Optimal. Leaf size=617 \[ \frac {\log (d+e x) \left (a+b \sin ^{-1}(c x)\right ) \left (3 d^2 i-2 d e h+e^2 g\right )}{e^4}-\frac {\left (a+b \sin ^{-1}(c x)\right ) \left (d^3 (-i)+d^2 e h-d e^2 g+e^3 f\right )}{e^4 (d+e x)}+\frac {x (e h-2 d i) \left (a+b \sin ^{-1}(c x)\right )}{e^3}+\frac {i x^2 \left (a+b \sin ^{-1}(c x)\right )}{2 e^2}-\frac {i b \left (3 d^2 i-2 d e h+e^2 g\right ) \text {Li}_2\left (\frac {i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt {c^2 d^2-e^2}}\right )}{e^4}-\frac {i b \left (3 d^2 i-2 d e h+e^2 g\right ) \text {Li}_2\left (\frac {i e e^{i \sin ^{-1}(c x)}}{c d+\sqrt {c^2 d^2-e^2}}\right )}{e^4}+\frac {b \sin ^{-1}(c x) \left (3 d^2 i-2 d e h+e^2 g\right ) \log \left (1-\frac {i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt {c^2 d^2-e^2}}\right )}{e^4}+\frac {b \sin ^{-1}(c x) \left (3 d^2 i-2 d e h+e^2 g\right ) \log \left (1-\frac {i e e^{i \sin ^{-1}(c x)}}{\sqrt {c^2 d^2-e^2}+c d}\right )}{e^4}+\frac {b c \tan ^{-1}\left (\frac {c^2 d x+e}{\sqrt {1-c^2 x^2} \sqrt {c^2 d^2-e^2}}\right ) \left (d^3 (-i)+d^2 e h-d e^2 g+e^3 f\right )}{e^4 \sqrt {c^2 d^2-e^2}}+\frac {b \sqrt {1-c^2 x^2} (e h-2 d i)}{c e^3}+\frac {b i x \sqrt {1-c^2 x^2}}{4 c e^2}-\frac {b i \sin ^{-1}(c x)}{4 c^2 e^2}-\frac {i b \sin ^{-1}(c x)^2 \left (3 d^2 i-2 d e h+e^2 g\right )}{2 e^4}-\frac {b \sin ^{-1}(c x) \log (d+e x) \left (3 d^2 i-2 d e h+e^2 g\right )}{e^4} \]
[Out]
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Rubi [A] time = 1.74, antiderivative size = 617, normalized size of antiderivative = 1.00, number of steps used = 18, number of rules used = 15, integrand size = 31, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.484, Rules used = {1850, 4753, 12, 6742, 261, 321, 216, 725, 204, 2404, 4741, 4519, 2190, 2279, 2391} \[ -\frac {i b \left (3 d^2 i-2 d e h+e^2 g\right ) \text {PolyLog}\left (2,\frac {i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt {c^2 d^2-e^2}}\right )}{e^4}-\frac {i b \left (3 d^2 i-2 d e h+e^2 g\right ) \text {PolyLog}\left (2,\frac {i e e^{i \sin ^{-1}(c x)}}{\sqrt {c^2 d^2-e^2}+c d}\right )}{e^4}-\frac {\left (a+b \sin ^{-1}(c x)\right ) \left (d^2 e h+d^3 (-i)-d e^2 g+e^3 f\right )}{e^4 (d+e x)}+\frac {\log (d+e x) \left (a+b \sin ^{-1}(c x)\right ) \left (3 d^2 i-2 d e h+e^2 g\right )}{e^4}+\frac {x (e h-2 d i) \left (a+b \sin ^{-1}(c x)\right )}{e^3}+\frac {i x^2 \left (a+b \sin ^{-1}(c x)\right )}{2 e^2}+\frac {b c \tan ^{-1}\left (\frac {c^2 d x+e}{\sqrt {1-c^2 x^2} \sqrt {c^2 d^2-e^2}}\right ) \left (d^2 e h+d^3 (-i)-d e^2 g+e^3 f\right )}{e^4 \sqrt {c^2 d^2-e^2}}+\frac {b \sin ^{-1}(c x) \left (3 d^2 i-2 d e h+e^2 g\right ) \log \left (1-\frac {i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt {c^2 d^2-e^2}}\right )}{e^4}+\frac {b \sin ^{-1}(c x) \left (3 d^2 i-2 d e h+e^2 g\right ) \log \left (1-\frac {i e e^{i \sin ^{-1}(c x)}}{\sqrt {c^2 d^2-e^2}+c d}\right )}{e^4}+\frac {b \sqrt {1-c^2 x^2} (e h-2 d i)}{c e^3}+\frac {b i x \sqrt {1-c^2 x^2}}{4 c e^2}-\frac {b i \sin ^{-1}(c x)}{4 c^2 e^2}-\frac {i b \sin ^{-1}(c x)^2 \left (3 d^2 i-2 d e h+e^2 g\right )}{2 e^4}-\frac {b \sin ^{-1}(c x) \log (d+e x) \left (3 d^2 i-2 d e h+e^2 g\right )}{e^4} \]
Antiderivative was successfully verified.
