Optimal. Leaf size=700 \[ -\frac {9 b^{7/2} \left (11 a^2+2 b^2\right ) \text {ArcTan}\left (\frac {\sqrt {b} \sqrt {e \sin (c+d x)}}{\sqrt [4]{-a^2+b^2} \sqrt {e}}\right )}{8 \left (-a^2+b^2\right )^{17/4} d e^{7/2}}+\frac {9 b^{7/2} \left (11 a^2+2 b^2\right ) \tanh ^{-1}\left (\frac {\sqrt {b} \sqrt {e \sin (c+d x)}}{\sqrt [4]{-a^2+b^2} \sqrt {e}}\right )}{8 \left (-a^2+b^2\right )^{17/4} d e^{7/2}}-\frac {b}{2 \left (a^2-b^2\right ) d e (a+b \cos (c+d x))^2 (e \sin (c+d x))^{5/2}}-\frac {13 a b}{4 \left (a^2-b^2\right )^2 d e (a+b \cos (c+d x)) (e \sin (c+d x))^{5/2}}+\frac {9 b \left (11 a^2+2 b^2\right )-a \left (8 a^2+109 b^2\right ) \cos (c+d x)}{20 \left (a^2-b^2\right )^3 d e (e \sin (c+d x))^{5/2}}-\frac {3 \left (15 b^3 \left (11 a^2+2 b^2\right )+a \left (8 a^4-64 a^2 b^2-139 b^4\right ) \cos (c+d x)\right )}{20 \left (a^2-b^2\right )^4 d e^3 \sqrt {e \sin (c+d x)}}+\frac {9 a b^3 \left (11 a^2+2 b^2\right ) \Pi \left (\frac {2 b}{b-\sqrt {-a^2+b^2}};\left .\frac {1}{2} \left (c-\frac {\pi }{2}+d x\right )\right |2\right ) \sqrt {\sin (c+d x)}}{8 \left (a^2-b^2\right )^4 \left (b-\sqrt {-a^2+b^2}\right ) d e^3 \sqrt {e \sin (c+d x)}}+\frac {9 a b^3 \left (11 a^2+2 b^2\right ) \Pi \left (\frac {2 b}{b+\sqrt {-a^2+b^2}};\left .\frac {1}{2} \left (c-\frac {\pi }{2}+d x\right )\right |2\right ) \sqrt {\sin (c+d x)}}{8 \left (a^2-b^2\right )^4 \left (b+\sqrt {-a^2+b^2}\right ) d e^3 \sqrt {e \sin (c+d x)}}-\frac {3 a \left (8 a^4-64 a^2 b^2-139 b^4\right ) E\left (\left .\frac {1}{2} \left (c-\frac {\pi }{2}+d x\right )\right |2\right ) \sqrt {e \sin (c+d x)}}{20 \left (a^2-b^2\right )^4 d e^4 \sqrt {\sin (c+d x)}} \]
[Out]
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Rubi [A]
time = 1.35, antiderivative size = 700, normalized size of antiderivative = 1.00, number
of steps used = 16, number of rules used = 13, integrand size = 25, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.520, Rules
used = {2773, 2943, 2945, 2946, 2721, 2719, 2780, 2886, 2884, 335, 304, 211, 214}
\begin {gather*} -\frac {9 b^{7/2} \left (11 a^2+2 b^2\right ) \text {ArcTan}\left (\frac {\sqrt {b} \sqrt {e \sin (c+d x)}}{\sqrt {e} \sqrt [4]{b^2-a^2}}\right )}{8 d e^{7/2} \left (b^2-a^2\right )^{17/4}}-\frac {13 a b}{4 d e \left (a^2-b^2\right )^2 (e \sin (c+d x))^{5/2} (a+b \cos (c+d x))}-\frac {b}{2 d e \left (a^2-b^2\right ) (e \sin (c+d x))^{5/2} (a+b \cos (c+d x))^2}+\frac {9 b \left (11 a^2+2 b^2\right )-a \left (8 a^2+109 b^2\right ) \cos (c+d x)}{20 d e \left (a^2-b^2\right )^3 (e \sin (c+d x))^{5/2}}+\frac {9 b^{7/2} \left (11 a^2+2 b^2\right ) \tanh ^{-1}\left (\frac {\sqrt {b} \sqrt {e \sin (c+d x)}}{\sqrt {e} \sqrt [4]{b^2-a^2}}\right )}{8 d e^{7/2} \left (b^2-a^2\right )^{17/4}}+\frac {9 a b^3 \left (11 a^2+2 b^2\right ) \sqrt {\sin (c+d x)} \Pi \left (\frac {2 b}{b-\sqrt {b^2-a^2}};\left .