Optimal. Leaf size=692 \[ \frac {f^3 \sqrt {1-c^2 x^2} \left (a+b \sin ^{-1}(c x)\right )^3}{3 b c \sqrt {d-c^2 d x^2}}-\frac {3 f^2 g \left (1-c^2 x^2\right ) \left (a+b \sin ^{-1}(c x)\right )^2}{c^2 \sqrt {d-c^2 d x^2}}+\frac {6 b f^2 g x \sqrt {1-c^2 x^2} \left (a+b \sin ^{-1}(c x)\right )}{c \sqrt {d-c^2 d x^2}}-\frac {3 f g^2 x \left (1-c^2 x^2\right ) \left (a+b \sin ^{-1}(c x)\right )^2}{2 c^2 \sqrt {d-c^2 d x^2}}+\frac {3 b f g^2 x^2 \sqrt {1-c^2 x^2} \left (a+b \sin ^{-1}(c x)\right )}{2 c \sqrt {d-c^2 d x^2}}-\frac {g^3 x^2 \left (1-c^2 x^2\right ) \left (a+b \sin ^{-1}(c x)\right )^2}{3 c^2 \sqrt {d-c^2 d x^2}}+\frac {2 b g^3 x^3 \sqrt {1-c^2 x^2} \left (a+b \sin ^{-1}(c x)\right )}{9 c \sqrt {d-c^2 d x^2}}-\frac {2 g^3 \left (1-c^2 x^2\right ) \left (a+b \sin ^{-1}(c x)\right )^2}{3 c^4 \sqrt {d-c^2 d x^2}}+\frac {f g^2 \sqrt {1-c^2 x^2} \left (a+b \sin ^{-1}(c x)\right )^3}{2 b c^3 \sqrt {d-c^2 d x^2}}+\frac {4 b g^3 x \sqrt {1-c^2 x^2} \left (a+b \sin ^{-1}(c x)\right )}{3 c^3 \sqrt {d-c^2 d x^2}}+\frac {6 b^2 f^2 g \left (1-c^2 x^2\right )}{c^2 \sqrt {d-c^2 d x^2}}+\frac {3 b^2 f g^2 x \left (1-c^2 x^2\right )}{4 c^2 \sqrt {d-c^2 d x^2}}-\frac {2 b^2 g^3 \left (1-c^2 x^2\right )^2}{27 c^4 \sqrt {d-c^2 d x^2}}+\frac {14 b^2 g^3 \left (1-c^2 x^2\right )}{9 c^4 \sqrt {d-c^2 d x^2}}-\frac {3 b^2 f g^2 \sqrt {1-c^2 x^2} \sin ^{-1}(c x)}{4 c^3 \sqrt {d-c^2 d x^2}} \]
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Rubi [A] time = 0.70, antiderivative size = 692, normalized size of antiderivative = 1.00, number of steps used = 17, number of rules used = 10, integrand size = 33, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.303, Rules used = {4777, 4773, 3317, 3296, 2638, 3311, 32, 2635, 8, 2633} \[ -\frac {3 f^2 g \left (1-c^2 x^2\right ) \left (a+b \sin ^{-1}(c x)\right )^2}{c^2 \sqrt {d-c^2 d x^2}}+\frac {6 b f^2 g x \sqrt {1-c^2 x^2} \left (a+b \sin ^{-1}(c x)\right )}{c \sqrt {d-c^2 d x^2}}+\frac {f^3 \sqrt {1-c^2 x^2} \left (a+b \sin ^{-1}(c x)\right )^3}{3 b c \sqrt {d-c^2 d x^2}}+\frac {f g^2 \sqrt {1-c^2 x^2} \left (a+b \sin ^{-1}(c x)\right )^3}{2 b c^3 \sqrt {d-c^2 d x^2}}-\frac {3 f g^2 x \left (1-c^2 x^2\right ) \left (a+b \sin ^{-1}(c x)\right )^2}{2 c^2 \sqrt {d-c^2 d x^2}}+\frac {3 b f g^2 x^2 \sqrt {1-c^2 x^2} \left (a+b \sin ^{-1}(c x)\right )}{2 c \sqrt {d-c^2 d x^2}}-\frac {g^3 x^2 \left (1-c^2 x^2\right ) \left (a+b \sin ^{-1}(c