Optimal. Leaf size=701 \[ \frac {2 b c \left (c^2 d-e\right ) \sqrt {-1+c^2 x^2} \sqrt {d+e x^2}}{9 d^3 \sqrt {c^2 x^2}}-\frac {4 b c e \sqrt {-1+c^2 x^2} \sqrt {d+e x^2}}{3 d^3 \sqrt {c^2 x^2}}+\frac {b c \sqrt {-1+c^2 x^2} \sqrt {d+e x^2}}{9 d^2 x^2 \sqrt {c^2 x^2}}-\frac {a+b \sec ^{-1}(c x)}{3 d x^3 \sqrt {d+e x^2}}+\frac {4 e \left (a+b \sec ^{-1}(c x)\right )}{3 d^2 x \sqrt {d+e x^2}}+\frac {8 e^2 x \left (a+b \sec ^{-1}(c x)\right )}{3 d^3 \sqrt {d+e x^2}}-\frac {2 b c^2 \left (c^2 d-e\right ) x \sqrt {1-c^2 x^2} \sqrt {d+e x^2} E\left (\text {ArcSin}(c x)\left |-\frac {e}{c^2 d}\right .\right )}{9 d^3 \sqrt {c^2 x^2} \sqrt {-1+c^2 x^2} \sqrt {1+\frac {e x^2}{d}}}+\frac {4 b c^2 e x \sqrt {1-c^2 x^2} \sqrt {d+e x^2} E\left (\text {ArcSin}(c x)\left |-\frac {e}{c^2 d}\right .\right )}{3 d^3 \sqrt {c^2 x^2} \sqrt {-1+c^2 x^2} \sqrt {1+\frac {e x^2}{d}}}+\frac {b c^2 \left (2 c^2 d-e\right ) x \sqrt {1-c^2 x^2} \sqrt {1+\frac {e x^2}{d}} F\left (\text {ArcSin}(c x)\left |-\frac {e}{c^2 d}\right .\right )}{9 d^2 \sqrt {c^2 x^2} \sqrt {-1+c^2 x^2} \sqrt {d+e x^2}}-\frac {4 b c^2 e x \sqrt {1-c^2 x^2} \sqrt {1+\frac {e x^2}{d}} F\left (\text {ArcSin}(c x)\left |-\frac {e}{c^2 d}\right .\right )}{3 d^2 \sqrt {c^2 x^2} \sqrt {-1+c^2 x^2} \sqrt {d+e x^2}}-\frac {8 b e^2 x \sqrt {1-c^2 x^2} \sqrt {1+\frac {e x^2}{d}} F\left (\text {ArcSin}(c x)\left |-\frac {e}{c^2 d}\right .\right )}{3 d^3 \sqrt {c^2 x^2} \sqrt {-1+c^2 x^2} \sqrt {d+e x^2}} \]
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Rubi [A]
time = 1.04, antiderivative size = 701, normalized size of antiderivative = 1.00, number of steps
used = 25, number of rules used = 14, integrand size = 23, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.609, Rules used = {277, 197,
5346, 12, 6874, 432, 430, 491, 597, 538, 438, 437, 435, 507} \begin {gather*} \frac {8 e^2 x \left (a+b \sec ^{-1}(c x)\right )}{3 d^3 \sqrt {d+e x^2}}+\frac {4 e \left (a+b \sec ^{-1}(c x)\right )}{3 d^2 x \sqrt {d+e x^2}}-\frac {a+b \sec ^{-1}(c x)}{3 d x^3 \sqrt {d+e x^2}}-\frac {8 b e^2 x \sqrt {1-c^2 x^2} \sqrt {\frac {e x^2}{d}+1} F\left (\text {ArcSin}(c x)\left |-\frac {e}{c^2 d}\right .\right )}{3 d^3 \sqrt {c^2 x^2} \sqrt {c^2 x^2-1} \sqrt {d+e x^2}}-\frac {2 b c^2 x \sqrt {1-c^2 x^2} \left (c^2 d-e\right ) \sqrt {d+e x^2} E\left (\text {ArcSin}(c x)\left |-\frac {e}{c^2 d}\right .