\frac {1}{2} \left (c+d x-\frac {\pi }{2}\right )\right |2\right )}{8 d e^3 \left (a^2-b^2\right )^4 \left (b-\sqrt {b^2-a^2}\right ) \sqrt {e \sin (c+d x)}}+\frac {9 a b^3 \left (11 a^2+2 b^2\right ) \sqrt {\sin (c+d x)} \Pi \left (\frac {2 b}{b+\sqrt {b^2-a^2}};\left .\frac {1}{2} \left (c+d x-\frac {\pi }{2}\right )\right |2\right )}{8 d e^3 \left (a^2-b^2\right )^4 \left (\sqrt {b^2-a^2}+b\right ) \sqrt {e \sin (c+d x)}}-\frac {3 a \left (8 a^4-64 a^2 b^2-139 b^4\right ) E\left (\left .\frac {1}{2} \left (c+d x-\frac {\pi }{2}\right )\right |2\right ) \sqrt {e \sin (c+d x)}}{20 d e^4 \left (a^2-b^2\right )^4 \sqrt {\sin (c+d x)}}-\frac {3 \left (15 b^3 \left (11 a^2+2 b^2\right )+a \left (8 a^4-64 a^2 b^2-139 b^4\right ) \cos (c+d x)\right )}{20 d e^3 \left (a^2-b^2\right )^4 \sqrt {e \sin (c+d x)}} \end {gather*}
Antiderivative was successfully verified.
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Rule 211
Rule 214
Rule 304
Rule 335
Rule 2719
Rule 2721
Rule 2773
Rule 2780
Rule 2884
Rule 2886
Rule 2943
Rule 2945
Rule 2946
Rubi steps
\begin {align*} \int \frac {1}{(a+b \cos (c+d x))^3 (e \sin (c+d x))^{7/2}} \, dx &=-\frac {b}{2 \left (a^2-b^2\right ) d e (a+b \cos (c+d x))^2 (e \sin (c+d x))^{5/2}}-\frac {\int \frac {-2 a+\frac {9}{2} b \cos (c+d x)}{(a+b \cos (c+d x))^2 (e \sin (c+d x))^{7/2}} \, dx}{2 \left (a^2-b^2\right )}\\ &=-\frac {b}{2 \left (a^2-b^2\right ) d e (a+b \cos (c+d x))^2 (e \sin (c+d x))^{5/2}}-\frac {13 a b}{4 \left (a^2-b^2\right )^2 d e (a+b \cos (c+d x)) (e \sin (c+d x))^{5/2}}+\frac {\int \frac {\frac {1}{2} \left (4 a^2+9 b^2\right )-\frac {91}{4} a b \cos (c+d x)}{(a+b \cos (c+d x)) (e \sin (c+d x))^{7/2}} \, dx}{2 \left (a^2-b^2\right )^2}\\ &=-\frac {b}{2 \left (a^2-b^2\right ) d e (a+b \cos (c+d x))^2 (e \sin (c+d x))^{5/2}}-\frac {13 a b}{4 \left (a^2-b^2\right )^2 d e (a+b \cos (c+d x)) (e \sin (c+d x))^{5/2}}+\frac {9 b \left (11 a^2+2 b^2\right )-a \left (8 a^2+109 b^2\right ) \cos (c+d x)}{20 \left (a^2-b^2\right )^3 d e (e \sin (c+d x))^{5/2}}-\frac {\int \frac {-\frac {3}{4} \left (4 a^4-28 a^2 b^2-15 b^4\right )-\frac {3}{8} a b \left (8 a^2+109 b^2\right ) \cos (c+d x)}{(a+b \cos (c+d x)) (e \sin (c+d x))^{3/2}} \, dx}{5 \left (a^2-b^2\right )^3 e^2}\\ &=-\frac {b}{2 \left (a^2-b^2\right ) d e (a+b \cos (c+d x))^2 (e \sin (c+d x))^{5/2}}-\frac {13 a b}{4 \left (a^2-b^2\right )^2 d e (a+b \cos (c+d x)) (e \sin (c+d x))^{5/2}}+\frac {9 b \left (11 a^2+2 b^2\right )-a \left (8 a^2+109 b^2\right ) \cos (c+d x)}{20 \left (a^2-b^2\right )^3 d e (e \sin (c+d x))^{5/2}}-\frac {3 \left (15 b^3 \left (11 a^2+2 b^2\right )+a \left (8 a^4-64 a^2 b^2-139 b^4\right ) \cos (c+d x)\right )}{20 \left (a^2-b^2\right )^4 d e^3 \sqrt {e \sin (c+d x)}}+\frac {2 \int \frac {\left (-\frac {3}{8} \left (4 a^6-32 a^4 b^2-152 a^2 b^4-15 b^6\right )-\frac {3}{16} a b \left (8 a^4-64 a^2 b^2-139 b^4\right ) \cos (c+d x)\right ) \sqrt {e \sin (c+d x)}}{a+b \cos (c+d x)} \, dx}{5 \left (a^2-b^2\right )^4 e^4}\\ &=-\frac {b}{2 \left (a^2-b^2\right ) d e (a+b \cos (c+d x))^2 (e \sin (c+d x))^{5/2}}-\frac {13 a b}{4 \left (a^2-b^2\right )^2 d e (a+b \cos (c+d x)) (e \sin (c+d x))^{5/2}}+\frac {9 b \left (11 a^2+2 b^2\right )-a \left (8 a^2+109 b^2\right ) \cos (c+d x)}{20 \left (a^2-b^2\right )^3 d e (e \sin (c+d x))^{5/2}}-\frac {3 \left (15 b^3 \left (11 a^2+2 b^2\right )+a \left (8 a^4-64 a^2 b^2-139 b^4\right ) \cos (c+d x)\right )}{20 \left (a^2-b^2\right )^4 d e^3 \sqrt {e \sin (c+d x)}}+\frac {\left (9 b^4 \left (11 a^2+2 b^2\right )\right ) \int \frac {\sqrt {e \sin (c+d x)}}{a+b \cos (c+d x)} \, dx}{8 \left (a^2-b^2\right )^4 e^4}-\frac {\left (3 a \left (8 a^4-64 a^2 b^2-139 b^4\right )\right ) \int \sqrt {e \sin (c+d x)} \, dx}{40 \left (a^2-b^2\right )^4 e^4}\\ &=-\frac {b}{2 \left (a^2-b^2\right ) d e (a+b \cos (c+d x))^2 (e \sin (c+d x))^{5/2}}-\frac {13 a b}{4 \left (a^2-b^2\right )^2 d e (a+b \cos (c+d x)) (e \sin (c+d x))^{5/2}}+\frac {9 b \left (11 a^2+2 b^2\right )-a \left (8 a^2+109 b^2\right ) \cos (c+d x)}{20 \left (a^2-b^2\right )^3 d e (e \sin (c+d x))^{5/2}}-\frac {3 \left (15 b^3 \left (11 a^2+2 b^2\right )+a \left (8 a^4-64 a^2 b^2-139 b^4\right ) \cos (c+d x)\right )}{20 \left (a^2-b^2\right )^4 d e^3 \sqrt {e \sin (c+d x)}}-\frac {\left (9 a b^3 \left (11 a^2+2 b^2\right )\right ) \int \frac {1}{\sqrt {e \sin (c+d x)} \left (\sqrt {-a^2+b^2}-b \sin (c+d x)\right )} \, dx}{16 \left (a^2-b^2\right )^4 e^3}+\frac {\left (9 a b^3 \left (11 a^2+2 b^2\right )\right ) \int \frac {1}{\sqrt {e \sin (c+d x)} \left (\sqrt {-a^2+b^2}+b \sin (c+d x)\right )} \, dx}{16 \left (a^2-b^2\right )^4 e^3}-\frac {\left (9 b^5 \left (11 a^2+2 b^2\right )\right ) \text {Subst}\left (\int \frac {\sqrt {x}}{\left (a^2-b^2\right ) e^2+b^2 x^2} \, dx,x,e \sin (c+d x)\right )}{8 \left (a^2-b^2\right )^4 d e^3}-\frac {\left (3 a \left (8 a^4-64 a^2 b^2-139 b^4\right ) \sqrt {e \sin (c+d x)}\right ) \int \sqrt {\sin (c+d x)} \, dx}{40 \left (a^2-b^2\right )^4 e^4 \sqrt {\sin (c+d x)}}\\ &=-\frac {b}{2 \left (a^2-b^2\right ) d e (a+b \cos (c+d x))^2 (e \sin (c+d x))^{5/2}}-\frac {13 a b}{4 \left (a^2-b^2\right )^2 d e (a+b \cos (c+d x)) (e \sin (c+d x))^{5/2}}+\frac {9 b \left (11 a^2+2 b^2\right )-a \left (8 a^2+109 b^2\right ) \cos (c+d x)}{20 \left (a^2-b^2\right )^3 d e (e \sin (c+d x))^{5/2}}-\frac {3 \left (15 b^3 \left (11 a^2+2 b^2\right )+a \left (8 a^4-64 a^2 b^2-139 b^4\right ) \cos (c+d x)\right )}{20 \left (a^2-b^2\right )^4 d e^3 \sqrt {e \sin (c+d x)}}-\frac {3 a \left (8 a^4-64 a^2 b^2-139 b^4\right ) E\left (\left .\frac {1}{2} \left (c-\frac {\pi }{2}+d x\right )\right |2\right ) \sqrt {e \sin (c+d x)}}{20 \left (a^2-b^2\right )^4 d e^4 \sqrt {\sin (c+d x)}}-\frac {\left (9 b^5 \left (11 a^2+2 b^2\right )\right ) \text {Subst}\left (\int \frac {x^2}{\left (a^2-b^2\right ) e^2+b^2 x^4} \, dx,x,\sqrt {e \sin (c+d x)}\right )}{4 \left (a^2-b^2\right )^4 d e^3}-\frac {\left (9 a b^3 \left (11 a^2+2 b^2\right ) \sqrt {\sin (c+d x)}\right ) \int \frac {1}{\sqrt {\sin (c+d x)} \left (\sqrt {-a^2+b^2}-b \sin (c+d x)\right )} \, dx}{16 \left (a^2-b^2\right )^4 e^3 \sqrt {e \sin (c+d x)}}+\frac {\left (9 a b^3 \left (11 a^2+2 b^2\right ) \sqrt {\sin (c+d x)}\right ) \int \frac {1}{\sqrt {\sin (c+d x)} \left (\sqrt {-a^2+b^2}+b \sin (c+d x)\right )} \, dx}{16 \left (a^2-b^2\right )^4 e^3 \sqrt {e \sin (c+d x)}}\\ &=-\frac {b}{2 \left (a^2-b^2\right ) d e (a+b \cos (c+d x))^2 (e \sin (c+d x))^{5/2}}-\frac {13 a b}{4 \left (a^2-b^2\right )^2 d e (a+b \cos (c+d x)) (e \sin (c+d x))^{5/2}}+\frac {9 b \left (11 a^2+2 b^2\right )-a \left (8 a^2+109 b^2\right ) \cos (c+d x)}{20 \left (a^2-b^2\right )^3 d e (e \sin (c+d x))^{5/2}}-\frac {3 \left (15 b^3 \left (11 a^2+2 b^2\right )+a \left (8 a^4-64 a^2 b^2-139 b^4\right ) \cos (c+d x)\right )}{20 \left (a^2-b^2\right )^4 d e^3 \sqrt {e \sin (c+d x)}}+\frac {9 a b^3 \left (11 a^2+2 b^2\right ) \Pi \left (\frac {2 b}{b-\sqrt {-a^2+b^2}};\left .\frac {1}{2} \left (c-\frac {\pi }{2}+d x\right )\right |2\right ) \sqrt {\sin (c+d x)}}{8 \left (a^2-b^2\right )^4 \left (b-\sqrt {-a^2+b^2}\right ) d e^3 \sqrt {e \sin (c+d x)}}+\frac {9 a b^3 \left (11 a^2+2 b^2\right ) \Pi \left (\frac {2 b}{b+\sqrt {-a^2+b^2}};\left .