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Rule 12
Rule 204
Rule 216
Rule 261
Rule 321
Rule 725
Rule 1850
Rule 2190
Rule 2279
Rule 2391
Rule 2404
Rule 4519
Rule 4741
Rule 4753
Rule 6742
Rubi steps
\begin {align*} \int \frac {\left (f+g x+h x^2+110 x^3\right ) \left (a+b \sin ^{-1}(c x)\right )}{(d+e x)^2} \, dx &=-\frac {(220 d-e h) x \left (a+b \sin ^{-1}(c x)\right )}{e^3}+\frac {55 x^2 \left (a+b \sin ^{-1}(c x)\right )}{e^2}+\frac {\left (110 d^3-e^3 f+d e^2 g-d^2 e h\right ) \left (a+b \sin ^{-1}(c x)\right )}{e^4 (d+e x)}+\frac {\left (330 d^2+e^2 g-2 d e h\right ) \left (a+b \sin ^{-1}(c x)\right ) \log (d+e x)}{e^4}-(b c) \int \frac {110 d^3-d^2 e (h+220 x)+d e^2 (g+(h-165 x) x)+e^3 \left (-f+x^2 (h+55 x)\right )+\left (330 d^2+e^2 g-2 d e h\right ) (d+e x) \log (d+e x)}{e^4 (d+e x) \sqrt {1-c^2 x^2}} \, dx\\ &=-\frac {(220 d-e h) x \left (a+b \sin ^{-1}(c x)\right )}{e^3}+\frac {55 x^2 \left (a+b \sin ^{-1}(c x)\right )}{e^2}+\frac {\left (110 d^3-e^3 f+d e^2 g-d^2 e h\right ) \left (a+b \sin ^{-1}(c x)\right )}{e^4 (d+e x)}+\frac {\left (330 d^2+e^2 g-2 d e h\right ) \left (a+b \sin ^{-1}(c x)\right ) \log (d+e x)}{e^4}-\frac {(b c) \int \frac {110 d^3-d^2 e (h+220 x)+d e^2 (g+(h-165 x) x)+e^3 \left (-f+x^2 (h+55 x)\right )+\left (330 d^2+e^2 g-2 d e h\right ) (d+e x) \log (d+e x)}{(d+e x) \sqrt {1-c^2 x^2}} \, dx}{e^4}\\ &=-\frac {(220 d-e h) x \left (a+b \sin ^{-1}(c x)\right )}{e^3}+\frac {55 x^2 \left (a+b \sin ^{-1}(c x)\right )}{e^2}+\frac {\left (110 d^3-e^3 f+d e^2 g-d^2 e h\right ) \left (a+b \sin ^{-1}(c x)\right )}{e^4 (d+e x)}+\frac {\left (330 d^2+e^2 g-2 d e h\right ) \left (a+b \sin ^{-1}(c x)\right ) \log (d+e x)}{e^4}-\frac {(b c) \int \left (\frac {110 d^3-e^3 f+d e^2 g-d^2 e h-d e (220 d-e h) x-e^2 (165 d-e h) x^2+55 e^3 x^3}{(d+e x) \sqrt {1-c^2 x^2}}+\frac {\left (330 d^2+e^2 g-2 d e h\right ) \log (d+e x)}{\sqrt {1-c^2 x^2}}\right ) \, dx}{e^4}\\ &=-\frac {(220 d-e h) x \left (a+b \sin ^{-1}(c x)\right )}{e^3}+\frac {55 x^2 \left (a+b \sin ^{-1}(c x)\right )}{e^2}+\frac {\left (110 d^3-e^3 f+d e^2 g-d^2 e h\right ) \left (a+b \sin ^{-1}(c x)\right )}{e^4 (d+e x)}+\frac {\left (330 d^2+e^2 g-2 d e h\right ) \left (a+b \sin ^{-1}(c x)\right ) \log (d+e x)}{e^4}-\frac {(b c) \int \frac {110 d^3-e^3 f+d e^2 g-d^2 e h-d e (220 d-e h) x-e^2 (165 d-e h) x^2+55 e^3 x^3}{(d+e x) \sqrt {1-c^2 x^2}} \, dx}{e^4}-\frac {\left (b c \left (330 d^2+e^2 g-2 d e h\right )\right ) \int \frac {\log (d+e x)}{\sqrt {1-c^2 x^2}} \, dx}{e^4}\\ &=\frac {55 b (d+e x) \sqrt {1-c^2 x^2}}{2 c e^3}-\frac {(220 d-e h) x \left (a+b \sin ^{-1}(c x)\right )}{e^3}+\frac {55 x^2 \left (a+b \sin ^{-1}(c x)\right )}{e^2}+\frac {\left (110 d^3-e^3 f+d e^2 g-d^2 e h\right ) \left (a+b \sin ^{-1}(c x)\right )}{e^4 (d+e x)}-\frac {b \left (330 d^2+e^2 g-2 d e h\right ) \sin ^{-1}(c x) \log (d+e x)}{e^4}+\frac {\left (330 d^2+e^2 g-2 d e h\right ) \left (a+b \sin ^{-1}(c x)\right ) \log (d+e x)}{e^4}+\frac {b \int \frac {-e^3 \left (55 d e^2+2 c^2 \left (110 d^3-e^3 f+d e^2 g-d^2 e h\right )\right )-e^4 \left (55 e^2-c^2 d (495 d-2 e h)\right ) x+c^2 e^5 (495 d-2 e h) x^2}{(d+e x) \sqrt {1-c^2 x^2}} \, dx}{2 c e^7}+\frac {\left (b c \left (330 d^2+e^2 g-2 d e h\right )\right ) \int \frac {\sin ^{-1}(c x)}{c d+c e x} \, dx}{e^3}\\ &=-\frac {b (495 d-2 e h) \sqrt {1-c^2 x^2}}{2 c e^3}+\frac {55 b (d+e x) \sqrt {1-c^2 x^2}}{2 c e^3}-\frac {(220 d-e h) x \left (a+b \sin ^{-1}(c x)\right )}{e^3}+\frac {55 x^2 \left (a+b \sin ^{-1}(c x)\right )}{e^2}+\frac {\left (110 d^3-e^3 f+d e^2 g-d^2 e h\right ) \left (a+b \sin ^{-1}(c x)\right )}{e^4 (d+e x)}-\frac {b \left (330 d^2+e^2 g-2 d e h\right ) \sin ^{-1}(c x) \log (d+e x)}{e^4}+\frac {\left (330 d^2+e^2 g-2 d e h\right ) \left (a+b \sin ^{-1}(c x)\right ) \log (d+e x)}{e^4}-\frac {b \int \frac {c^2 e^5 \left (55 d e^2+2 c^2 \left (110 d^3-e^3 f+d e^2 g-d^2 e h\right )\right )+55 c^2 e^8 x}{(d+e x) \sqrt {1-c^2 x^2}} \, dx}{2 c^3 e^9}+\frac {\left (b c \left (330 d^2+e^2 g-2 d e h\right )\right ) \operatorname {Subst}\left (\int \frac {x \cos (x)}{c^2 d+c e \sin (x)} \, dx,x,\sin ^{-1}(c x)\right )}{e^3}\\ &=-\frac {b (495 d-2 e h) \sqrt {1-c^2 x^2}}{2 c e^3}+\frac {55 b (d+e x) \sqrt {1-c^2 x^2}}{2 c e^3}-\frac {i b \left (330 d^2+e^2 g-2 d e h\right ) \sin ^{-1}(c x)^2}{2 e^4}-\frac {(220 d-e h) x \left (a+b \sin ^{-1}(c x)\right )}{e^3}+\frac {55 x^2 \left (a+b \sin ^{-1}(c x)\right )}{e^2}+\frac {\left (110 d^3-e^3 f+d e^2 g-d^2 e h\right ) \left (a+b \sin ^{-1}(c x)\right )}{e^4 (d+e x)}-\frac {b \left (330 d^2+e^2 g-2 d e h\right ) \sin ^{-1}(c x) \log (d+e x)}{e^4}+\frac {\left (330 d^2+e^2 g-2 d e h\right ) \left (a+b \sin ^{-1}(c x)\right ) \log (d+e x)}{e^4}-\frac {(55 b) \int \frac {1}{\sqrt {1-c^2 x^2}} \, dx}{2 c e^2}+\frac {\left (b c \left (330 d^2+e^2 g-2 d e h\right )\right ) \operatorname {Subst}\left (\int \frac {e^{i x} x}{c^2 d-c \sqrt {c^2 d^2-e^2}-i c e e^{i