Optimal. Leaf size=716 \[ \frac {2 (b c-a d)^2 \cos (e+f x) (a+b \sin (e+f x))}{7 d \left (c^2-d^2\right ) f (c+d \sin (e+f x))^{7/2}}+\frac {8 (b c-a d)^2 \left (3 a c d+b \left (c^2-4 d^2\right )\right ) \cos (e+f x)}{35 d^2 \left (c^2-d^2\right )^2 f (c+d \sin (e+f x))^{5/2}}-\frac {2 (b c-a d) \left (a^2 d^2 \left (71 c^2+25 d^2\right )+a b \left (26 c^3 d-218 c d^3\right )+b^2 \left (8 c^4-17 c^2 d^2+105 d^4\right )\right ) \cos (e+f x)}{105 d^2 \left (c^2-d^2\right )^3 f (c+d \sin (e+f x))^{3/2}}+\frac {2 \left (16 a^3 c d^3 \left (11 c^2+13 d^2\right )-6 a b^2 c d \left (3 c^4-62 c^2 d^2-133 d^4\right )-9 a^2 b d^2 \left (5 c^4+102 c^2 d^2+21 d^4\right )-b^3 \left (8 c^6-23 c^4 d^2+294 c^2 d^4+105 d^6\right )\right ) \cos (e+f x)}{105 d^2 \left (c^2-d^2\right )^4 f \sqrt {c+d \sin (e+f x)}}+\frac {2 \left (16 a^3 c d^3 \left (11 c^2+13 d^2\right )-6 a b^2 c d \left (3 c^4-62 c^2 d^2-133 d^4\right )-9 a^2 b d^2 \left (5 c^4+102 c^2 d^2+21 d^4\right )-b^3 \left (8 c^6-23 c^4 d^2+294 c^2 d^4+105 d^6\right )\right ) E\left (\frac {1}{2} \left (e-\frac {\pi }{2}+f x\right )|\frac {2 d}{c+d}\right ) \sqrt {c+d \sin (e+f x)}}{105 d^3 \left (c^2-d^2\right )^4 f \sqrt {\frac {c+d \sin (e+f x)}{c+d}}}+\frac {2 (b c-a d) \left (a^2 d^2 \left (71 c^2+25 d^2\right )+a b \left (26 c^3 d-218 c d^3\right )+b^2 \left (8 c^4-17 c^2 d^2+105 d^4\right )\right ) F\left (\frac {1}{2} \left (e-\frac {\pi }{2}+f x\right )|\frac {2 d}{c+d}\right ) \sqrt {\frac {c+d \sin (e+f x)}{c+d}}}{105 d^3 \left (c^2-d^2\right )^3 f \sqrt {c+d \sin (e+f x)}} \]
[Out]
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Rubi [A]
time = 0.95, antiderivative size = 716, normalized size of antiderivative = 1.00, number of steps
used = 9, number of rules used = 8, integrand size = 27, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.296, Rules used = {2871, 3100,
2833, 2831, 2742, 2740, 2734, 2732} \begin {gather*} -\frac {2 \left (a^2 d^2 \left (71 c^2+25 d^2\right )+a b \left (26 c^3 d-218 c d^3\right )+b^2 \left (8 c^4-17 c^2 d^2+105 d^4\right )\right ) (b c-a d) \cos (e+f x)}{105 d^2 f \left (c^2-d^2\right )^3 (c+d \sin (e+f x))^{3/2}}+\frac {2 \left (a^2 d^2 \left (71 c^2+25 d^2\right )+a b \left (26 c^3 d-218 c d^3\right )+b^2 \left (8 c^4-17 c^2 d^2+105 d^4\right )\right ) (b c-a d) \sqrt {\frac {c+d \sin (e+f x)}{c+d}} F\left (\frac {1}{2} \left (e+f x-\frac {\pi }{2}\right )|\frac {2 d}{c+d}\right )}{105 d^3 f \left (c^2-d^2\right )^3 \sqrt {c+d \sin (e+f x)}}+\frac {2 \left (16 a^3 c d^3 \left (11 c^2+13 d^2\right )-9 a^2 b d^2 \left (5 c^4+102 c^2 d^2+21 d^4\right )-6 a b^2 c d \left (3 c^4-62 c^2 d^2-133 d^4\right )-\left (b^3 \left (8 c^6-23 c^4 d^2+294 c^2 d^4+105 d^6\right )\right )\right ) \cos (e+f x)}{105 d^2 f \left (c^2-d^2\right )^4 \sqrt {c+d \sin (e+f x)}}+\frac {2 \left (16 a^3 c d^3 \left (11 c^2+13 d^2\right )-9 a^2 b d^2 \left (5 c^4+102 c^2 d^2+21 d^4\right )-6 a b^2 c d \left (3 c^4-62 c^2 d^2-133 d^4\right )-\left (b^3 \left (8 c^6-23 c^4 d^2+294 c^2 d^4+105 d^6\right )\right )\right ) \sqrt {c+d \sin (e+f x)} E\left (\frac {1}{2} \left (e+f x-\frac {\pi }{2}\right )|\frac {2 d}{c+d}\right )}{105 d^3 f \left (c^2-d^2\right )^4 \sqrt {\frac {c+d \sin (e+f x)}{c+d}}}+\frac {8 \left (3 a c d+b \left (c^2-4 d^2\right )\right ) (b c-a d)^2 \cos (e+f x)}{35 d^2 f \left (c^2-d^2\right )^2 (c+d \sin (e+f x))^{5/2}}+\frac {2 (b c-a d)^2 \cos (e+f x) (a+b \sin (e+f x))}{7 d f \left (c^2-d^2\right ) (c+d \sin (e+f x))^{7/2}} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 2732
Rule 2734
Rule 2740
Rule 2742
Rule 2831
Rule 2833
Rule 2871
Rule 3100
Rubi steps
\begin {align*} \int \frac {(a+b \sin (e+f x))^3}{(c+d \sin (e+f x))^{9/2}} \, dx &=\frac {2 (b c-a d)^2 \cos (e+f x) (a+b \sin (e+f x))}{7 d \left (c^2-d^2\right ) f (c+d \sin (e+f x))^{7/2}}-\frac {2 \int \frac {\frac {1}{2} \left (2 b (b c-a d)^2-7 a d \left (\left (a^2+b^2\right ) c-2 a b d\right )\right )+\frac {1}{2} \left (5 a (b c-a d)^2-7 b \left (a b c^2+\left (a^2+b^2\right ) c d-3 a b d^2\right )\right ) \sin (e+f x)-\frac {1}{2} b \left (6 a b c d-3 a^2 d^2+b^2 \left (4 c^2-7 d^2\right )\right ) \sin ^2(e+f x)}{(c+d \sin (e+f x))^{7/2}} \, dx}{7 d \left (c^2-d^2\right )}\\ &=\frac {2 (b c-a d)^2 \cos (e+f x) (a+b \sin (e+f x))}{7 d \left (c^2-d^2\right ) f (c+d \sin (e+f x))^{7/2}}+\frac {8 (b c-a d)^2 \left (3 a c d+b \left (c^2-4 d^2\right )\right ) \cos (e+f x)}{35 d^2 \left (c^2-d^2\right )^2 f (c+d \sin (e+f x))^{5/2}}+\frac {4 \int \frac {-\frac {5}{4} d \left (36 a^2 b c d^2-a^3 d \left (7 c^2+5 d^2\right )-3 a b^2 d \left (5 c^2+7 d^2\right )-2 b^3 \left (c^3-7 c d^2\right )\right )-\frac {1}{4} \left (36 a^3 c d^3-18 a b^2 c d \left (c^2-7 d^2\right )-9 a^2 b d^2 \left (5 c^2+7 d^2\right )-b^3 \left (8 c^4-7 c^2 d^2+35 d^4\right )\right ) \sin (e+f x)}{(c+d \sin (e+f x))^{5/2}} \, dx}{35 d^2 \left (c^2-d^2\right )^2}\\ &=\frac {2 (b c-a d)^2 \cos (e+f x) (a+b \sin (e+f x))}{7 d \left (c^2-d^2\right ) f (c+d \sin (e+f x))^{7/2}}+\frac {8 (b c-a d)^2 \left (3 a c d+b \left (c^2-4 d^2\right )\right ) \cos (e+f x)}{35 d^2 \left (c^2-d^2\right )^2 f (c+d \sin (e+f x))^{5/2}}-\frac {2 (b c-a d) \left (a^2 d^2 \left (71 c^2+25 d^2\right )+a b \left (26 c^3 d-218 c d^3\right )+b^2 \left (8 c^4-17 c^2 d^2+105 d^4\right )\right ) \cos (e+f x)}{105 d^2 \left (c^2-d^2\right )^3 f (c+d \sin (e+f x))^{3/2}}-\frac {8 \int \frac {\frac {3}{8} d \left (9 a^2 b d^2 \left (25 c^2+7 d^2\right )-a^3 c d \left (35 c^2+61 d^2\right )-3 a b^2 d \left (19 c^3+77 c d^2\right )-b^3 \left (2 c^4-63 c^2 d^2-35 d^4\right )\right )-\frac {1}{8} (b c-a d) \left (8 b^2 c^4+26 a b c^3 d+71 a^2 c^2 d^2-17 b^2 c^2 d^2-218 a b c d^3+25 a^2 d^4+105 b^2 d^4\right ) \sin (e+f x)}{(c+d \sin (e+f x))^{3/2}} \, dx}{105 d^2 \left (c^2-d^2\right )^3}\\ &=\frac {2 (b c-a d)^2 \cos (e+f x) (a+b \sin (e+f x))}{7 d \left (c^2-d^2\right ) f (c+d \sin (e+f x))^{7/2}}+\frac {8 (b c-a d)^2 \left (3 a c d+b \left (c^2-4 d^2\right )\right ) \cos (e+f x)}{35 d^2 \left (c^2-d^2\right )^2 f (c+d \sin (e+f x))^{5/2}}-\frac {2 (b c-a d) \left (a^2 d^2 \left (71 c^2+25 d^2\right )+a b \left (26 c^3 d-218 c d^3\right )+b^2 \left (8 c^4-17 c^2 d^2+105 d^4\right )\right ) \cos (e+f x)}{105 d^2 \left (c^2-d^2\right )^3 f (c+d \sin (e+f x))^{3/2}}+\frac {2 \left (16 a^3 c d^3 \left (11 c^2+13 d^2\right )-6 a b^2 c d \left (3 c^4-62 c^2 d^2-133 d^4\right )-9 a^2 b d^2 \left (5 c^4+102 c^2 d^2+21 d^4\right )-b^3 \left (8 c^6-23 c^4 d^2+294 c^2 d^4+105 d^6\right )\right ) \cos (e+f x)}{105 d^2 \left (c^2-d^2\right )^4 f \sqrt {c+d \sin (e+f x)}}+\frac {16 \int \frac {-\frac {1}{16} d \left (144 a^2 b c d^2 \left (5 c^2+3 d^2\right )-a^3 d \left (105 c^4+254 c^2 d^2+25 d^4\right )-3 a b^2 d \left (51 c^4+298 c^2 d^2+35 d^4\right )+2 b^3 \left (c^5+86 c^3 d^2+105 c d^4\right )\right )+\frac {1}{16} \left (16 a^3 c d^3 \left (11 c^2+13 d^2\right )-6 a b^2 c d \left (3 c^4-62 c^2 d^2-133 d^4\right )-9 a^2 b d^2 \left (5 c^4+102 c^2 d^2+21 d^4\right )-b^3 \left (8 c^6-23 c^4 d^2+294 c^2 d^4+105 d^6\right )\right ) \sin (e+f x)}{\sqrt {c+d \sin (e+f x)}} \, dx}{105 d^2 \left (c^2-d^2\right )^4}\\ &=\frac {2 (b c-a d)^2 \cos (e+f x) (a+b \sin (e+f x))}{7 d \left (c^2-d^2\right ) f (c+d \sin (e+f x))^{7/2}}+\frac {8 (b c-a d)^2 \left (3 a c d+b \left (c^2-4 d^2\right )\right ) \cos (e+f x)}{35 d^2 \left (c^2-d^2\right )^2 f (c+d \sin (e+f x))^{5/2}}-\frac {2 (b c-a d) \left (a^2 d^2 \left (71 c^2+25 d^2\right )+a b \left (26 c^3 d-218 c d^3\right )+b^2 \left (8 c^4-17 c^2 d^2+105 d^4\right )\right ) \cos (e+f x)}{105 d^2 \left (c^2-d^2\right )^3 f (c+d \sin (e+f x))^{3/2}}+\frac {2 \left (16 a^3 c d^3 \left (11 