\frac {1}{2} \left (c-\frac {\pi }{2}+d x\right )\right |2\right ) \sqrt {\sin (c+d x)}}{8 \left (a^2-b^2\right )^4 \left (b+\sqrt {-a^2+b^2}\right ) d e^3 \sqrt {e \sin (c+d x)}}-\frac {3 a \left (8 a^4-64 a^2 b^2-139 b^4\right ) E\left (\left .\frac {1}{2} \left (c-\frac {\pi }{2}+d x\right )\right |2\right ) \sqrt {e \sin (c+d x)}}{20 \left (a^2-b^2\right )^4 d e^4 \sqrt {\sin (c+d x)}}+\frac {\left (9 b^4 \left (11 a^2+2 b^2\right )\right ) \text {Subst}\left (\int \frac {1}{\sqrt {-a^2+b^2} e-b x^2} \, dx,x,\sqrt {e \sin (c+d x)}\right )}{8 \left (a^2-b^2\right )^4 d e^3}-\frac {\left (9 b^4 \left (11 a^2+2 b^2\right )\right ) \text {Subst}\left (\int \frac {1}{\sqrt {-a^2+b^2} e+b x^2} \, dx,x,\sqrt {e \sin (c+d x)}\right )}{8 \left (a^2-b^2\right )^4 d e^3}\\ &=-\frac {9 b^{7/2} \left (11 a^2+2 b^2\right ) \tan ^{-1}\left (\frac {\sqrt {b} \sqrt {e \sin (c+d x)}}{\sqrt [4]{-a^2+b^2} \sqrt {e}}\right )}{8 \left (-a^2+b^2\right )^{17/4} d e^{7/2}}+\frac {9 b^{7/2} \left (11 a^2+2 b^2\right ) \tanh ^{-1}\left (\frac {\sqrt {b} \sqrt {e \sin (c+d x)}}{\sqrt [4]{-a^2+b^2} \sqrt {e}}\right )}{8 \left (-a^2+b^2\right )^{17/4} d e^{7/2}}-\frac {b}{2 \left (a^2-b^2\right ) d e (a+b \cos (c+d x))^2 (e \sin (c+d x))^{5/2}}-\frac {13 a b}{4 \left (a^2-b^2\right )^2 d e (a+b \cos (c+d x)) (e \sin (c+d x))^{5/2}}+\frac {9 b \left (11 a^2+2 b^2\right )-a \left (8 a^2+109 b^2\right ) \cos (c+d x)}{20 \left (a^2-b^2\right )^3 d e (e \sin (c+d x))^{5/2}}-\frac {3 \left (15 b^3 \left (11 a^2+2 b^2\right )+a \left (8 a^4-64 a^2 b^2-139 b^4\right ) \cos (c+d x)\right )}{20 \left (a^2-b^2\right )^4 d e^3 \sqrt {e \sin (c+d x)}}+\frac {9 a b^3 \left (11 a^2+2 b^2\right ) \Pi \left (\frac {2 b}{b-\sqrt {-a^2+b^2}};\left .\frac {1}{2} \left (c-\frac {\pi }{2}+d x\right )\right |2\right ) \sqrt {\sin (c+d x)}}{8 \left (a^2-b^2\right )^4 \left (b-\sqrt {-a^2+b^2}\right ) d e^3 \sqrt {e \sin (c+d x)}}+\frac {9 a b^3 \left (11 a^2+2 b^2\right ) \Pi \left (\frac {2 b}{b+\sqrt {-a^2+b^2}};\left .\frac {1}{2} \left (c-\frac {\pi }{2}+d x\right )\right |2\right ) \sqrt {\sin (c+d x)}}{8 \left (a^2-b^2\right )^4 \left (b+\sqrt {-a^2+b^2}\right ) d e^3 \sqrt {e \sin (c+d x)}}-\frac {3 a \left (8 a^4-64 a^2 b^2-139 b^4\right ) E\left (\left .\frac {1}{2} \left (c-\frac {\pi }{2}+d x\right )\right |2\right ) \sqrt {e \sin (c+d x)}}{20 \left (a^2-b^2\right )^4 d e^4 \sqrt {\sin (c+d x)}}\\ \end {align*}
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Mathematica [C] Result contains higher order function than in optimal. Order 6 vs. order 4 in
optimal.
