Optimal. Leaf size=648 \[ \frac {11275 (14627273-35058731 x)}{3966920982528 (3-2 x)^{19/2} \left (2 x^2+x+1\right )}+\frac {451 (14627273 x+28962039)}{283351498752 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^2}+\frac {451 (998691 x+811091)}{10119696384 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^3}+\frac {41 (5677637 x+3436375)}{5059848192 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^4}+\frac {41 (92875 x+47471)}{90354432 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^5}+\frac {5 (47471 x+21409)}{6453888 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^6}+\frac {21409 x+8477}{691488 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^7}+\frac {173 x+53}{7056 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^8}+\frac {x}{63 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^9}-\frac {24229218097975}{22757389978742816768 \sqrt {3-2 x}}-\frac {46601678385075}{11378694989371408384 (3-2 x)^{3/2}}-\frac {11557581705725}{812763927812243456 (3-2 x)^{5/2}}-\frac {132355162272575}{2844673747342852096 (3-2 x)^{7/2}}-\frac {37283626871975}{261245548225363968 (3-2 x)^{9/2}}-\frac {5846828446875}{14513641568075776 (3-2 x)^{11/2}}-\frac {13515743021825}{13476952884641792 (3-2 x)^{13/2}}-\frac {3029508823715}{1555033025150976 (3-2 x)^{15/2}}-\frac {815900548375}{629418129227776 (3-2 x)^{17/2}}+\frac {4718120139975}{351733660450816 (3-2 x)^{19/2}}+\frac {11275 \left (9756589235-2148932869 \sqrt {14}\right ) \sqrt {\frac {1}{2} \left (2 \sqrt {14}-7\right )} \log \left (-2 x-\sqrt {7+2 \sqrt {14}} \sqrt {3-2 x}+\sqrt {14}+3\right )}{637206919404798869504}-\frac {11275 \left (9756589235-2148932869 \sqrt {14}\right ) \sqrt {\frac {1}{2} \left (2 \sqrt {14}-7\right )} \log \left (-2 x+\sqrt {7+2 \sqrt {14}} \sqrt {3-2 x}+\sqrt {14}+3\right )}{637206919404798869504}+\frac {11275 \sqrt {\frac {1}{2} \left (7+2 \sqrt {14}\right )} \left (9756589235+2148932869 \sqrt {14}\right ) \tan ^{-1}\left (\frac {\sqrt {7+2 \sqrt {14}}-2 \sqrt {3-2 x}}{\sqrt {2 \sqrt {14}-7}}\right )}{318603459702399434752}-\frac {11275 \sqrt {\frac {1}{2} \left (7+2 \sqrt {14}\right )} \left (9756589235+2148932869 \sqrt {14}\right ) \tan ^{-1}\left (\frac {2 \sqrt {3-2 x}+\sqrt {7+2 \sqrt {14}}}{\sqrt {2 \sqrt {14}-7}}\right )}{318603459702399434752} \]
[Out]
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Rubi [A] time = 1.16, antiderivative size = 648, normalized size of antiderivative = 1.00, number of steps used = 29, number of rules used = 9, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.450, Rules used = {740, 822, 828, 826, 1169, 634, 618, 204, 628} \[ \frac {11275 (14627273-35058731 x)}{3966920982528 (3-2 x)^{19/2} \left (2 x^2+x+1\right )}+\frac {451 (14627273 x+28962039)}{283351498752 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^2}+\frac {451 (998691 x+811091)}{10119696384 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^3}+\frac {41 (5677637 x+3436375)}{5059848192 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^4}+\frac {41 (92875 x+47471)}{90354432 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^5}+\frac {5 (47471 x+21409)}{6453888 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^6}+\frac {21409 x+8477}{691488 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^7}+\frac {173 x+53}{7056 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^8}+\frac {x}{63 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^9}-\frac {24229218097975}{22757389978742816768 \sqrt {3-2 x}}-\frac {46601678385075}{11378694989371408384 (3-2 x)^{3/2}}-\frac {11557581705725}{812763927812243456 (3-2 x)^{5/2}}-\frac {132355162272575}{2844673747342852096 (3-2 x)^{7/2}}-\frac {37283626871975}{261245548225363968 (3-2 x)^{9/2}}-\frac {5846828446875}{14513641568075776 (3-2 x)^{11/2}}-\frac {13515743021825}{13476952884641792 (3-2 x)^{13/2}}-\frac {3029508823715}{1555033025150976 (3-2 x)^{15/2}}-\frac {815900548375}{629418129227776 (3-2 x)^{17/2}}+\frac {4718120139975}{351733660450816 (3-2 x)^{19/2}}+\frac {11275 \left (9756589235-2148932869 \sqrt {14}\right ) \sqrt {\frac {1}{2} \left (2 \sqrt {14}-7\right )} \log \left (-2 x-\sqrt {7+2 \sqrt {14}} \sqrt {3-2 x}+\sqrt {14}+3\right )}{637206919404798869504}-\frac {11275 \left (9756589235-2148932869 \sqrt {14}\right ) \sqrt {\frac {1}{2} \left (2 \sqrt {14}-7\right )} \log \left (-2 x+\sqrt {7+2 \sqrt {14}} \sqrt {3-2 x}+\sqrt {14}+3\right )}{637206919404798869504}+\frac {11275 \sqrt {\frac {1}{2} \left (7+2 \sqrt {14}\right )} \left (9756589235+2148932869 \sqrt {14}\right ) \tan ^{-1}\left (\frac {\sqrt {7+2 \sqrt {14}}-2 \sqrt {3-2 x}}{\sqrt {2 \sqrt {14}-7}}\right )}{318603459702399434752}-\frac {11275 \sqrt {\frac {1}{2} \left (7+2 \sqrt {14}\right )} \left (9756589235+2148932869 \sqrt {14}\right ) \tan ^{-1}\left (\frac {2 \sqrt {3-2 x}+\sqrt {7+2 \sqrt {14}}}{\sqrt {2 \sqrt {14}-7}}\right )}{318603459702399434752} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 204