\right )}{9 d^3 \sqrt {c^2 x^2} \sqrt {c^2 x^2-1} \sqrt {\frac {e x^2}{d}+1}}+\frac {4 b c^2 e x \sqrt {1-c^2 x^2} \sqrt {d+e x^2} E\left (\text {ArcSin}(c x)\left |-\frac {e}{c^2 d}\right .\right )}{3 d^3 \sqrt {c^2 x^2} \sqrt {c^2 x^2-1} \sqrt {\frac {e x^2}{d}+1}}+\frac {b c^2 x \sqrt {1-c^2 x^2} \left (2 c^2 d-e\right ) \sqrt {\frac {e x^2}{d}+1} F\left (\text {ArcSin}(c x)\left |-\frac {e}{c^2 d}\right .\right )}{9 d^2 \sqrt {c^2 x^2} \sqrt {c^2 x^2-1} \sqrt {d+e x^2}}-\frac {4 b c^2 e x \sqrt {1-c^2 x^2} \sqrt {\frac {e x^2}{d}+1} F\left (\text {ArcSin}(c x)\left |-\frac {e}{c^2 d}\right .\right )}{3 d^2 \sqrt {c^2 x^2} \sqrt {c^2 x^2-1} \sqrt {d+e x^2}}+\frac {2 b c \sqrt {c^2 x^2-1} \left (c^2 d-e\right ) \sqrt {d+e x^2}}{9 d^3 \sqrt {c^2 x^2}}-\frac {4 b c e \sqrt {c^2 x^2-1} \sqrt {d+e x^2}}{3 d^3 \sqrt {c^2 x^2}}+\frac {b c \sqrt {c^2 x^2-1} \sqrt {d+e x^2}}{9 d^2 x^2 \sqrt {c^2 x^2}} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 197
Rule 277
Rule 430
Rule 432
Rule 435
Rule 437
Rule 438
Rule 491
Rule 507
Rule 538
Rule 597
Rule 5346
Rule 6874
Rubi steps
\begin {align*} \int \frac {a+b \sec ^{-1}(c x)}{x^4 \left (d+e x^2\right )^{3/2}} \, dx &=-\frac {a+b \sec ^{-1}(c x)}{3 d x^3 \sqrt {d+e x^2}}+\frac {4 e \left (a+b \sec ^{-1}(c x)\right )}{3 d^2 x \sqrt {d+e x^2}}+\frac {8 e^2 x \left (a+b \sec ^{-1}(c x)\right )}{3 d^3 \sqrt {d+e x^2}}-\frac {(b c x) \int \frac {-d^2+4 d e x^2+8 e^2 x^4}{3 d^3 x^4 \sqrt {-1+c^2 x^2} \sqrt {d+e x^2}} \, dx}{\sqrt {c^2 x^2}}\\ &=-\frac {a+b \sec ^{-1}(c x)}{3 d x^3 \sqrt {d+e x^2}}+\frac {4 e \left (a+b \sec ^{-1}(c x)\right )}{3 d^2 x \sqrt {d+e x^2}}+\frac {8 e^2 x \left (a+b \sec ^{-1}(c x)\right )}{3 d^3 \sqrt {d+e x^2}}-\frac {(b c x) \int \frac {-d^2+4 d e x^2+8 e^2 x^4}{x^4 \sqrt {-1+c^2 x^2} \sqrt {d+e x^2}} \, dx}{3 d^3 \sqrt {c^2 x^2}}\\ &=-\frac {a+b \sec ^{-1}(c x)}{3 d x^3 \sqrt {d+e x^2}}+\frac {4 e \left (a+b \sec ^{-1}(c x)\right )}{3 d^2 x \sqrt {d+e x^2}}+\frac {8 e^2 x \left (a+b \sec ^{-1}(c x)\right )}{3 d^3 \sqrt {d+e x^2}}-\frac {(b c x) \int \left (\frac {8 e^2}{\sqrt {-1+c^2 x^2} \sqrt {d+e x^2}}-\frac {d^2}{x^4 \sqrt {-1+c^2 x^2} \sqrt {d+e x^2}}+\frac {4 d e}{x^2 \sqrt {-1+c^2 x^2} \sqrt {d+e x^2}}\right ) \, dx}{3 d^3 \sqrt {c^2 x^2}}\\ &=-\frac {a+b \sec ^{-1}(c x)}{3 d x^3 \sqrt {d+e x^2}}+\frac {4 e \left (a+b \sec ^{-1}(c x)\right )}{3 d^2 x \sqrt {d+e x^2}}+\frac {8 e^2 x \left (a+b \sec ^{-1}(c x)\right )}{3 d^3 \sqrt {d+e x^2}}+\frac {(b c x) \int \frac {1}{x^4 \sqrt {-1+c^2 x^2} \sqrt {d+e x^2}} \, dx}{3 d \sqrt {c^2 x^2}}-\frac {(4 b c e x) \int \frac {1}{x^2 \sqrt {-1+c^2 x^2} \sqrt {d+e x^2}} \, dx}{3 d^2 \sqrt {c^2 x^2}}-\frac {\left (8 b c e^2 x\right ) \int \frac {1}{\sqrt {-1+c^2 x^2} \sqrt {d+e x^2}} \, dx}{3 d^3 \sqrt {c^2 x^2}}\\ &=-\frac {4 b c e \sqrt {-1+c^2 x^2} \sqrt {d+e x^2}}{3 d^3 \sqrt {c^2 x^2}}+\frac {b c \sqrt {-1+c^2 x^2} \sqrt {d+e x^2}}{9 d^2 x^2 \sqrt {c^2 x^2}}-\frac {a+b \sec ^{-1}(c x)}{3 d x^3 \sqrt {d+e x^2}}+\frac {4 e \left (a+b \sec ^{-1}(c x)\right )}{3 d^2 x \sqrt {d+e x^2}}+\frac {8 e^2 x \left (a+b \sec ^{-1}(c x)\right )}{3 d^3 \sqrt {d+e x^2}}-\frac {(b c x) \int \frac {-2 \left (c^2 d-e\right )-c^2 e x^2}{x^2 \sqrt {-1+c^2 x^2} \sqrt {d+e x^2}} \, dx}{9 d^2 \sqrt {c^2 x^2}}+\frac {(4 b c e x) \int \frac {c^2 e x^2}{\sqrt {-1+c^2 x^2} \sqrt {d+e x^2}} \, dx}{3 d^3 \sqrt {c^2 x^2}}-\frac {\left (8 b c e^2 x \sqrt {1+\frac {e x^2}{d}}\right ) \int \frac {1}{\sqrt {-1+c^2 x^2} \sqrt {1+\frac {e x^2}{d}}} \, dx}{3 d^3 \sqrt {c^2 x^2} \sqrt {d+e x^2}}\\ &=\frac {2 b c \left (c^2 d-e\right ) \sqrt {-1+c^2 x^2} \sqrt {d+e x^2}}{9 d^3 \sqrt {c^2 x^2}}-\frac {4 b c e \sqrt {-1+c^2 x^2} \sqrt {d+e x^2}}{3 d^3 \sqrt {c^2 x^2}}+\frac {b c \sqrt {-1+c^2 x^2} \sqrt {d+e x^2}}{9 d^2 x^2 \sqrt {c^2 x^2}}-\frac {a+b \sec ^{-1}(c x)}{3 d x^3 \sqrt {d+e x^2}}+\frac {4 e \left (a+b \sec ^{-1}(c x)\right )}{3 d^2 x \sqrt {d+e x^2}}+\frac {8 e^2 x \left (a+b \sec ^{-1}(c x)\right )}{3 d^3 \sqrt {d+e x^2}}-\frac {(b c x) \int \frac {-c^2 d e+2 c^2 \left (c^2 d-e\right ) e x^2}{\sqrt {-1+c^2 x^2} \sqrt {d+e x^2}} \, dx}{9 d^3 \sqrt {c^2 x^2}}+\frac {\left (4 b c^3 e^2 x\right ) \int \frac {x^2}{\sqrt {-1+c^2 x^2} \sqrt {d+e x^2}} \, dx}{3 d^3 \sqrt {c^2 x^2}}-\frac {\left (8 b c e^2 x \sqrt {1-c^2 x^2} \sqrt {1+\frac {e x^2}{d}}\right ) \int \frac {1}{\sqrt {1-c^2 x^2} \sqrt {1+\frac {e x^2}{d}}} \, dx}{3 d^3 \sqrt {c^2 x^2} \sqrt {-1+c^2 x^2} \sqrt {d+e x^2}}\\ &=\frac {2 b c \left (c^2 d-e\right ) \sqrt {-1+c^2 x^2} \sqrt {d+e x^2}}{9 d^3 \sqrt {c^2 x^2}}-\frac {4 b c e \sqrt {-1+c^2 x^2} \sqrt {d+e x^2}}{3 d^3 \sqrt {c^2 x^2}}+\frac {b c \sqrt {-1+c^2 x^2} \sqrt {d+e x^2}}{9 d^2 x^2 \sqrt {c^2 x^2}}-\frac {a+b \sec ^{-1}(c x)}{3 d x^3 \sqrt {d+e x^2}}+\frac {4 e \left (a+b \sec ^{-1}(c x)\right )}{3 d^2 x \sqrt {d+e x^2}}+\frac {8 e^2 x \left (a+b \sec ^{-1}(c x)\right )}{3 d^3 \sqrt {d+e x^2}}-\frac {8 b e^2 x \sqrt {1-c^2 x^2} \sqrt {1+\frac {e x^2}{d}} F\left (\sin ^{-1}(c x)|-\frac {e}{c^2 d}\right )}{3 d^3 \sqrt {c^2 x^2} \sqrt {-1+c^2 x^2} \sqrt {d+e x^2}}-\frac {\left (2 b c^3 \left (c^2 d-e\right ) x\right ) \int \frac {\sqrt {d+e x^2}}{\sqrt {-1+c^2 x^2}} \, dx}{9 d^3 \sqrt {c^2 x^2}}+\frac {\left (b c^3 \left (2 c^2 d-e\right ) x\right ) \int \frac {1}{\sqrt {-1+c^2 x^2} \sqrt {d+e x^2}} \, dx}{9 d^2 \sqrt {c^2 x^2}}+\frac {\left (4 b c^3 e x\right ) \int \frac {\sqrt {d+e x^2}}{\sqrt {-1+c^2 x^2}} \, dx}{3 d^3 \sqrt {c^2 x^2}}-\frac {\left (4 b c^3 e x\right ) \int \frac {1}{\sqrt {-1+c^2 x^2} \sqrt {d+e x^2}} \, dx}{3 d^2 \sqrt {c^2 x^2}}\\ &=\frac {2 b c \left (c^2 d-e\right ) \sqrt {-1+c^2 x^2} \sqrt {d+e x^2}}{9 d^3 \sqrt {c^2 x^2}}-\frac {4 b c e \sqrt {-1+c^2 x^2} \sqrt {d+e x^2}}{3 d^3 \sqrt {c^2 x^2}}+\frac {b c \sqrt {-1+c^2 x^2} \sqrt {d+e x^2}}{9 d^2 x^2 \sqrt {c^2 x^2}}-\frac {a+b \sec ^{-1}(c x)}{3 d x^3 \sqrt {d+e x^2}}+\frac {4 e \left (a+b \sec ^{-1}(c x)\right )}{3 d^2 x \sqrt {d+e x^2}}+\frac {8 e^2 x \left (a+b \sec ^{-1}(c x)\right )}{3 d^3 \sqrt {d+e x^2}}-\frac {8 b e^2 x \sqrt {1-c^2 x^2} \sqrt {1+\frac {e x^2}{d}} F\left (\sin ^{-1}(c x)|-\frac {e}{c^2 d}\right )}{3 d^3 \sqrt {c^2 x^2} \sqrt {-1+c^2 x^2} \sqrt {d+e x^2}}-\frac {\left (2 b c^3 \left (c^2 d-e\right ) x \sqrt {1-c^2 x^2}\right ) \int \frac {\sqrt {d+e x^2}}{\sqrt {1-c^2 x^2}} \, dx}{9 d^3 \sqrt {c^2 x^2} \sqrt {-1+c^2 x^2}}+\frac {\left (4 b c^3 e x \sqrt {1-c^2 x^2}\right ) \int \frac {\sqrt {d+e x^2}}{\sqrt {1-c^2 x^2}} \, dx}{3 d^3 \sqrt {c^2 x^2} \sqrt {-1+c^2 x^2}}+\frac {\left (b c^3 \left (2 c^2 d-e\right ) x \sqrt {1+\frac {e x^2}{d}}\right ) \int \frac {1}{\sqrt {-1+c^2 x^2} \sqrt {1+\frac {e x^2}{d}}} \, dx}{9 d^2 \sqrt {c^2 x^2} \sqrt {d+e x^2}}-\frac {\left (4 b c^3 e x \sqrt {1+\frac {e x^2}{d}}\right ) \int \frac {1}{\sqrt {-1+c^2 x^2} \sqrt {1+\frac {e x^2}{d}}} \, dx}{3 d^2 \sqrt {c^2 x^2} \sqrt {d+e x^2}}\\ &=\frac {2 b