x)\right )^2}{3 c^2 \sqrt {d-c^2 d x^2}}-\frac {2 g^3 \left (1-c^2 x^2\right ) \left (a+b \sin ^{-1}(c x)\right )^2}{3 c^4 \sqrt {d-c^2 d x^2}}+\frac {2 b g^3 x^3 \sqrt {1-c^2 x^2} \left (a+b \sin ^{-1}(c x)\right )}{9 c \sqrt {d-c^2 d x^2}}+\frac {4 b g^3 x \sqrt {1-c^2 x^2} \left (a+b \sin ^{-1}(c x)\right )}{3 c^3 \sqrt {d-c^2 d x^2}}+\frac {6 b^2 f^2 g \left (1-c^2 x^2\right )}{c^2 \sqrt {d-c^2 d x^2}}+\frac {3 b^2 f g^2 x \left (1-c^2 x^2\right )}{4 c^2 \sqrt {d-c^2 d x^2}}-\frac {3 b^2 f g^2 \sqrt {1-c^2 x^2} \sin ^{-1}(c x)}{4 c^3 \sqrt {d-c^2 d x^2}}-\frac {2 b^2 g^3 \left (1-c^2 x^2\right )^2}{27 c^4 \sqrt {d-c^2 d x^2}}+\frac {14 b^2 g^3 \left (1-c^2 x^2\right )}{9 c^4 \sqrt {d-c^2 d x^2}} \]
Antiderivative was successfully verified.
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Rule 8
Rule 32
Rule 2633
Rule 2635
Rule 2638
Rule 3296
Rule 3311
Rule 3317
Rule 4773
Rule 4777
Rubi steps
\begin {align*} \int \frac {(f+g x)^3 \left (a+b \sin ^{-1}(c x)\right )^2}{\sqrt {d-c^2 d x^2}} \, dx &=\frac {\sqrt {1-c^2 x^2} \int \frac {(f+g x)^3 \left (a+b \sin ^{-1}(c x)\right )^2}{\sqrt {1-c^2 x^2}} \, dx}{\sqrt {d-c^2 d x^2}}\\ &=\frac {\sqrt {1-c^2 x^2} \operatorname {Subst}\left (\int (a+b x)^2 (c f+g \sin (x))^3 \, dx,x,\sin ^{-1}(c x)\right )}{c^4 \sqrt {d-c^2 d x^2}}\\ &=\frac {\sqrt {1-c^2 x^2} \operatorname {Subst}\left (\int \left (c^3 f^3 (a+b x)^2+3 c^2 f^2 g (a+b x)^2 \sin (x)+3 c f g^2 (a+b x)^2 \sin ^2(x)+g^3 (a+b x)^2 \sin ^3(x)\right ) \, dx,x,\sin ^{-1}(c x)\right )}{c^4 \sqrt {d-c^2 d x^2}}\\ &=\frac {f^3 \sqrt {1-c^2 x^2} \left (a+b \sin ^{-1}(c x)\right )^3}{3 b c \sqrt {d-c^2 d x^2}}+\frac {\left (3 f^2 g \sqrt {1-c^2 x^2}\right ) \operatorname {Subst}\left (\int (a+b x)^2 \sin (x) \, dx,x,\sin ^{-1}(c x)\right )}{c^2 \sqrt {d-c^2 d x^2}}+\frac {\left (3 f g^2 \sqrt {1-c^2 x^2}\right ) \operatorname {Subst}\left (\int (a+b x)^2 \sin ^2(x) \, dx,x,\sin ^{-1}(c x)\right )}{c^3 \sqrt {d-c^2 d x^2}}+\frac {\left (g^3 \sqrt {1-c^2 x^2}\right ) \operatorname {Subst}\left (\int (a+b x)^2 \sin ^3(x) \, dx,x,\sin ^{-1}(c x)\right )}{c^4 \sqrt {d-c^2 d x^2}}\\ &=\frac {3 b f g^2 x^2 \sqrt {1-c^2 x^2} \left (a+b \sin ^{-1}(c x)\right )}{2 c \sqrt {d-c^2 d x^2}}+\frac {2 b g^3 x^3 \sqrt {1-c^2 x^2} \left (a+b \sin ^{-1}(c x)\right )}{9 c \sqrt {d-c^2 d x^2}}-\frac {3 f^2 g \left (1-c^2 x^2\right ) \left (a+b \sin ^{-1}(c x)\right )^2}{c^2 \sqrt {d-c^2 d x^2}}-\frac {3 f g^2 x \left (1-c^2 x^2\right ) \left (a+b \sin ^{-1}(c x)\right )^2}{2 c^2 \sqrt {d-c^2 d x^2}}-\frac {g^3 x^2 \left (1-c^2 x^2\right ) \left (a+b \sin ^{-1}(c x)\right )^2}{3 c^2 \sqrt {d-c^2 d x^2}}+\frac {f^3 \sqrt {1-c^2 x^2} \left (a+b \sin ^{-1}(c x)\right )^3}{3 b c \sqrt {d-c^2 d x^2}}+\frac {\left (6 b f^2 g \sqrt {1-c^2 x^2}\right ) \operatorname {Subst}\left (\int (a+b x) \cos (x) \, dx,x,\sin ^{-1}(c x)\right )}{c^2 \sqrt {d-c^2 d x^2}}+\frac {\left (3 f g^2 \sqrt {1-c^2 x^2}\right ) \operatorname {Subst}\left (\int (a+b x)^2 \, dx,x,\sin ^{-1}(c x)\right )}{2 c^3 \sqrt {d-c^2 d x^2}}-\frac {\left (3 b^2 f g^2 \sqrt {1-c^2 x^2}\right ) \operatorname {Subst}\left (\int \sin ^2(x) \, dx,x,\sin ^{-1}(c x)\right )}{2 c^3 \sqrt {d-c^2 d x^2}}+\frac {\left (2 g^3 \sqrt {1-c^2 x^2}\right ) \operatorname {Subst}\left (\int (a+b x)^2 \sin (x) \, dx,x,\sin ^{-1}(c x)\right )}{3 c^4 \sqrt {d-c^2 d x^2}}-\frac {\left (2 b^2 g^3 \sqrt {1-c^2 x^2}\right ) \operatorname {Subst}\left (\int \sin ^3(x) \, dx,x,\sin ^{-1}(c x)\right )}{9 c^4 \sqrt {d-c^2 d x^2}}\\ &=\frac {3 b^2 f g^2 x \left (1-c^2 x^2\right )}{4 c^2 \sqrt {d-c^2 d x^2}}+\frac {6 b f^2 g x \sqrt {1-c^2 x^2} \left (a+b \sin ^{-1}(c x)\right )}{c \sqrt {d-c^2 d x^2}}+\frac {3 b f g^2 x^2 \sqrt {1-c^2 x^2} \left (a+b \sin ^{-1}(c x)\right )}{2 c \sqrt {d-c^2 d x^2}}+\frac {2 b g^3 x^3 \sqrt {1-c^2 x^2} \left (a+b \sin ^{-1}(c x)\right )}{9 c \sqrt {d-c^2 d x^2}}-\frac {3 f^2 g \left (1-c^2 x^2\right ) \left (a+b \sin ^{-1}(c x)\right )^2}{c^2 \sqrt {d-c^2 d x^2}}-\frac {2 g^3 \left (1-c^2 x^2\right ) \left (a+b \sin ^{-1}(c x)\right )^2}{3 c^4 \sqrt {d-c^2 d x^2}}-\frac {3 f g^2 x \left (1-c^2 x^2\right ) \left (a+b \sin ^{-1}(c x)\right )^2}{2 c^2 \sqrt {d-c^2 d x^2}}-\frac {g^3 x^2 \left (1-c^2 x^2\right ) \left (a+b \sin ^{-1}(c x)\right )^2}{3 c^2 \sqrt {d-c^2 d x^2}}+\frac {f^3 \sqrt {1-c^2 x^2} \left (a+b \sin ^{-1}(c x)\right )^3}{3 b c \sqrt {d-c^2 d x^2}}+\frac {f g^2 \sqrt {1-c^2 x^2} \left (a+b \sin ^{-1}(c x)\right )^3}{2 b c^3 \sqrt {d-c^2 d x^2}}-\frac {\left (6 b^2 f^2 g \sqrt {1-c^2 x^2}\right ) \operatorname {Subst}\left (\int \sin (x) \, dx,x,\sin ^{-1}(c x)\right )}{c^2 \sqrt {d-c^2 d x^2}}-\frac {\left (3 b^2 f g^2 \sqrt {1-c^2 x^2}\right ) \operatorname {Subst}\left (\int 1 \, dx,x,\sin ^{-1}(c x)\right )}{4 c^3 \sqrt {d-c^2 d x^2}}+\frac {\left (4 b g^3 \sqrt {1-c^2 x^2}\right ) \operatorname {Subst}\left (\int (a+b x) \cos (x) \, dx,x,\sin ^{-1}(c x)\right )}{3 c^4 \sqrt {d-c^2 d x^2}}+\frac {\left (2 b^2 g^3 \sqrt {1-c^2 x^2}\right ) \operatorname {Subst}\left (\int \left (1-x^2\right ) \, dx,x,\sqrt {1-c^2 x^2}\right )}{9 c^4 \sqrt {d-c^2 d x^2}}\\ &=\frac {6 b^2 f^2 g \left (1-c^2 x^2\right )}{c^2 \sqrt {d-c^2 d x^2}}+\frac {2 b^2 g^3 \left (1-c^2 x^2\right )}{9 c^4 \sqrt {d-c^2 d x^2}}+\frac {3 b^2 f g^2 x \left (1-c^2 x^2\right )}{4 c^2 \sqrt {d-c^2 d x^2}}-\frac {2 b^2 g^3 \left (1-c^2 x^2\right )^2}{27 c^4 \sqrt {d-c^2 d x^2}}-\frac {3 b^2 f g^2 \sqrt {1-c^2 x^2} \sin ^{-1}(c x)}{4 c^3 \sqrt {d-c^2 d x^2}}+\frac {6 b f^2 g x \sqrt {1-c^2 x^2} \left (a+b \sin ^{-1}(c x)\right )}{c \sqrt {d-c^2 d x^2}}+\frac {4 b g^3 x \sqrt {1-c^2 x^2} \left (a+b \sin ^{-1}(c x)\right )}{3 c^3 \sqrt {d-c^2 d x^2}}+\frac {3 b f g^2 x^2 \sqrt {1-c^2 x^2} \left (a+b \sin ^{-1}(c x)\right )}{2 c \sqrt {d-c^2 d x^2}}+\frac {2 b g^3 x^3 \sqrt {1-c^2 x^2} \left (a+b \sin ^{-1}(c x)\right )}{9 c \sqrt {d-c^2 d x^2}}-\frac {3 f^2 g \left (1-c^2 x^2\right ) \left (a+b \sin ^{-1}(c x)\right )^2}{c^2 \sqrt {d-c^2 d x^2}}-\frac {2 g^3 \left (1-c^2 x^2\right ) \left (a+b \sin ^{-1}(c x)\right )^2}{3 c^4 \sqrt {d-c^2 d x^2}}-\frac {3 f g^2 x \left (1-c^2 x^2\right ) \left (a+b \sin ^{-1}(c x)\right )^2}{2 c^2 \sqrt {d-c^2 d x^2}}-\frac {g^3 x^2 \left (1-c^2 x^2\right ) \left (a+b \sin ^{-1}(c x)\right )^2}{3 c^2 \sqrt {d-c^2 d x^2}}+\frac {f^3 \sqrt {1-c^2 x^2} \left (a+b \sin ^{-1}(c x)\right )^3}{3 b c \sqrt {d-c^2 d x^2}}+\frac {f g^2 \sqrt {1-c^2 x^2} \left (a+b \sin ^{-1}(c x)\right )^3}{2 b c^3 \sqrt {d-c^2 d x^2}}-\frac {\left (4 b^2 g^3 \sqrt {1-c^2 x^2}\right ) \operatorname {Subst}\left (\int \sin (x) \, dx,x,\sin ^{-1}(c x)\right )}{3 c^4 \sqrt {d-c^2 d x^2}}\\ &=\frac {6 b^2 f^2 g \left (1-c^2 x^2\right )}{c^2 \sqrt {d-c^2 d x^2}}+\frac {14 b^2 g^3 \left (1-c^2 x^2\right )}{9 c^4 \sqrt {d-c^2 d x^2}}+\frac {3 b^2 f g^2 x \left (1-c^2 x^2\right )}{4 c^2 \sqrt {d-c^2 d x^2}}-\frac {2 b^2 g^3 \left (1-c^2 x^2\right )^2}{27 c^4 \sqrt {d-c^2 d x^2}}-\frac {3 b^2 f g^2 \sqrt {1-c^2 x^2} \sin ^{-1}(c x)}{4 c^3 \sqrt {d-c^2 d x^2}}+\frac {6 b f^2 g x \sqrt {1-c^2 x^2} \left (a+b \sin ^{-1}(c x)\right )}{c \sqrt {d-c^2 d x^2}}+\frac {4 b g^3 x \sqrt {1-c^2 x^2} \left (a+b \sin ^{-1}(c x)\right )}{3 c^3 \sqrt {d-c^2 d x^2}}+\frac {3 b f g^2 x^2 \sqrt {1-c^2 x^2} \left (a+b \sin ^{-1}(c x)\right )}{2 c \sqrt {d-c^2 d x^2}}+\frac {2 b g^3 x^3 \sqrt {1-c^2 x^2} \left (a+b \sin ^{-1}(c x)\right )}{9 c \sqrt {d-c^2 d x^2}}-\frac {3 f^2 g \left (1-c^2 x^2\right ) \left (a+b \sin ^{-1}(c x)\right )^2}{c^2 \sqrt {d-c^2 d x^2}}-\frac {2 g^3 \left (1-c^2 x^2\right ) \left (a+b \sin ^{-1}(c x)\right )^2}{3 c^4 \sqrt {d-c^2 d x^2}}-\frac {3 f g^2 x \left (1-c^2 x^2\right ) \left (a+b \sin ^{-1}(c x)\right )^2}{2 c^2 \sqrt {d-c^2 d x^2}}-\frac {g^3 x^2 \left (1-c^2 x^2\right ) \left (a+b \sin ^{-1}(c x)\right )^2}{3 c^2 \sqrt {d-c^2 d x^2}}+\frac {f^3 \sqrt {1-c^2 x^2} \left (a+b \sin ^{-1}(c x)\right )^3}{3 b c \sqrt {d-c^2 d x^2}}+\frac {f g^2 \sqrt {1-c^2 x^2} \left (a+b \sin ^{-1}(c x)\right )^3}{2 b c^3 \sqrt {d-c^2 d x^2}}\\ \end {align*}
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Mathematica [A] time = 1.52, size = 582, normalized size = 0.84 \[ \frac {-108 a^2 c \sqrt {d} f \sqrt {1-c^2 x^2} \sqrt {d-c^2 d x^2} \left (2 c^2 f^2+3 g^2\right ) \tan ^{-1}\left (\frac {c x \sqrt {d-c^2 d x^2}}{\sqrt {d} \left (c^2 x^2-1\right )}\right )-36 a^2 d \left (1-c^2 x^2\right )^{3/2} \left (c^2 g \left (18 f^2+9 f g x+2 g^2 x^2\right )+4 g^3\right )-1296 a b c^2 d f^2 g \left (c^2 x^2-1\right ) \left (c x-\sqrt {1-c^2 x^2} \sin ^{-1}(c x)\right )+162 a b c d f g^2 \left (c^2 x^2-1\right ) \left (-2 \sin ^{-1}(c x)^2+2 \sin \left (2 \sin ^{-1}(c x)\right ) \sin ^{-1}(c x)+\cos \left (2 \sin ^{-1}(c x)\right )\right )-216 a b c^3 d f^3 \left (c^2 x^2-1\right ) \sin ^{-1}(c x)^2-48 a b d g^3 \left (c^2 x^2-1\right ) \left (c^3 x^3-3 \sqrt {1-c^2 x^2} \left (c^2 x^2+2\right ) \sin ^{-1}(c x)+6 c x\right )+648 b^2 c^2 d f^2 g \left (1-c^2 x^2\right ) \left (2 c x \sin ^{-1}(c x)-\sqrt {1-c^2 x^2} \left (\sin ^{-1}(c x)^2-2\right )\right )+27 b^2 c d f g^2 \left (1-c^2 x^2\right ) \left (4 \sin ^{-1}(c x)^3+\left (3-6 \sin ^{-1}(c x)^2\right ) \sin \left (2 \sin ^{-1}(c x)\right )-6 \sin ^{-1}(c x) \cos \left (2 \sin ^{-1}(c x)\right )\right )-2 b^2 d g^3 \left (1-c^2 x^2\right ) \left (81 \sqrt {1-c^2 x^2} \left (\sin ^{-1}(c x)^2-2\right )+6 \sin ^{-1}(c x) \left (\sin \left (3 \sin ^{-1}(c x)\right )-27 c x\right )-\left (9 \sin ^{-1}(c x)^2-2\right ) \cos \left (3 \sin ^{-1}(c x)\right )\right )-72 b^2 c^3 d f^3 \left (c^2 x^2-1\right ) \sin ^{-1}(c x)^3}{216 c^4 d \sqrt {1-c^2 x^2} \sqrt {d-c^2 d x^2}} \]
Antiderivative was successfully verified.
