Optimal. Leaf size=535 \[ -\frac {(5 b c-4 a d) \sqrt {c-d x^2}}{2 a^2 c (b c-a d) e \sqrt {e x}}+\frac {b \sqrt {c-d x^2}}{2 a (b c-a d) e \sqrt {e x} \left (a-b x^2\right )}-\frac {\sqrt [4]{d} (5 b c-4 a d) \sqrt {1-\frac {d x^2}{c}} E\left (\left .\sin ^{-1}\left (\frac {\sqrt [4]{d} \sqrt {e x}}{\sqrt [4]{c} \sqrt {e}}\right )\right |-1\right )}{2 a^2 \sqrt [4]{c} (b c-a d) e^{3/2} \sqrt {c-d x^2}}+\frac {\sqrt [4]{d} (5 b c-4 a d) \sqrt {1-\frac {d x^2}{c}} F\left (\left .\sin ^{-1}\left (\frac {\sqrt [4]{d} \sqrt {e x}}{\sqrt [4]{c} \sqrt {e}}\right )\right |-1\right )}{2 a^2 \sqrt [4]{c} (b c-a d) e^{3/2} \sqrt {c-d x^2}}-\frac {\sqrt {b} \sqrt [4]{c} (5 b c-7 a d) \sqrt {1-\frac {d x^2}{c}} \Pi \left (-\frac {\sqrt {b} \sqrt {c}}{\sqrt {a} \sqrt {d}};\left .\sin ^{-1}\left (\frac {\sqrt [4]{d} \sqrt {e x}}{\sqrt [4]{c} \sqrt {e}}\right )\right |-1\right )}{4 a^{5/2} \sqrt [4]{d} (b c-a d) e^{3/2} \sqrt {c-d x^2}}+\frac {\sqrt {b} \sqrt [4]{c} (5 b c-7 a d) \sqrt {1-\frac {d x^2}{c}} \Pi \left (\frac {\sqrt {b} \sqrt {c}}{\sqrt {a} \sqrt {d}};\left .\sin ^{-1}\left (\frac {\sqrt [4]{d} \sqrt {e x}}{\sqrt [4]{c} \sqrt {e}}\right )\right |-1\right )}{4 a^{5/2} \sqrt [4]{d} (b c-a d) e^{3/2} \sqrt {c-d x^2}} \]
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Rubi [A]
time = 0.75, antiderivative size = 535, normalized size of antiderivative = 1.00, number of steps
used = 16, number of rules used = 13, integrand size = 30, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.433, Rules used = {477, 483,
597, 598, 313, 230, 227, 1214, 1213, 435, 504, 1233, 1232} \begin {gather*} -\frac {\sqrt {b} \sqrt [4]{c} \sqrt {1-\frac {d x^2}{c}} (5 b c-7 a d) \Pi \left (-\frac {\sqrt {b} \sqrt {c}}{\sqrt {a} \sqrt {d}};\left .\text {ArcSin}\left (\frac {\sqrt [4]{d} \sqrt {e x}}{\sqrt [4]{c} \sqrt {e}}\right )\right |-1\right )}{4 a^{5/2} \sqrt [4]{d} e^{3/2} \sqrt {c-d x^2} (b c-a d)}+\frac {\sqrt {b} \sqrt [4]{c} \sqrt {1-\frac {d x^2}{c}} (5 b c-7 a d) \Pi \left (\frac {\sqrt {b} \sqrt {c}}{\sqrt {a} \sqrt {d}};\left .\text {ArcSin}\left (\frac {\sqrt [4]{d} \sqrt {e x}}{\sqrt [4]{c} \sqrt {e}}\right )\right |-1\right )}{4 a^{5/2} \sqrt [4]{d} e^{3/2} \sqrt {c-d x^2} (b c-a d)}+\frac {\sqrt [4]{d} \sqrt {1-\frac {d x^2}{c}} (5 b c-4 a d) F\left (\left .\text {ArcSin}\left (\frac {\sqrt [4]{d} \sqrt {e x}}{\sqrt [4]{c} \sqrt {e}}\right )\right |-1\right )}{2 a^2 \sqrt [4]{c} e^{3/2} \sqrt {c-d x^2} (b c-a d)}-\frac {\sqrt [4]{d} \sqrt {1-\frac {d x^2}{c}} (5 b c-4 a d) E\left (\left .\text {ArcSin}\left (\frac {\sqrt [4]{d} \sqrt {e x}}{\sqrt [4]{c} \sqrt {e}}\right )\right |-1\right )}{2 a^2 \sqrt [4]{c} e^{3/2} \sqrt {c-d x^2} (b c-a d)}-\frac {\sqrt {c-d x^2} (5 b c-4 a d)}{2 a^2 c e \sqrt {e x} (b c-a d)}+\frac {b \sqrt {c-d x^2}}{2 a e \sqrt {e x} \left (a-b x^2\right ) (b c-a d)} \end {gather*}
Antiderivative was successfully verified.