time = 16.65, size = 1014, normalized size = 1.45 \begin {gather*} \frac {\sin ^4(c+d x) \left (-\frac {2 \left (50 a^2 b^3+10 b^5+3 a^5 \cos (c+d x)-24 a^3 b^2 \cos (c+d x)-39 a b^4 \cos (c+d x)\right ) \csc (c+d x)}{5 \left (a^2-b^2\right )^4}-\frac {2 \left (-3 a^2 b-b^3+a^3 \cos (c+d x)+3 a b^2 \cos (c+d x)\right ) \csc ^3(c+d x)}{5 \left (a^2-b^2\right )^3}-\frac {b^5 \sin (c+d x)}{2 \left (a^2-b^2\right )^3 (a+b \cos (c+d x))^2}-\frac {21 a b^5 \sin (c+d x)}{4 \left (a^2-b^2\right )^4 (a+b \cos (c+d x))}\right )}{d (e \sin (c+d x))^{7/2}}-\frac {3 \sin ^{\frac {7}{2}}(c+d x) \left (\frac {\left (8 a^5 b-64 a^3 b^3-139 a b^5\right ) \cos ^2(c+d x) \left (3 \sqrt {2} a \left (a^2-b^2\right )^{3/4} \left (2 \text {ArcTan}\left (1-\frac {\sqrt {2} \sqrt {b} \sqrt {\sin (c+d x)}}{\sqrt [4]{a^2-b^2}}\right )-2 \text {ArcTan}\left (1+\frac {\sqrt {2} \sqrt {b} \sqrt {\sin (c+d x)}}{\sqrt [4]{a^2-b^2}}\right )-\log \left (\sqrt {a^2-b^2}-\sqrt {2} \sqrt {b} \sqrt [4]{a^2-b^2} \sqrt {\sin (c+d x)}+b \sin (c+d x)\right )+\log \left (\sqrt {a^2-b^2}+\sqrt {2} \sqrt {b} \sqrt [4]{a^2-b^2} \sqrt {\sin (c+d x)}+b \sin (c+d x)\right )\right )+8 b^{5/2} F_1\left (\frac {3}{4};-\frac {1}{2},1;\frac {7}{4};\sin ^2(c+d x),\frac {b^2 \sin ^2(c+d x)}{-a^2+b^2}\right ) \sin ^{\frac {3}{2}}(c+d x)\right ) \left (a+b \sqrt {1-\sin ^2(c+d x)}\right )}{12 b^{3/2} \left (-a^2+b^2\right ) (a+b \cos (c+d x)) \left (1-\sin ^2(c+d x)\right )}+\frac {2 \left (8 a^6-64 a^4 b^2-304 a^2 b^4-30 b^6\right ) \cos (c+d x) \left (\frac {\left (\frac {1}{8}+\frac {i}{8}\right ) \left (2 \text {ArcTan}\left (1-\frac {(1+i) \sqrt {b} \sqrt {\sin (c+d x)}}{\sqrt [4]{-a^2+b^2}}\right )-2 \text {ArcTan}\left (1+\frac {(1+i) \sqrt {b} \sqrt {\sin (c+d x)}}{\sqrt [4]{-a^2+b^2}}\right )-\log \left (\sqrt {-a^2+b^2}-(1+i) \sqrt {b} \sqrt [4]{-a^2+b^2} \sqrt {\sin (c+d x)}+i b \sin (c+d x)\right )+\log \left (\sqrt {-a^2+b^2}+(1+i) \sqrt {b} \sqrt [4]{-a^2+b^2} \sqrt {\sin (c+d x)}+i b \sin (c+d x)\right )\right )}{\sqrt {b} \sqrt [4]{-a^2+b^2}}+\frac {a F_1\left (\frac {3}{4};\frac {1}{2},1;\frac {7}{4};\sin ^2(c+d x),\frac {b^2 \sin ^2(c+d x)}{-a^2+b^2}\right ) \sin ^{\frac {3}{2}}(c+d x)}{3 \left (a^2-b^2\right )}\right ) \left (a+b \sqrt {1-\sin ^2(c+d x)}\right )}{(a+b \cos (c+d x)) \sqrt {1-\sin ^2(c+d x)}}\right )}{40 (a-b)^4 (a+b)^4 d (e \sin (c+d x))^{7/2}} \end {gather*}
Warning: Unable to verify antiderivative.
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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(3708\) vs.
\(2(716)=1432\).
time = 0.87, size = 3709, normalized size = 5.30
method | result | size |
default | \(\text {Expression too large to display}\) | \(3709\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [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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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(-2)]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: SystemError} \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\,\sin \left (c+d\,x\right )\right )}^{7/2}\,{\left (a+b\,\cos \left (c+d\,x\right )\right )}^3} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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