c^2+13 d^2\right )-6 a b^2 c d \left (3 c^4-62 c^2 d^2-133 d^4\right )-9 a^2 b d^2 \left (5 c^4+102 c^2 d^2+21 d^4\right )-b^3 \left (8 c^6-23 c^4 d^2+294 c^2 d^4+105 d^6\right )\right ) \cos (e+f x)}{105 d^2 \left (c^2-d^2\right )^4 f \sqrt {c+d \sin (e+f x)}}+\frac {\left (16 a^3 c d^3 \left (11 c^2+13 d^2\right )-6 a b^2 c d \left (3 c^4-62 c^2 d^2-133 d^4\right )-9 a^2 b d^2 \left (5 c^4+102 c^2 d^2+21 d^4\right )-b^3 \left (8 c^6-23 c^4 d^2+294 c^2 d^4+105 d^6\right )\right ) \int \sqrt {c+d \sin (e+f x)} \, dx}{105 d^3 \left (c^2-d^2\right )^4}--\frac {\left (16 \left (-\frac {1}{16} d^2 \left (144 a^2 b c d^2 \left (5 c^2+3 d^2\right )-a^3 d \left (105 c^4+254 c^2 d^2+25 d^4\right )-3 a b^2 d \left (51 c^4+298 c^2 d^2+35 d^4\right )+2 b^3 \left (c^5+86 c^3 d^2+105 c d^4\right )\right )-\frac {1}{16} c \left (16 a^3 c d^3 \left (11 c^2+13 d^2\right )-6 a b^2 c d \left (3 c^4-62 c^2 d^2-133 d^4\right )-9 a^2 b d^2 \left (5 c^4+102 c^2 d^2+21 d^4\right )-b^3 \left (8 c^6-23 c^4 d^2+294 c^2 d^4+105 d^6\right )\right )\right )\right ) \int \frac {1}{\sqrt {c+d \sin (e+f x)}} \, dx}{105 d^3 \left (c^2-d^2\right )^4}\\ &=\frac {2 (b c-a d)^2 \cos (e+f x) (a+b \sin (e+f x))}{7 d \left (c^2-d^2\right ) f (c+d \sin (e+f x))^{7/2}}+\frac {8 (b c-a d)^2 \left (3 a c d+b \left (c^2-4 d^2\right )\right ) \cos (e+f x)}{35 d^2 \left (c^2-d^2\right )^2 f (c+d \sin (e+f x))^{5/2}}-\frac {2 (b c-a d) \left (a^2 d^2 \left (71 c^2+25 d^2\right )+a b \left (26 c^3 d-218 c d^3\right )+b^2 \left (8 c^4-17 c^2 d^2+105 d^4\right )\right ) \cos (e+f x)}{105 d^2 \left (c^2-d^2\right )^3 f (c+d \sin (e+f x))^{3/2}}+\frac {2 \left (16 a^3 c d^3 \left (11 c^2+13 d^2\right )-6 a b^2 c d \left (3 c^4-62 c^2 d^2-133 d^4\right )-9 a^2 b d^2 \left (5 c^4+102 c^2 d^2+21 d^4\right )-b^3 \left (8 c^6-23 c^4 d^2+294 c^2 d^4+105 d^6\right )\right ) \cos (e+f x)}{105 d^2 \left (c^2-d^2\right )^4 f \sqrt {c+d \sin (e+f x)}}+\frac {\left (\left (16 a^3 c d^3 \left (11 c^2+13 d^2\right )-6 a b^2 c d \left (3 c^4-62 c^2 d^2-133 d^4\right )-9 a^2 b d^2 \left (5 c^4+102 c^2 d^2+21 d^4\right )-b^3 \left (8 c^6-23 c^4 d^2+294 c^2 d^4+105 d^6\right )\right ) \sqrt {c+d \sin (e+f x)}\right ) \int \sqrt {\frac {c}{c+d}+\frac {d \sin (e+f x)}{c+d}} \, dx}{105 d^3 \left (c^2-d^2\right )^4 \sqrt {\frac {c+d \sin (e+f x)}{c+d}}}--\frac {\left (16 \left (-\frac {1}{16} d^2 \left (144 a^2 b c d^2 \left (5 c^2+3 d^2\right )-a^3 d \left (105 c^4+254 c^2 d^2+25 d^4\right )-3 a b^2 d \left (51 c^4+298 c^2 d^2+35 d^4\right )+2 b^3 \left (c^5+86 c^3 d^2+105 c d^4\right )\right )-\frac {1}{16} c \left (16 a^3 c d^3 \left (11 c^2+13 d^2\right )-6 a b^2 c d \left (3 c^4-62 c^2 d^2-133 d^4\right )-9 a^2 b d^2 \left (5 c^4+102 c^2 d^2+21 d^4\right )-b^3 \left (8 c^6-23 c^4 d^2+294 c^2 d^4+105 d^6\right )\right )\right ) \sqrt {\frac {c+d \sin (e+f x)}{c+d}}\right ) \int \frac {1}{\sqrt {\frac {c}{c+d}+\frac {d \sin (e+f x)}{c+d}}} \, dx}{105 d^3 \left (c^2-d^2\right )^4 \sqrt {c+d \sin (e+f x)}}\\ &=\frac {2 (b c-a d)^2 \cos (e+f x) (a+b \sin (e+f x))}{7 d \left (c^2-d^2\right ) f (c+d \sin (e+f x))^{7/2}}+\frac {8 (b c-a d)^2 \left (3 a c d+b \left (c^2-4 d^2\right )\right ) \cos (e+f x)}{35 d^2 \left (c^2-d^2\right )^2 f (c+d \sin (e+f x))^{5/2}}-\frac {2 (b c-a d) \left (a^2 d^2 \left (71 c^2+25 d^2\right )+a b \left (26 c^3 d-218 c d^3\right )+b^2 \left (8 c^4-17 c^2 d^2+105 d^4\right )\right ) \cos (e+f x)}{105 d^2 \left (c^2-d^2\right )^3 f (c+d \sin (e+f x))^{3/2}}+\frac {2 \left (16 a^3 c d^3 \left (11 c^2+13 d^2\right )-6 a b^2 c d \left (3 c^4-62 c^2 d^2-133 d^4\right )-9 a^2 b d^2 \left (5 c^4+102 c^2 d^2+21 d^4\right )-b^3 \left (8 c^6-23 c^4 d^2+294 c^2 d^4+105 d^6\right )\right ) \cos (e+f x)}{105 d^2 \left (c^2-d^2\right )^4 f \sqrt {c+d \sin (e+f x)}}+\frac {2 \left (16 a^3 c d^3 \left (11 c^2+13 d^2\right )-6 a b^2 c d \left (3 c^4-62 c^2 d^2-133 d^4\right )-9 a^2 b d^2 \left (5 c^4+102 c^2 d^2+21 d^4\right )-b^3 \left (8 c^6-23 c^4 d^2+294 c^2 d^4+105 d^6\right )\right ) E\left (\frac {1}{2} \left (e-\frac {\pi }{2}+f x\right )|\frac {2 d}{c+d}\right ) \sqrt {c+d \sin (e+f x)}}{105 d^3 \left (c^2-d^2\right )^4 f \sqrt {\frac {c+d \sin (e+f x)}{c+d}}}+\frac {2 (b c-a d) \left (8 b^2 c^4+26 a b c^3 d+71 a^2 c^2 d^2-17 b^2 c^2 d^2-218 a b c d^3+25 a^2 d^4+105 b^2 d^4\right ) F\left (\frac {1}{2} \left (e-\frac {\pi }{2}+f x\right )|\frac {2 d}{c+d}\right ) \sqrt {\frac {c+d \sin (e+f x)}{c+d}}}{105 d^3 \left (c^2-d^2\right )^3 f \sqrt {c+d \sin (e+f x)}}\\ \end {align*}
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Mathematica [A]
time = 7.11, size = 1127, normalized size = 1.57 \begin {gather*} \frac {\sqrt {c+d \sin (e+f x)} \left (-\frac {2 \left (-b^3 c^3 \cos (e+f x)+3 a b^2 c^2 d \cos (e+f x)-3 a^2 b c d^2 \cos (e+f x)+a^3 d^3 \cos (e+f x)\right )}{7 d^2 \left (-c^2+d^2\right ) (c+d \sin (e+f x))^4}-\frac {6 \left (-3 b^3 c^4 \cos (e+f x)+2 a b^2 c^3 d \cos (e+f x)+5 a^2 b c^2 d^2 \cos (e+f x)+7 b^3 c^2 d^2 \cos (e+f x)-4 a^3 c d^3 \cos (e+f x)-14 a b^2 c d^3 \cos (e+f x)+7 a^2 b d^4 \cos (e+f x)\right )}{35 d^2 \left (-c^2+d^2\right )^2 (c+d \sin (e+f x))^3}-\frac {2 \left (-8 b^3 c^5 \cos (e+f x)-18 a b^2 c^4 d \cos (e+f x)-45 a^2 b c^3 d^2 \cos (e+f x)+17 b^3 c^3 d^2 \cos (e+f x)+71 a^3 c^2 d^3 \cos (e+f x)+201 a b^2 c^2 d^3 \cos (e+f x)-243 a^2 b c d^4 \cos (e+f x)-105 b^3 c d^4 \cos (e+f x)+25 a^3 d^5 \cos (e+f x)+105 a b^2 d^5 \cos (e+f x)\right )}{105 d^2 \left (-c^2+d^2\right )^3 (c+d \sin (e+f x))^2}-\frac {2 \left (8 b^3 c^6 \cos (e+f x)+18 a b^2 c^5 d \cos (e+f x)+45 a^2 b c^4 d^2 \cos (e+f x)-23 b^3 c^4 d^2 \cos (e+f x)-176 a^3 c^3 d^3 \cos (e+f x)-372 a b^2 c^3 d^3 \cos (e+f x)+918 a^2 b c^2 d^4 \cos (e+f x)+294 b^3 c^2 d^4 \cos (e+f x)-208 a^3 c d^5 \cos (e+f x)-798 a b^2 c d^5 \cos (e+f x)+189 a^2 b d^6 \cos (e+f x)+105 b^3 d^6 \cos (e+f x)\right )}{105 d^2 \left (-c^2+d^2\right )^4 (c+d \sin (e+f x))}\right )}{f}-\frac {-\frac {2 \left (2 b^3 c^5 d-105 a^3 c^4 d^2-153 a b^2 c^4 d^2+720 a^2 b c^3 d^3+172 b^3 c^3 d^3-254 a^3 c^2 d^4-894 a b^2 c^2 d^4+432 a^2 b c d^5+210 b^3 c d^5-25 a^3 d^6-105 a b^2 d^6\right ) F\left (\frac {1}{2} \left (-e+\frac {\pi }{2}-f x\right )|\frac {2 d}{c+d}\right ) \sqrt {\frac {c+d \sin (e+f x)}{c+d}}}{\sqrt {c+d \sin (e+f x)}}-\frac {\left (8 b^3 c^6+18 a b^2 c^5 d+45 a^2 b c^4 d^2-23 b^3 c^4 d^2-176 a^3 c^3 d^3-372 a b^2 c^3 d^3+918 a^2 b c^2 d^4+294 b^3 c^2 d^4-208 a^3 c d^5-798 a b^2 c d^5+189 a^2 b d^6+105 b^3 d^6\right ) \left (\frac {2 (c+d) E\left (\frac {1}{2} \left (-e+\frac {\pi }{2}-f x\right )|\frac {2 d}{c+d}\right ) \sqrt {\frac {c+d \sin (e+f x)}{c+d}}}{\sqrt {c+d \sin (e+f x)}}-\frac {2 c F\left (\frac {1}{2} \left (-e+\frac {\pi }{2}-f x\right )|\frac {2 d}{c+d}\right ) \sqrt {\frac {c+d \sin (e+f x)}{c+d}}}{\sqrt {c+d \sin (e+f x)}}\right )}{d}}{105 (c-d)^4 d^2 (c+d)^4 f} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(2110\) vs.
\(2(754)=1508\).
time = 68.68, size = 2111, normalized size = 2.95
method | result | size |
default | \(\text {Expression too large to display}\) | \(2111\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
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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 [C] Result contains higher order function than in optimal. Order 9 vs. order
4.
time = 0.86, size = 4727, normalized size = 6.60 \begin {gather*} \text {Too large to display} \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 {{\left (a+b\,\sin \left (e+f\,x\right )\right )}^3}{{\left (c+d\,\sin \left (e+f\,x\right )\right )}^{9/2}} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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