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fricas [F] time = 3.03, size = 0, normalized size = 0.00 \[ {\rm integral}\left (-\frac {{\left (a^{2} g^{3} x^{3} + 3 \, a^{2} f g^{2} x^{2} + 3 \, a^{2} f^{2} g x + a^{2} f^{3} + {\left (b^{2} g^{3} x^{3} + 3 \, b^{2} f g^{2} x^{2} + 3 \, b^{2} f^{2} g x + b^{2} f^{3}\right )} \arcsin \left (c x\right )^{2} + 2 \, {\left (a b g^{3} x^{3} + 3 \, a b f g^{2} x^{2} + 3 \, a b f^{2} g x + a b f^{3}\right )} \arcsin \left (c x\right )\right )} \sqrt {-c^{2} d x^{2} + d}}{c^{2} d x^{2} - d}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {{\left (g x + f\right )}^{3} {\left (b \arcsin \left (c x\right ) + a\right )}^{2}}{\sqrt {-c^{2} d x^{2} + d}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 1.43, size = 1886, normalized size = 2.73 \[ \text {result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F] time = 0.00, size = 0, normalized size = 0.00 \[ -\frac {1}{3} \, a^{2} g^{3} {\left (\frac {\sqrt {-c^{2} d x^{2} + d} x^{2}}{c^{2} d} + \frac {2 \, \sqrt {-c^{2} d x^{2} + d}}{c^{4} d}\right )} - \frac {3}{2} \, a^{2} f g^{2} {\left (\frac {\sqrt {-c^{2} d x^{2} + d} x}{c^{2} d} - \frac {\arcsin \left (c x\right )}{c^{3} \sqrt {d}}\right )} + \frac {a b f^{3} \arcsin \left (c x\right )^{2}}{c \sqrt {d}} + \frac {6 \, a b f^{2} g x}{c \sqrt {d}} + \frac {a^{2} f^{3} \arcsin \left (c x\right )}{c \sqrt {d}} - \frac {6 \, \sqrt {-c^{2} d x^{2} + d} a b f^{2} g \arcsin \left (c x\right )}{c^{2} d} - \frac {3 \, \sqrt {-c^{2} d x^{2} + d} a^{2} f^{2} g}{c^{2} d} - \sqrt {d} \int \frac {{\left ({\left (b^{2} g^{3} x^{3} + 3 \, b^{2} f g^{2} x^{2} + 3 \, b^{2} f^{2} g x + b^{2} f^{3}\right )} \arctan \left (c x, \sqrt {c x + 1} \sqrt {-c x + 1}\right )^{2} + 2 \, {\left (a b g^{3} x^{3} + 3 \, a b f g^{2} x^{2}\right )} \arctan \left (c x, \sqrt {c x + 1} \sqrt {-c x + 1}\right )\right )} \sqrt {c x + 1} \sqrt {-c x + 1}}{c^{2} d x^{2} - d}\,{d x} \]
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 \[ \int \frac {{\left (f+g\,x\right )}^3\,{\left (a+b\,\mathrm {asin}\left (c\,x\right )\right )}^2}{\sqrt {d-c^2\,d\,x^2}} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F(-2)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Exception raised: TypeError} \]
Verification of antiderivative is not currently implemented for this CAS.
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