Rule 618
Rule 628
Rule 634
Rule 740
Rule 822
Rule 826
Rule 828
Rule 1169
Rubi steps
\begin {align*} \int \frac {1}{(3-2 x)^{21/2} \left (1+x+2 x^2\right )^{10}} \, dx &=\frac {x}{63 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^9}+\frac {\int \frac {1680-1484 x}{(3-2 x)^{21/2} \left (1+x+2 x^2\right )^9} \, dx}{1764}\\ &=\frac {x}{63 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^9}+\frac {53+173 x}{7056 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^8}+\frac {\int \frac {2534672-3322984 x}{(3-2 x)^{21/2} \left (1+x+2 x^2\right )^8} \, dx}{2765952}\\ &=\frac {x}{63 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^9}+\frac {53+173 x}{7056 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^8}+\frac {8477+21409 x}{691488 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^7}+\frac {\int \frac {3218135760-5287166640 x}{(3-2 x)^{21/2} \left (1+x+2 x^2\right )^7} \, dx}{3794886144}\\ &=\frac {x}{63 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^9}+\frac {53+173 x}{7056 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^8}+\frac {8477+21409 x}{691488 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^7}+\frac {5 (21409+47471 x)}{6453888 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^6}+\frac {\int \frac {3218122918080-6729253503840 x}{(3-2 x)^{21/2} \left (1+x+2 x^2\right )^6} \, dx}{4462786105344}\\ &=\frac {x}{63 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^9}+\frac {53+173 x}{7056 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^8}+\frac {8477+21409 x}{691488 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^7}+\frac {5 (21409+47471 x)}{6453888 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^6}+\frac {41 (47471+92875 x)}{90354432 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^5}+\frac {\int \frac {2223971291223360-6819728658120000 x}{(3-2 x)^{21/2} \left (1+x+2 x^2\right )^5} \, dx}{4373530383237120}\\ &=\frac {x}{63 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^9}+\frac {53+173 x}{7056 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^8}+\frac {8477+21409 x}{691488 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^7}+\frac {5 (21409+47471 x)}{6453888 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^6}+\frac {41 (47471+92875 x)}{90354432 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^5}+\frac {41 (3436375+5677637 x)}{5059848192 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^4}+\frac {\int \frac {602017891719552000-5205664113141824640 x}{(3-2 x)^{21/2} \left (1+x+2 x^2\right )^4} \, dx}{3428847820457902080}\\ &=\frac {x}{63 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^9}+\frac {53+173 x}{7056 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^8}+\frac {8477+21409 x}{691488 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^7}+\frac {5 (21409+47471 x)}{6453888 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^6}+\frac {41 (47471+92875 x)}{90354432 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^5}+\frac {41 (3436375+5677637 x)}{5059848192 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^4}+\frac {451 (811091+998691 x)}{10119696384 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^3}+\frac {\int \frac {-644013851165157876480-2602338158011857027840 x}{(3-2 x)^{21/2} \left (1+x+2 x^2\right )^3} \, dx}{2016162518429246423040}\\ &=\frac {x}{63 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^9}+\frac {53+173 x}{7056 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^8}+\frac {8477+21409 x}{691488 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^7}+\frac {5 (21409+47471 x)}{6453888 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^6}+\frac {41 (47471+92875 x)}{90354432 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^5}+\frac {41 (3436375+5677637 x)}{5059848192 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^4}+\frac {451 (811091+998691 x)}{10119696384 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^3}+\frac {451 (28962039+14627273 x)}{283351498752 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^2}+\frac {\int \frac {-781280013553524600192000-460008659488539446208000 x}{(3-2 x)^{21/2} \left (1+x+2 x^2\right )^2} \, dx}{790335707224264597831680}\\ &=\frac {x}{63 