2} \left (a+b \sin ^{-1}(c x)\right )}{441 c^5}+\frac{2 b d^2 \left (1-c^2 x^2\right )^{9/2} \left (a+b \sin ^{-1}(c x)\right )}{81 c^5}+\frac{8}{315} d^2 x^5 \left (a+b \sin ^{-1}(c x)\right )^2+\frac{4}{63} d^2 x^5 \left (1-c^2 x^2\right ) \left (a+b \sin ^{-1}(c x)\right )^2+\frac{1}{9} d^2 x^5 \left (1-c^2 x^2\right )^2 \left (a+b \sin ^{-1}(c x)\right )^2-\frac{\left (16 b^2 d^2\right ) \int x^4 \, dx}{1575}+\frac{\left (2 b^2 d^2\right ) \int \left (-8-4 c^2 x^2-3 c^4 x^4+50 c^6 x^6-35 c^8 x^8\right ) \, dx}{2835 c^4}+\frac{\left (8 b^2 d^2\right ) \int \left (-8-4 c^2 x^2-3 c^4 x^4+15 c^6 x^6\right ) \, dx}{6615 c^4}-\frac{\left (64 b d^2\right ) \int \frac{x^3 \left (a+b \sin ^{-1}(c x)\right )}{\sqrt{1-c^2 x^2}} \, dx}{1575 c}\\ &=-\frac{304 b^2 d^2 x}{19845 c^4}-\frac{152 b^2 d^2 x^3}{59535 c^2}-\frac{526 b^2 d^2 x^5}{165375}+\frac{212 b^2 c^2 d^2 x^7}{27783}-\frac{2}{729} b^2 c^4 d^2 x^9+\frac{64 b d^2 x^2 \sqrt{1-c^2 x^2} \left (a+b \sin ^{-1}(c x)\right )}{4725 c^3}+\frac{16 b d^2 x^4 \sqrt{1-c^2 x^2} \left (a+b \sin ^{-1}(c x)\right )}{1575 c}+\frac{8 b d^2 \left (1-c^2 x^2\right )^{3/2} \left (a+b \sin ^{-1}(c x)\right )}{189 c^5}-\frac{2 b d^2 \left (1-c^2 x^2\right )^{5/2} \left (a+b \sin ^{-1}(c x)\right )}{315 c^5}-\frac{20 b d^2 \left (1-c^2 x^2\right )^{7/2} \left (a+b \sin ^{-1}(c x)\right )}{441 c^5}+\frac{2 b d^2 \left (1-c^2 x^2\right )^{9/2} \left (a+b \sin ^{-1}(c x)\right )}{81 c^5}+\frac{8}{315} d^2 x^5 \left (a+b \sin ^{-1}(c x)\right )^2+\frac{4}{63} d^2 x^5 \left (1-c^2 x^2\right ) \left (a+b \sin ^{-1}(c x)\right )^2+\frac{1}{9} d^2 x^5 \left (1-c^2 x^2\right )^2 \left (a+b \sin ^{-1}(c x)\right )^2-\frac{\left (128 b d^2\right ) \int \frac{x \left (a+b \sin ^{-1}(c x)\right )}{\sqrt{1-c^2 x^2}} \, dx}{4725 c^3}-\frac{\left (64 b^2 d^2\right ) \int x^2 \, dx}{4725 c^2}\\ &=-\frac{304 b^2 d^2 x}{19845 c^4}-\frac{2104 b^2 d^2 x^3}{297675 c^2}-\frac{526 b^2 d^2 x^5}{165375}+\frac{212 b^2 c^2 d^2 x^7}{27783}-\frac{2}{729} b^2 c^4 d^2 x^9+\frac{128 b d^2 \sqrt{1-c^2 x^2} \left (a+b \sin ^{-1}(c x)\right )}{4725 c^5}+\frac{64 b d^2 x^2 \sqrt{1-c^2 x^2} \left (a+b \sin ^{-1}(c x)\right )}{4725 c^3}+\frac{16 b d^2 x^4 \sqrt{1-c^2 x^2} \left (a+b \sin ^{-1}(c x)\right )}{1575 c}+\frac{8 b d^2 \left (1-c^2 x^2\right )^{3/2} \left (a+b \sin ^{-1}(c x)\right )}{189 c^5}-\frac{2 b d^2 \left (1-c^2 x^2\right )^{5/2} \left (a+b \sin ^{-1}(c x)\right )}{315 c^5}-\frac{20 b d^2 \left (1-c^2 x^2\right )^{7/2} \left (a+b \sin ^{-1}(c x)\right )}{441 c^5}+\frac{2 b d^2 \left (1-c^2 x^2\right )^{9/2} \left (a+b \sin ^{-1}(c x)\right )}{81 c^5}+\frac{8}{315} d^2 x^5 \left (a+b \sin ^{-1}(c x)\right )^2+\frac{4}{63} d^2 x^5 \left (1-c^2 x^2\right ) \left (a+b \sin ^{-1}(c x)\right )^2+\frac{1}{9} d^2 x^5 \left (1-c^2 x^2\right )^2 \left (a+b \sin ^{-1}(c x)\right )^2-\frac{\left (128 b^2 d^2\right ) \int 1 \, dx}{4725 c^4}\\ &=-\frac{4208 b^2 d^2 x}{99225 c^4}-\frac{2104 b^2 d^2 x^3}{297675 c^2}-\frac{526 b^2 d^2 x^5}{165375}+\frac{212 b^2 c^2 d^2 x^7}{27783}-\frac{2}{729} b^2 c^4 d^2 x^9+\frac{128 b d^2 \sqrt{1-c^2 x^2} \left (a+b \sin ^{-1}(c x)\right )}{4725 c^5}+\frac{64 b d^2 x^2 \sqrt{1-c^2 x^2} \left (a+b \sin ^{-1}(c x)\right )}{4725 c^3}+\frac{16 b d^2 x^4 \sqrt{1-c^2 x^2} \left (a+b \sin ^{-1}(c x)\right )}{1575 c}+\frac{8 b d^2 \left (1-c^2 x^2\right )^{3/2} \left (a+b \sin ^{-1}(c x)\right )}{189 c^5}-\frac{2 b d^2 \left (1-c^2 x^2\right )^{5/2} \left (a+b \sin ^{-1}(c x)\right )}{315 c^5}-\frac{20 b d^2 \left (1-c^2 x^2\right )^{7/2} \left (a+b \sin ^{-1}(c x)\right )}{441 c^5}+\frac{2 b d^2 \left (1-c^2 x^2\right )^{9/2} \left (a+b \sin ^{-1}(c x)\right )}{81 c^5}+\frac{8}{315} d^2 x^5 \left (a+b \sin ^{-1}(c x)\right )^2+\frac{4}{63} d^2 x^5 \left (1-c^2 x^2\right ) \left (a+b \sin ^{-1}(c x)\right )^2+\frac{1}{9} d^2 x^5 \left (1-c^2 x^2\right )^2 \left (a+b \sin ^{-1}(c x)\right )^2\\ \end{align*}
Mathematica [A] time = 0.246725, size = 253, normalized size = 0.64 \[ \frac{d^2 \left (99225 a^2 c^5 x^5 \left (35 c^4 x^4-90 c^2 x^2+63\right )+630 a b \sqrt{1-c^2 x^2} \left (1225 c^8 x^8-2650 c^6 x^6+789 c^4 x^4+1052 c^2 x^2+2104\right )+630 b \sin ^{-1}(c x) \left (315 a c^5 x^5 \left (35 c^4 x^4-90 c^2 x^2+63\right )+b \sqrt{1-c^2 x^2} \left (1225 c^8 x^8-2650 c^6 x^6+789 c^4 x^4+1052 c^2 x^2+2104\right )\right )-2 b^2 c x \left (42875 c^8 x^8-119250 c^6 x^6+49707 c^4 x^4+110460 c^2 x^2+662760\right )+99225 b^2 c^5 x^5 \left (35 c^4 x^4-90 c^2 x^2+63\right ) \sin ^{-1}(c x)^2\right )}{31255875 c^5} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.159, size = 531, normalized size = 1.3 \begin{align*}{\frac{1}{{c}^{5}} \left ({d}^{2}{a}^{2} \left ({\frac{{c}^{9}{x}^{9}}{9}}-{\frac{2\,{c}^{7}{x}^{7}}{7}}+{\frac{{c}^{5}{x}^{5}}{5}} \right ) +{d}^{2}{b}^{2} \left ({\frac{ \left ( \arcsin \left ( cx \right ) \right ) ^{2} \left ( 3\,{c}^{4}{x}^{4}-10\,{c}^{2}{x}^{2}+15 \right ) cx}{15}}-{\frac{16\,cx}{315}}+{\frac{16\,\arcsin \left ( cx \right ) }{315}\sqrt{-{c}^{2}{x}^{2}+1}}+{\frac{2\,\arcsin \left ( cx \right ) \left ({c}^{2}{x}^{2}-1 \right ) ^{2}}{525}\sqrt{-{c}^{2}{x}^{2}+1}}-{\frac{ \left ( 6\,{c}^{4}{x}^{4}-20\,{c}^{2}{x}^{2}+30 \right ) cx}{7875}}-{\frac{8\, \left ({c}^{2}{x}^{2}-1 \right ) \arcsin \left ( cx \right ) }{945}\sqrt{-{c}^{2}{x}^{2}+1}}+{\frac{ \left ( 8\,{c}^{2}{x}^{2}-24 \right ) cx}{2835}}+{\frac{2\, \left ( \arcsin \left ( cx \right ) \right ) ^{2} \left ( 5\,{c}^{6}{x}^{6}-21\,{c}^{4}{x}^{4}+35\,{c}^{2}{x}^{2}-35 \right ) cx}{35}}+{\frac{20\,\arcsin \left ( cx \right ) \left ({c}^{2}{x}^{2}-1 \right ) ^{3}}{441}\sqrt{-{c}^{2}{x}^{2}+1}}-{\frac{ \left ( 20\,{c}^{6}{x}^{6}-84\,{c}^{4}{x}^{4}+140\,{c}^{2}{x}^{2}-140 \right ) cx}{3087}}+{\frac{ \left ( \arcsin \left ( cx \right ) \right ) ^{2} \left ( 35\,{c}^{8}{x}^{8}-180\,{c}^{6}{x}^{6}+378\,{c}^{4}{x}^{4}-420\,{c}^{2}{x}^{2}+315 \right ) cx}{315}}+{\frac{2\,\arcsin \left ( cx \right ) \left ({c}^{2}{x}^{2}-1 \right ) ^{4}}{81}\sqrt{-{c}^{2}{x}^{2}+1}}-{\frac{ \left ( 70\,{c}^{8}{x}^{8}-360\,{c}^{6}{x}^{6}+756\,{c}^{4}{x}^{4}-840\,{c}^{2}{x}^{2}+630 \right ) cx}{25515}} \right ) +2\,{d}^{2}ab \left ( 1/9\,\arcsin \left ( cx \right ){c}^{9}{x}^{9}-2/7\,\arcsin \left ( cx \right ){c}^{7}{x}^{7}+1/5\,\arcsin \left ( cx \right ){c}^{5}{x}^{5}+{\frac{{c}^{8}{x}^{8}\sqrt{-{c}^{2}{x}^{2}+1}}{81}}-{\frac{106\,{c}^{6}{x}^{6}\sqrt{-{c}^{2}{x}^{2}+1}}{3969}}+{\frac{263\,{c}^{4}{x}^{4}\sqrt{-{c}^{2}{x}^{2}+1}}{33075}}+{\frac{1052\,{c}^{2}{x}^{2}\sqrt{-{c}^{2}{x}^{2}+1}}{99225}}+{\frac{2104\,\sqrt{-{c}^{2}{x}^{2}+1}}{99225}} \right ) \right ) } \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] time = 1.76553, size = 1054, normalized size = 2.67 \begin{align*} \text{result too large to display} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.89997, size = 810, normalized size = 2.05 \begin{align*} \frac{42875 \,{\left (81 \, a^{2} - 2 \, b^{2}\right )} c^{9} d^{2} x^{9} - 2250 \,{\left (3969 \, a^{2} - 106 \, b^{2}\right )} c^{7} d^{2} x^{7} + 189 \,{\left (33075 \, a^{2} - 526 \, b^{2}\right )} c^{5} d^{2} x^{5} - 220920 \, b^{2} c^{3} d^{2} x^{3} - 1325520 \, b^{2} c d^{2} x + 99225 \,{\left (35 \, b^{2} c^{9} d^{2} x^{9} - 90 \, b^{2} c^{7} d^{2} x^{7} + 63 \, b^{2} c^{5} d^{2} x^{5}\right )} \arcsin \left (c x\right )^{2} + 198450 \,{\left (35 \, a b c^{9} d^{2} x^{9} - 90 \, a b c^{7} d^{2} x^{7} + 63 \, a b c^{5} d^{2} x^{5}\right )} \arcsin \left (c x\right ) + 630 \,{\left (1225 \, a b