x}} \, dx,x,\sin ^{-1}(c x)\right )}{e^3}+\frac {\left (b c \left (330 d^2+e^2 g-2 d e h\right )\right ) \operatorname {Subst}\left (\int \frac {e^{i x} x}{c^2 d+c \sqrt {c^2 d^2-e^2}-i c e e^{i x}} \, dx,x,\sin ^{-1}(c x)\right )}{e^3}-\frac {\left (b c \left (110 d^3-e^3 f+d e^2 g-d^2 e h\right )\right ) \int \frac {1}{(d+e x) \sqrt {1-c^2 x^2}} \, dx}{e^4}\\ &=-\frac {b (495 d-2 e h) \sqrt {1-c^2 x^2}}{2 c e^3}+\frac {55 b (d+e x) \sqrt {1-c^2 x^2}}{2 c e^3}-\frac {55 b \sin ^{-1}(c x)}{2 c^2 e^2}-\frac {i b \left (330 d^2+e^2 g-2 d e h\right ) \sin ^{-1}(c x)^2}{2 e^4}-\frac {(220 d-e h) x \left (a+b \sin ^{-1}(c x)\right )}{e^3}+\frac {55 x^2 \left (a+b \sin ^{-1}(c x)\right )}{e^2}+\frac {\left (110 d^3-e^3 f+d e^2 g-d^2 e h\right ) \left (a+b \sin ^{-1}(c x)\right )}{e^4 (d+e x)}+\frac {b \left (330 d^2+e^2 g-2 d e h\right ) \sin ^{-1}(c x) \log \left (1-\frac {i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt {c^2 d^2-e^2}}\right )}{e^4}+\frac {b \left (330 d^2+e^2 g-2 d e h\right ) \sin ^{-1}(c x) \log \left (1-\frac {i e e^{i \sin ^{-1}(c x)}}{c d+\sqrt {c^2 d^2-e^2}}\right )}{e^4}-\frac {b \left (330 d^2+e^2 g-2 d e h\right ) \sin ^{-1}(c x) \log (d+e x)}{e^4}+\frac {\left (330 d^2+e^2 g-2 d e h\right ) \left (a+b \sin ^{-1}(c x)\right ) \log (d+e x)}{e^4}-\frac {\left (b \left (330 d^2+e^2 g-2 d e h\right )\right ) \operatorname {Subst}\left (\int \log \left (1-\frac {i c e e^{i x}}{c^2 d-c \sqrt {c^2 d^2-e^2}}\right ) \, dx,x,\sin ^{-1}(c x)\right )}{e^4}-\frac {\left (b \left (330 d^2+e^2 g-2 d e h\right )\right ) \operatorname {Subst}\left (\int \log \left (1-\frac {i c e e^{i x}}{c^2 d+c \sqrt {c^2 d^2-e^2}}\right ) \, dx,x,\sin ^{-1}(c x)\right )}{e^4}+\frac {\left (b c \left (110 d^3-e^3 f+d e^2 g-d^2 e h\right )\right ) \operatorname {Subst}\left (\int \frac {1}{-c^2 d^2+e^2-x^2} \, dx,x,\frac {e+c^2 d x}{\sqrt {1-c^2 x^2}}\right )}{e^4}\\ &=-\frac {b (495 d-2 e h) \sqrt {1-c^2 x^2}}{2 c e^3}+\frac {55 b (d+e x) \sqrt {1-c^2 x^2}}{2 c e^3}-\frac {55 b \sin ^{-1}(c x)}{2 c^2 e^2}-\frac {i b \left (330 d^2+e^2 g-2 d e h\right ) \sin ^{-1}(c x)^2}{2 e^4}-\frac {(220 d-e h) x \left (a+b \sin ^{-1}(c x)\right )}{e^3}+\frac {55 x^2 \left (a+b \sin ^{-1}(c x)\right )}{e^2}+\frac {\left (110 d^3-e^3 f+d e^2 g-d^2 e h\right ) \left (a+b \sin ^{-1}(c x)\right )}{e^4 (d+e x)}-\frac {b c \left (110 d^3-e^3 f+d e^2 g-d^2 e h\right ) \tan ^{-1}\left (\frac {e+c^2 d x}{\sqrt {c^2 d^2-e^2} \sqrt {1-c^2 x^2}}\right )}{e^4 \sqrt {c^2 d^2-e^2}}+\frac {b \left (330 d^2+e^2 g-2 d e h\right ) \sin ^{-1}(c x) \log \left (1-\frac {i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt {c^2 d^2-e^2}}\right )}{e^4}+\frac {b \left (330 d^2+e^2 g-2 d e h\right ) \sin ^{-1}(c x) \log \left (1-\frac {i e e^{i \sin ^{-1}(c x)}}{c d+\sqrt {c^2 d^2-e^2}}\right )}{e^4}-\frac {b \left (330 d^2+e^2 g-2 d e h\right ) \sin ^{-1}(c x) \log (d+e x)}{e^4}+\frac {\left (330 d^2+e^2 g-2 d e h\right ) \left (a+b \sin ^{-1}(c x)\right ) \log (d+e x)}{e^4}+\frac {\left (i b \left (330 d^2+e^2 g-2 d e h\right )\right ) \operatorname {Subst}\left (\int \frac {\log \left (1-\frac {i c e x}{c^2 d-c \sqrt {c^2 d^2-e^2}}\right )}{x} \, dx,x,e^{i \sin ^{-1}(c x)}\right )}{e^4}+\frac {\left (i b \left (330 d^2+e^2 g-2 d e h\right )\right ) \operatorname {Subst}\left (\int \frac {\log \left (1-\frac {i c e x}{c^2 d+c \sqrt {c^2 d^2-e^2}}\right )}{x} \, dx,x,e^{i \sin ^{-1}(c x)}\right )}{e^4}\\ &=-\frac {b (495 d-2 e h) \sqrt {1-c^2 x^2}}{2 c e^3}+\frac {55 b (d+e x) \sqrt {1-c^2 x^2}}{2 c e^3}-\frac {55 b \sin ^{-1}(c x)}{2 c^2 e^2}-\frac {i b \left (330 d^2+e^2 g-2 d e h\right ) \sin ^{-1}(c x)^2}{2 e^4}-\frac {(220 d-e h) x \left (a+b \sin ^{-1}(c x)\right )}{e^3}+\frac {55 x^2 \left (a+b \sin ^{-1}(c x)\right )}{e^2}+\frac {\left (110 d^3-e^3 f+d e^2 g-d^2 e h\right ) \left (a+b \sin ^{-1}(c x)\right )}{e^4 (d+e x)}-\frac {b c \left (110 d^3-e^3 f+d e^2 g-d^2 e h\right ) \tan ^{-1}\left (\frac {e+c^2 d x}{\sqrt {c^2 d^2-e^2} \sqrt {1-c^2 x^2}}\right )}{e^4 \sqrt {c^2 d^2-e^2}}+\frac {b \left (330 d^2+e^2 g-2 d e h\right ) \sin ^{-1}(c x) \log \left (1-\frac {i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt {c^2 d^2-e^2}}\right )}{e^4}+\frac {b \left (330 d^2+e^2 g-2 d e h\right ) \sin ^{-1}(c x) \log \left (1-\frac {i e e^{i \sin ^{-1}(c x)}}{c d+\sqrt {c^2 d^2-e^2}}\right )}{e^4}-\frac {b \left (330 d^2+e^2 g-2 d e h\right ) \sin ^{-1}(c x) \log (d+e x)}{e^4}+\frac {\left (330 d^2+e^2 g-2 d e h\right ) \left (a+b \sin ^{-1}(c x)\right ) \log (d+e x)}{e^4}-\frac {i b \left (330 d^2+e^2 g-2 d e h\right ) \text {Li}_2\left (\frac {i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt {c^2 d^2-e^2}}\right )}{e^4}-\frac {i b \left (330 d^2+e^2 g-2 d e h\right ) \text {Li}_2\left (\frac {i e e^{i \sin ^{-1}(c x)}}{c d+\sqrt {c^2 d^2-e^2}}\right )}{e^4}\\ \end {align*}