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Rule 227
Rule 230
Rule 313
Rule 435
Rule 477
Rule 483
Rule 504
Rule 597
Rule 598
Rule 1213
Rule 1214
Rule 1232
Rule 1233
Rubi steps
\begin {align*} \int \frac {1}{(e x)^{3/2} \left (a-b x^2\right )^2 \sqrt {c-d x^2}} \, dx &=\frac {2 \text {Subst}\left (\int \frac {1}{x^2 \left (a-\frac {b x^4}{e^2}\right )^2 \sqrt {c-\frac {d x^4}{e^2}}} \, dx,x,\sqrt {e x}\right )}{e}\\ &=\frac {b \sqrt {c-d x^2}}{2 a (b c-a d) e \sqrt {e x} \left (a-b x^2\right )}+\frac {e \text {Subst}\left (\int \frac {\frac {5 b c-4 a d}{e^2}-\frac {3 b d x^4}{e^4}}{x^2 \left (a-\frac {b x^4}{e^2}\right ) \sqrt {c-\frac {d x^4}{e^2}}} \, dx,x,\sqrt {e x}\right )}{2 a (b c-a d)}\\ &=-\frac {(5 b c-4 a d) \sqrt {c-d x^2}}{2 a^2 c (b c-a d) e \sqrt {e x}}+\frac {b \sqrt {c-d x^2}}{2 a (b c-a d) e \sqrt {e x} \left (a-b x^2\right )}-\frac {e \text {Subst}\left (\int \frac {x^2 \left (-\frac {(b c-2 a d) (5 b c-2 a d)}{e^4}-\frac {b d (5 b c-4 a d) x^4}{e^6}\right )}{\left (a-\frac {b x^4}{e^2}\right ) \sqrt {c-\frac {d x^4}{e^2}}} \, dx,x,\sqrt {e x}\right )}{2 a^2 c (b c-a d)}\\ &=-\frac {(5 b c-4 a d) \sqrt {c-d x^2}}{2 a^2 c (b c-a d) e \sqrt {e x}}+\frac {b \sqrt {c-d x^2}}{2 a (b c-a d) e \sqrt {e x} \left (a-b x^2\right )}-\frac {e \text {Subst}\left (\int \left (\frac {d (5 b c-4 a d) x^2}{e^4 \sqrt {c-\frac {d x^4}{e^2}}}-\frac {\left (5 b^2 c^2-7 a b c d\right ) x^2}{e^4 \left (a-\frac {b x^4}{e^2}\right ) \sqrt {c-\frac {d x^4}{e^2}}}\right ) \, dx,x,\sqrt {e x}\right )}{2 a^2 c (b c-a d)}\\ &=-\frac {(5 b c-4 a d) \sqrt {c-d x^2}}{2 a^2 c (b c-a d) e \sqrt {e x}}+\frac {b \sqrt {c-d x^2}}{2 a (b c-a d) e \sqrt {e x} \left (a-b x^2\right )}+\frac {(b (5 b c-7 a d)) \text {Subst}\left (\int \frac {x^2}{\left (a-\frac {b x^4}{e^2}\right ) \sqrt {c-\frac {d x^4}{e^2}}} \, dx,x,\sqrt {e x}\right )}{2 a^2 (b c-a d) e^3}-\frac {(d (5 b c-4 a d)) \text {Subst}\left (\int \frac {x^2}{\sqrt {c-\frac {d x^4}{e^2}}} \, dx,x,\sqrt {e x}\right )}{2 a^2 c (b c-a d) e^3}\\ &=-\frac {(5 b c-4 a d) \sqrt {c-d x^2}}{2 a^2 c (b c-a d) e \sqrt {e x}}+\frac {b \sqrt {c-d x^2}}{2 a (b c-a d) e \sqrt {e x} \left (a-b x^2\right )}+\frac {\left (\sqrt {d} (5 b c-4 a d)\right ) \text {Subst}\left (\int \frac {1}{\sqrt {c-\frac {d x^4}{e^2}}} \, dx,x,\sqrt {e x}\right )}{2 a^2 \sqrt {c} (b c-a d) e^2}-\frac {\left (\sqrt {d} (5 b c-4 a d)\right ) \text {Subst}\left (\int \frac {1+\frac {\sqrt {d} x^2}{\sqrt {c} e}}{\sqrt {c-\frac {d x^4}{e^2}}} \, dx,x,\sqrt {e x}\right )}{2 a^2 \sqrt {c} (b c-a d) e^2}+\frac {\left (\sqrt {b} (5 b c-7 a d)\right ) \text {Subst}\left (\int \frac {1}{\left (\sqrt {a} e-\sqrt {b} x^2\right ) \sqrt {c-\frac {d x^4}{e^2}}} \, dx,x,\sqrt {e x}\right )}{4 a^2 (b c-a d) e}-\frac {\left (\sqrt {b} (5 b c-7 a d)\right ) \text {Subst}\left (\int \frac {1}{\left (\sqrt {a} e+\sqrt {b} x^2\right ) \sqrt {c-\frac {d x^4}{e^2}}} \, dx,x,\sqrt {e x}\right )}{4 a^2 (b c-a d) e}\\ &=-\frac {(5 b c-4 a d) \sqrt {c-d x^2}}{2 a^2 c (b c-a d) e \sqrt {e x}}+\frac {b \sqrt {c-d x^2}}{2 a (b c-a d) e \sqrt {e x} \left (a-b x^2\right )}+\frac {\left (\sqrt {d} (5 b c-4 a d) \sqrt {1-\frac {d x^2}{c}}\right ) \text {Subst}\left (\int \frac {1}{\sqrt {1-\frac {d x^4}{c e^2}}} \, dx,x,\sqrt {e x}\right )}{2 a^2 \sqrt {c} (b c-a d) e^2 \sqrt {c-d x^2}}-\frac {\left (\sqrt {d} (5 b c-4 a d) \sqrt {1-\frac {d x^2}{c}}\right ) \text {Subst}\left (\int \frac {1+\frac {\sqrt {d} x^2}{\sqrt {c} e}}{\sqrt {1-\frac {d x^4}{c e^2}}} \, dx,x,\sqrt {e x}\right )}{2 a^2 \sqrt {c} (b c-a d) e^2 \sqrt {c-d x^2}}+\frac {\left (\sqrt {b} (5 b c-7 a d) \sqrt {1-\frac {d x^2}{c}}\right ) \text {Subst}\left (\int \frac {1}{\left (\sqrt {a} e-\sqrt {b} x^2\right ) \sqrt {1-\frac {d x^4}{c e^2}}} \, dx,x,\sqrt {e x}\right )}{4 a^2 (b c-a d) e \sqrt {c-d x^2}}-\frac {\left (\sqrt {b} (5 b c-7 a d) \sqrt {1-\frac {d x^2}{c}}\right ) \text {Subst}\left (\int \frac {1}{\left (\sqrt {a} e+\sqrt {b} x^2\right ) \sqrt {1-\frac {d x^4}{c e^2}}} \, dx,x,\sqrt {e x}\right )}{4 a^2 (b c-a d) e \sqrt {c-d x^2}}\\ &=-\frac {(5 b c-4 a d) \sqrt {c-d x^2}}{2 a^2 c (b c-a d) e \sqrt {e x}}+\frac {b \sqrt {c-d x^2}}{2 a (b c-a d) e \sqrt {e x} \left (a-b x^2\right )}+\frac {\sqrt [4]{d} (5 b c-4 a d) \sqrt {1-\frac {d x^2}{c}} F\left (\left .\sin ^{-1}\left (\frac {\sqrt [4]{d} \sqrt {e x}}{\sqrt [4]{c} \sqrt {e}}\right )\right |-1\right )}{2 a^2 \sqrt [4]{c} (b c-a d) e^{3/2} \sqrt {c-d x^2}}-\frac {\sqrt {b} \sqrt [4]{c} (5 b c-7 a d) \sqrt {1-\frac {d x^2}{c}} \Pi \left (-\frac {\sqrt {b} \sqrt {c}}{\sqrt {a} \sqrt {d}};\left .