c^{8} d^{2} x^{8} - 2650 \, a b c^{6} d^{2} x^{6} + 789 \, a b c^{4} d^{2} x^{4} + 1052 \, a b c^{2} d^{2} x^{2} + 2104 \, a b d^{2} +{\left (1225 \, b^{2} c^{8} d^{2} x^{8} - 2650 \, b^{2} c^{6} d^{2} x^{6} + 789 \, b^{2} c^{4} d^{2} x^{4} + 1052 \, b^{2} c^{2} d^{2} x^{2} + 2104 \, b^{2} d^{2}\right )} \arcsin \left (c x\right )\right )} \sqrt{-c^{2} x^{2} + 1}}{31255875 \, c^{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 57.5583, size = 563, normalized size = 1.43 \begin{align*} \begin{cases} \frac{a^{2} c^{4} d^{2} x^{9}}{9} - \frac{2 a^{2} c^{2} d^{2} x^{7}}{7} + \frac{a^{2} d^{2} x^{5}}{5} + \frac{2 a b c^{4} d^{2} x^{9} \operatorname{asin}{\left (c x \right )}}{9} + \frac{2 a b c^{3} d^{2} x^{8} \sqrt{- c^{2} x^{2} + 1}}{81} - \frac{4 a b c^{2} d^{2} x^{7} \operatorname{asin}{\left (c x \right )}}{7} - \frac{212 a b c d^{2} x^{6} \sqrt{- c^{2} x^{2} + 1}}{3969} + \frac{2 a b d^{2} x^{5} \operatorname{asin}{\left (c x \right )}}{5} + \frac{526 a b d^{2} x^{4} \sqrt{- c^{2} x^{2} + 1}}{33075 c} + \frac{2104 a b d^{2} x^{2} \sqrt{- c^{2} x^{2} + 1}}{99225 c^{3}} + \frac{4208 a b d^{2} \sqrt{- c^{2} x^{2} + 1}}{99225 c^{5}} + \frac{b^{2} c^{4} d^{2} x^{9} \operatorname{asin}^{2}{\left (c x \right )}}{9} - \frac{2 b^{2} c^{4} d^{2} x^{9}}{729} + \frac{2 b^{2} c^{3} d^{2} x^{8} \sqrt{- c^{2} x^{2} + 1} \operatorname{asin}{\left (c x \right )}}{81} - \frac{2 b^{2} c^{2} d^{2} x^{7} \operatorname{asin}^{2}{\left (c x \right )}}{7} + \frac{212 b^{2} c^{2} d^{2} x^{7}}{27783} - \frac{212 b^{2} c d^{2} x^{6} \sqrt{- c^{2} x^{2} + 1} \operatorname{asin}{\left (c x \right )}}{3969} + \frac{b^{2} d^{2} x^{5} \operatorname{asin}^{2}{\left (c x \right )}}{5} - \frac{526 b^{2} d^{2} x^{5}}{165375} + \frac{526 b^{2} d^{2} x^{4} \sqrt{- c^{2} x^{2} + 1} \operatorname{asin}{\left (c x \right )}}{33075 c} - \frac{2104 b^{2} d^{2} x^{3}}{297675 c^{2}} + \frac{2104 b^{2} d^{2} x^{2} \sqrt{- c^{2} x^{2} + 1} \operatorname{asin}{\left (c x \right )}}{99225 c^{3}} - \frac{4208 b^{2} d^{2} x}{99225 c^{4}} + \frac{4208 b^{2} d^{2} \sqrt{- c^{2} x^{2} + 1} \operatorname{asin}{\left (c x \right )}}{99225 c^{5}} & \text{for}\: c \neq 0 \\\frac{a^{2} d^{2} x^{5}}{5} & \text{otherwise} \end{cases} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] time = 1.58319, size = 948, normalized size = 2.4 \begin{align*} \text{result too large to display} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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