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Mathematica [A] time = 1.48, size = 515, normalized size = 0.83 \[ \frac {2 \log (d+e x) \left (a+b \sin ^{-1}(c x)\right ) \left (3 d^2 i-2 d e h+e^2 g\right )-\frac {2 \left (a+b \sin ^{-1}(c x)\right ) \left (d^3 (-i)+d^2 e h-d e^2 g+e^3 f\right )}{d+e x}+2 e x (e h-2 d i) \left (a+b \sin ^{-1}(c x)\right )+e^2 i x^2 \left (a+b \sin ^{-1}(c x)\right )-i b \left (3 d^2 i-2 d e h+e^2 g\right ) \left (2 \text {Li}_2\left (\frac {i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt {c^2 d^2-e^2}}\right )+2 \text {Li}_2\left (\frac {i e e^{i \sin ^{-1}(c x)}}{c d+\sqrt {c^2 d^2-e^2}}\right )+\sin ^{-1}(c x) \left (\sin ^{-1}(c x)+2 i \left (\log \left (1+\frac {i e e^{i \sin ^{-1}(c x)}}{\sqrt {c^2 d^2-e^2}-c d}\right )+\log \left (1-\frac {i e e^{i \sin ^{-1}(c x)}}{\sqrt {c^2 d^2-e^2}+c d}\right )\right )\right )\right )+\frac {2 b c \tan ^{-1}\left (\frac {c^2 d x+e}{\sqrt {1-c^2 x^2} \sqrt {c^2 d^2-e^2}}\right ) \left (d^3 (-i)+d^2 e h-d e^2 g+e^3 f\right )}{\sqrt {c^2 d^2-e^2}}+\frac {2 b e \sqrt {1-c^2 x^2} (e h-2 d i)}{c}+\frac {b e^2 i x \sqrt {1-c^2 x^2}}{2 c}-\frac {b e^2 i \sin ^{-1}(c x)}{2 c^2}-2 b \sin ^{-1}(c x) \log (d+e x) \left (3 d^2 i-2 d e h+e^2 g\right )}{2 e^4} \]
Antiderivative was successfully verified.
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fricas [F] time = 0.92, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {a i x^{3} + a h x^{2} + a g x + a f + {\left (b i x^{3} + b h x^{2} + b g x + b f\right )} \arcsin \left (c x\right )}{e^{2} x^{2} + 2 \, d e x + d^{2}}, x\right ) \]
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 \[ \int \frac {{\left (i x^{3} + h x^{2} + g x + f\right )} {\left (b \arcsin \left (c x\right ) + a\right )}}{{\left (e x + d\right )}^{2}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 1.62, size = 2921, normalized size = 4.73 \[ \text {output too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F(-2)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Exception raised: ValueError} \]
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 \[ \int \frac {\left (a+b\,\mathrm {asin}\left (c\,x\right )\right )\,\left (i\,x^3+h\,x^2+g\,x+f\right )}{{\left (d+e\,x\right )}^2} \,d x \]
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 \[ \int \frac {\left (a + b \operatorname {asin}{\left (c x \right )}\right ) \left (f + g x + h x^{2} + i x^{3}\right )}{\left (d + e x\right )^{2}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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