c \left (c^2 d-e\right ) \sqrt {-1+c^2 x^2} \sqrt {d+e x^2}}{9 d^3 \sqrt {c^2 x^2}}-\frac {4 b c e \sqrt {-1+c^2 x^2} \sqrt {d+e x^2}}{3 d^3 \sqrt {c^2 x^2}}+\frac {b c \sqrt {-1+c^2 x^2} \sqrt {d+e x^2}}{9 d^2 x^2 \sqrt {c^2 x^2}}-\frac {a+b \sec ^{-1}(c x)}{3 d x^3 \sqrt {d+e x^2}}+\frac {4 e \left (a+b \sec ^{-1}(c x)\right )}{3 d^2 x \sqrt {d+e x^2}}+\frac {8 e^2 x \left (a+b \sec ^{-1}(c x)\right )}{3 d^3 \sqrt {d+e x^2}}-\frac {8 b e^2 x \sqrt {1-c^2 x^2} \sqrt {1+\frac {e x^2}{d}} F\left (\sin ^{-1}(c x)|-\frac {e}{c^2 d}\right )}{3 d^3 \sqrt {c^2 x^2} \sqrt {-1+c^2 x^2} \sqrt {d+e x^2}}-\frac {\left (2 b c^3 \left (c^2 d-e\right ) x \sqrt {1-c^2 x^2} \sqrt {d+e x^2}\right ) \int \frac {\sqrt {1+\frac {e x^2}{d}}}{\sqrt {1-c^2 x^2}} \, dx}{9 d^3 \sqrt {c^2 x^2} \sqrt {-1+c^2 x^2} \sqrt {1+\frac {e x^2}{d}}}+\frac {\left (4 b c^3 e x \sqrt {1-c^2 x^2} \sqrt {d+e x^2}\right ) \int \frac {\sqrt {1+\frac {e x^2}{d}}}{\sqrt {1-c^2 x^2}} \, dx}{3 d^3 \sqrt {c^2 x^2} \sqrt {-1+c^2 x^2} \sqrt {1+\frac {e x^2}{d}}}+\frac {\left (b c^3 \left (2 c^2 d-e\right ) x \sqrt {1-c^2 x^2} \sqrt {1+\frac {e x^2}{d}}\right ) \int \frac {1}{\sqrt {1-c^2 x^2} \sqrt {1+\frac {e x^2}{d}}} \, dx}{9 d^2 \sqrt {c^2 x^2} \sqrt {-1+c^2 x^2} \sqrt {d+e x^2}}-\frac {\left (4 b c^3 e x \sqrt {1-c^2 x^2} \sqrt {1+\frac {e x^2}{d}}\right ) \int \frac {1}{\sqrt {1-c^2 x^2} \sqrt {1+\frac {e x^2}{d}}} \, dx}{3 d^2 \sqrt {c^2 x^2} \sqrt {-1+c^2 x^2} \sqrt {d+e x^2}}\\ &=\frac {2 b c \left (c^2 d-e\right ) \sqrt {-1+c^2 x^2} \sqrt {d+e x^2}}{9 d^3 \sqrt {c^2 x^2}}-\frac {4 b c e \sqrt {-1+c^2 x^2} \sqrt {d+e x^2}}{3 d^3 \sqrt {c^2 x^2}}+\frac {b c \sqrt {-1+c^2 x^2} \sqrt {d+e x^2}}{9 d^2 x^2 \sqrt {c^2 x^2}}-\frac {a+b \sec ^{-1}(c x)}{3 d x^3 \sqrt {d+e x^2}}+\frac {4 e \left (a+b \sec ^{-1}(c x)\right )}{3 d^2 x \sqrt {d+e x^2}}+\frac {8 e^2 x \left (a+b \sec ^{-1}(c x)\right )}{3 d^3 \sqrt {d+e x^2}}-\frac {2 b c^2 \left (c^2 d-e\right ) x \sqrt {1-c^2 x^2} \sqrt {d+e x^2} E\left (\sin ^{-1}(c x)|-\frac {e}{c^2 d}\right )}{9 d^3 \sqrt {c^2 x^2} \sqrt {-1+c^2 x^2} \sqrt {1+\frac {e x^2}{d}}}+\frac {4 b c^2 e x \sqrt {1-c^2 x^2} \sqrt {d+e x^2} E\left (\sin ^{-1}(c x)|-\frac {e}{c^2 d}\right )}{3 d^3 \sqrt {c^2 x^2} \sqrt {-1+c^2 x^2} \sqrt {1+\frac {e x^2}{d}}}+\frac {b c^2 \left (2 c^2 d-e\right ) x \sqrt {1-c^2 x^2} \sqrt {1+\frac {e x^2}{d}} F\left (\sin ^{-1}(c x)|-\frac {e}{c^2 d}\right )}{9 d^2 \sqrt {c^2 x^2} \sqrt {-1+c^2 x^2} \sqrt {d+e x^2}}-\frac {4 b c^2 e x \sqrt {1-c^2 x^2} \sqrt {1+\frac {e x^2}{d}} F\left (\sin ^{-1}(c x)|-\frac {e}{c^2 d}\right )}{3 d^2 \sqrt {c^2 x^2} \sqrt {-1+c^2 x^2} \sqrt {d+e x^2}}-\frac {8 b e^2 x \sqrt {1-c^2 x^2} \sqrt {1+\frac {e x^2}{d}} F\left (\sin ^{-1}(c x)|-\frac {e}{c^2 d}\right )}{3 d^3 \sqrt {c^2 x^2} \sqrt {-1+c^2 x^2} \sqrt {d+e x^2}}\\ \end {align*}
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Mathematica [C] Result contains complex when optimal does not.
time = 5.41, size = 292, normalized size = 0.42 \begin {gather*} \frac {-3 a \left (d^2-4 d e x^2-8 e^2 x^4\right )+b c \sqrt {1-\frac {1}{c^2 x^2}} x \left (-14 e^2 x^4+d e x^2 \left (-13+2 c^2 x^2\right )+d^2 \left (1+2 c^2 x^2\right )\right )-3 b \left (d^2-4 d e x^2-8 e^2 x^4\right ) \sec ^{-1}(c x)}{9 d^3 x^3 \sqrt {d+e x^2}}-\frac {i b c \sqrt {1-\frac {1}{c^2 x^2}} x \sqrt {1+\frac {e x^2}{d}} \left (2 c^2 d \left (c^2 d-7 e\right ) E\left (i \sinh ^{-1}\left (\sqrt {-c^2} x\right )|-\frac {e}{c^2 d}\right )+\left (-2 c^4 d^2+13 c^2 d e+24 e^2\right ) F\left (i \sinh ^{-1}\left (\sqrt {-c^2} x\right )|-\frac {e}{c^2 d}\right )\right )}{9 \sqrt {-c^2} d^3 \sqrt {1-c^2 x^2} \sqrt {d+e x^2}} \end {gather*}
Antiderivative was successfully verified.
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Maple [F]
time = 2.79, size = 0, normalized size = 0.00 \[\int \frac {a +b \,\mathrm {arcsec}\left (c x \right )}{x^{4} \left (e \,x^{2}+d \right )^{\frac {3}{2}}}\, dx\]
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 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [F(-2)]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: TypeError} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] Timed out
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
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 \begin {gather*} \text {could not integrate} \end {gather*}
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 \begin {gather*} \int \frac {a+b\,\mathrm {acos}\left (\frac {1}{c\,x}\right )}{x^4\,{\left (e\,x^2+d\right )}^{3/2}} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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