\sin ^{-1}\left (\frac {\sqrt [4]{d} \sqrt {e x}}{\sqrt [4]{c} \sqrt {e}}\right )\right |-1\right )}{4 a^{5/2} \sqrt [4]{d} (b c-a d) e^{3/2} \sqrt {c-d x^2}}+\frac {\sqrt {b} \sqrt [4]{c} (5 b c-7 a d) \sqrt {1-\frac {d x^2}{c}} \Pi \left (\frac {\sqrt {b} \sqrt {c}}{\sqrt {a} \sqrt {d}};\left .\sin ^{-1}\left (\frac {\sqrt [4]{d} \sqrt {e x}}{\sqrt [4]{c} \sqrt {e}}\right )\right |-1\right )}{4 a^{5/2} \sqrt [4]{d} (b c-a d) e^{3/2} \sqrt {c-d x^2}}-\frac {\left (\sqrt {d} (5 b c-4 a d) \sqrt {1-\frac {d x^2}{c}}\right ) \text {Subst}\left (\int \frac {\sqrt {1+\frac {\sqrt {d} x^2}{\sqrt {c} e}}}{\sqrt {1-\frac {\sqrt {d} x^2}{\sqrt {c} e}}} \, dx,x,\sqrt {e x}\right )}{2 a^2 \sqrt {c} (b c-a d) e^2 \sqrt {c-d x^2}}\\ &=-\frac {(5 b c-4 a d) \sqrt {c-d x^2}}{2 a^2 c (b c-a d) e \sqrt {e x}}+\frac {b \sqrt {c-d x^2}}{2 a (b c-a d) e \sqrt {e x} \left (a-b x^2\right )}-\frac {\sqrt [4]{d} (5 b c-4 a d) \sqrt {1-\frac {d x^2}{c}} E\left (\left .\sin ^{-1}\left (\frac {\sqrt [4]{d} \sqrt {e x}}{\sqrt [4]{c} \sqrt {e}}\right )\right |-1\right )}{2 a^2 \sqrt [4]{c} (b c-a d) e^{3/2} \sqrt {c-d x^2}}+\frac {\sqrt [4]{d} (5 b c-4 a d) \sqrt {1-\frac {d x^2}{c}} F\left (\left .\sin ^{-1}\left (\frac {\sqrt [4]{d} \sqrt {e x}}{\sqrt [4]{c} \sqrt {e}}\right )\right |-1\right )}{2 a^2 \sqrt [4]{c} (b c-a d) e^{3/2} \sqrt {c-d x^2}}-\frac {\sqrt {b} \sqrt [4]{c} (5 b c-7 a d) \sqrt {1-\frac {d x^2}{c}} \Pi \left (-\frac {\sqrt {b} \sqrt {c}}{\sqrt {a} \sqrt {d}};\left .\sin ^{-1}\left (\frac {\sqrt [4]{d} \sqrt {e x}}{\sqrt [4]{c} \sqrt {e}}\right )\right |-1\right )}{4 a^{5/2} \sqrt [4]{d} (b c-a d) e^{3/2} \sqrt {c-d x^2}}+\frac {\sqrt {b} \sqrt [4]{c} (5 b c-7 a d) \sqrt {1-\frac {d x^2}{c}} \Pi \left (\frac {\sqrt {b} \sqrt {c}}{\sqrt {a} \sqrt {d}};\left .\sin ^{-1}\left (\frac {\sqrt [4]{d} \sqrt {e x}}{\sqrt [4]{c} \sqrt {e}}\right )\right |-1\right )}{4 a^{5/2} \sqrt [4]{d} (b c-a d) e^{3/2} \sqrt {c-d x^2}}\\ \end {align*}
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Mathematica [C] Result contains higher order function than in optimal. Order 6 vs. order 4 in
optimal.
time = 10.23, size = 235, normalized size = 0.44 \begin {gather*} \frac {x \left (-21 a \left (c-d x^2\right ) \left (4 a^2 d+5 b^2 c x^2-4 a b \left (c+d x^2\right )\right )+7 \left (5 b^2 c^2-12 a b c d+4 a^2 d^2\right ) x^2 \left (-a+b x^2\right ) \sqrt {1-\frac {d x^2}{c}} F_1\left (\frac {3}{4};\frac {1}{2},1;\frac {7}{4};\frac {d x^2}{c},\frac {b x^2}{a}\right )+3 b d (-5 b c+4 a d) x^4 \left (a-b x^2\right ) \sqrt {1-\frac {d x^2}{c}} F_1\left (\frac {7}{4};\frac {1}{2},1;\frac {11}{4};\frac {d x^2}{c},\frac {b x^2}{a}\right )\right )}{42 a^3 c (b c-a d) (e x)^{3/2} \left (-a+b x^2\right ) \sqrt {c-d x^2}} \end {gather*}
Antiderivative was successfully verified.
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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(2969\) vs.
\(2(419)=838\).
time = 0.14, size = 2970, normalized size = 5.55
method | result | size |
elliptic | \(\frac {\sqrt {\left (-d \,x^{2}+c \right ) e x}\, \left (-\frac {b^{2} x \sqrt {-d e \,x^{3}+c e x}}{2 \left (a d -b c \right ) a^{2} e^{2} \left (-b \,x^{2}+a \right )}-\frac {2 \left (-d e \,x^{2}+c e \right )}{e^{2} c \,a^{2} \sqrt {x \left (-d e \,x^{2}+c e \right )}}-\frac {c \sqrt {\frac {d x}{\sqrt {c d}}+1}\, \sqrt {-\frac {2 d x}{\sqrt {c d}}+2}\, \sqrt {-\frac {d x}{\sqrt {c d}}}\, b \EllipticE \left (\sqrt {\frac {\left (x +\frac {\sqrt {c d}}{d}\right ) d}{\sqrt {c d}}}, \frac {\sqrt {2}}{2}\right )}{2 \sqrt {-d e \,x^{3}+c e x}\, a^{2} \left (a d -b c \right ) e}+\frac {c \sqrt {\frac {d x}{\sqrt {c d}}+1}\, \sqrt {-\frac {2 d x}{\sqrt {c d}}+2}\, \sqrt {-\frac {d x}{\sqrt {c d}}}\, b \EllipticF \left (\sqrt {\frac {\left (x +\frac {\sqrt {c d}}{d}\right ) d}{\sqrt {c d}}}, \frac {\sqrt {2}}{2}\right )}{4 \sqrt {-d e \,x^{3}+c e x}\, a^{2} \left (a d -b c \right ) e}+\frac {2 \sqrt {\frac {d x}{\sqrt {c d}}+1}\, \sqrt {-\frac {2 d x}{\sqrt {c d}}+2}\, \sqrt {-\frac {d x}{\sqrt {c d}}}\, \EllipticE \left (\sqrt {\frac {\left (x +\frac {\sqrt {c d}}{d}\right ) d}{\sqrt {c d}}}, \frac {\sqrt {2}}{2}\right )}{\sqrt {-d e \,x^{3}+c e x}\, e \,a^{2}}-\frac {\sqrt {\frac {d x}{\sqrt {c d}}+1}\, \sqrt {-\frac {2 d x}{\sqrt {c d}}+2}\, \sqrt {-\frac {d x}{\sqrt {c d}}}\, \EllipticF \left (\sqrt {\frac {\left (x +\frac {\sqrt {c d}}{d}\right ) d}{\sqrt {c d}}}, \frac {\sqrt {2}}{2}\right )}{\sqrt {-d e \,x^{3}+c e x}\, e \,a^{2}}-\frac {7 \sqrt {c d}\, \sqrt {\frac {d x}{\sqrt {c d}}+1}\, \sqrt {-\frac {2 d x}{\sqrt {c d}}+2}\, \sqrt {-\frac {d x}{\sqrt {c d}}}\, \EllipticPi \left (\sqrt {\frac {\left (x +\frac {\sqrt {c d}}{d}\right ) d}{\sqrt {c d}}}, -\frac {\sqrt {c d}}{d \left (-\frac {\sqrt {c d}}{d}-\frac {\sqrt {a b}}{b}\right )}, \frac {\sqrt {2}}{2}\right )}{8 a \left (a d -b c \right ) e \sqrt {-d e \,x^{3}+c e x}\, \left (-\frac {\sqrt {c d}}{d}-\frac {\sqrt {a b}}{b}\right )}+\frac {5 \sqrt {c d}\, \sqrt {\frac {d x}{\sqrt {c d}}+1}\, \sqrt {-\frac {2 d x}{\sqrt {c d}}+2}\, \sqrt {-\frac {d x}{\sqrt {c d}}}\, \EllipticPi \left (\sqrt {\frac {\left (x +\frac {\sqrt {c d}}{d}\right ) d}{\sqrt {c d}}}, -\frac {\sqrt {c d}}{d \left (-\frac {\sqrt {c d}}{d}-\frac {\sqrt {a b}}{b}\right )}, \frac {\sqrt {2}}{2}\right ) b c}{8 a^{2} \left (a d -b c \right ) e d \sqrt {-d e \,x^{3}+c e x}\, \left (-\frac {\sqrt {c d}}{d}-\frac {\sqrt {a b}}{b}\right )}-\frac {7 \sqrt {c d}\, \sqrt {\frac {d x}{\sqrt {c d}}+1}\, \sqrt {-\frac {2 d x}{\sqrt {c d}}+2}\, \sqrt {-\frac {d x}{\sqrt {c d}}}\, \EllipticPi \left (\sqrt {\frac {\left (x +\frac {\sqrt {c d}}{d}\right ) d}{\sqrt {c d}}}, -\frac {\sqrt {c d}}{d \left (-\frac {\sqrt {c d}}{d}+\frac {\sqrt {a b}}{b}\right )}, \frac {\sqrt {2}}{2}\right )}{8 a \left (a d -b c \right ) e \sqrt {-d e \,x^{3}+c e x}\, \left (-\frac {\sqrt {c d}}{d}+\frac {\sqrt {a b}}{b}\right )}+\frac {5 \sqrt {c d}\, \sqrt {\frac {d x}{\sqrt {c d}}+1}\, \sqrt {-\frac {2 d x}{\sqrt {c d}}+2}\, \sqrt {-\frac {d x}{\sqrt {c d}}}\, \EllipticPi \left (\sqrt {\frac {\left (x +\frac {\sqrt {c d}}{d}\right ) d}{\sqrt {c d}}}, -\frac {\sqrt {c d}}{d \left (-\frac {\sqrt {c d}}{d}+\frac {\sqrt {a b}}{b}\right )}, \frac {\sqrt {2}}{2}\right ) b c}{8 a^{2} \left (a d -b c \right ) e d \sqrt {-d e \,x^{3}+c e x}\, \left (-\frac {\sqrt {c d}}{d}+\frac {\sqrt {a b}}{b}\right )}\right )}{\sqrt {e x}\, \sqrt {-d \,x^{2}+c}}\) | \(1100\) |
default | \(\text {Expression too large to display}\) | \(2970\) |
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(-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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Sympy [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{\left (e x\right )^{\frac {3}{2}} \left (- a + b x^{2}\right )^{2} \sqrt {c - d x^{2}}}\, dx \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 {1}{{\left (e\,x\right )}^{3/2}\,{\left (a-b\,x^2\right )}^2\,\sqrt {c-d\,x^2}} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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