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^9}+\frac {53+173 x}{7056 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^8}+\frac {8477+21409 x}{691488 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^7}+\frac {5 (21409+47471 x)}{6453888 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^6}+\frac {41 (47471+92875 x)}{90354432 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^5}+\frac {41 (3436375+5677637 x)}{5059848192 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^4}+\frac {451 (811091+998691 x)}{10119696384 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^3}+\frac {451 (28962039+14627273 x)}{283351498752 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^2}+\frac {11275 (14627273-35058731 x)}{3966920982528 (3-2 x)^{19/2} \left (1+x+2 x^2\right )}+\frac {\int \frac {-209865664941946247912832000+324150102079841867727744000 x}{(3-2 x)^{21/2} \left (1+x+2 x^2\right )} \, dx}{154905798615955861175009280}\\ &=\frac {4718120139975}{351733660450816 (3-2 x)^{19/2}}+\frac {x}{63 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^9}+\frac {53+173 x}{7056 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^8}+\frac {8477+21409 x}{691488 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^7}+\frac {5 (21409+47471 x)}{6453888 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^6}+\frac {41 (47471+92875 x)}{90354432 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^5}+\frac {41 (3436375+5677637 x)}{5059848192 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^4}+\frac {451 (811091+998691 x)}{10119696384 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^3}+\frac {451 (28962039+14627273 x)}{283351498752 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^2}+\frac {11275 (14627273-35058731 x)}{3966920982528 (3-2 x)^{19/2} \left (1+x+2 x^2\right )}+\frac {\int \frac {-2327225523695253718758144000+1105437952711266214715136000 x}{(3-2 x)^{19/2} \left (1+x+2 x^2\right )} \, dx}{4337362361246764112900259840}\\ &=\frac {4718120139975}{351733660450816 (3-2 x)^{19/2}}-\frac {815900548375}{629418129227776 (3-2 x)^{17/2}}+\frac {x}{63 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^9}+\frac {53+173 x}{7056 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^8}+\frac {8477+21409 x}{691488 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^7}+\frac {5 (21409+47471 x)}{6453888 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^6}+\frac {41 (47471+92875 x)}{90354432 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^5}+\frac {41 (3436375+5677637 x)}{5059848192 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^4}+\frac {451 (811091+998691 x)}{10119696384 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^3}+\frac {451 (28962039+14627273 x)}{283351498752 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^2}+\frac {11275 (14627273-35058731 x)}{3966920982528 (3-2 x)^{19/2} \left (1+x+2 x^2\right )}+\frac {\int \frac {-20828680094984562179495424000-2676274378513417586741760000 x}{(3-2 x)^{17/2} \left (1+x+2 x^2\right )} \, dx}{121446146114909395161207275520}\\ &=\frac {4718120139975}{351733660450816 (3-2 x)^{19/2}}-\frac {815900548375}{629418129227776 (3-2 x)^{17/2}}-\frac {3029508823715}{1555033025150976 (3-2 x)^{15/2}}+\frac {x}{63 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^9}+\frac {53+173 x}{7056 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^8}+\frac {8477+21409 x}{691488 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^7}+\frac {5 (21409+47471 x)}{6453888 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^6}+\frac {41 (47471+92875 x)}{90354432 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^5}+\frac {41 (3436375+5677637 x)}{5059848192 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^4}+\frac {451 (811091+998691 x)}{10119696384 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^3}+\frac {451 (28962039+14627273 x)}{283351498752 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^2}+\frac {11275 (14627273-35058731 x)}{3966920982528 (3-2 x)^{19/2} \left (1+x+2 x^2\right )}+\frac {\int \frac {-161276892002849662262479872000-99372366651018754238432256000 x}{(3-2 x)^{15/2} \left (1+x+2 x^2\right )} \, dx}{3400492091217463064513803714560}\\ &=\frac {4718120139975}{351733660450816 (3-2 x)^{19/2}}-\frac {815900548375}{629418129227776 (3-2 x)^{17/2}}-\frac {3029508823715}{1555033025150976 (3-2 x)^{15/2}}-\frac {13515743021825}{13476952884641792 (3-2 x)^{13/2}}+\frac {x}{63 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^9}+\frac {53+173 x}{7056 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^8}+\frac {8477+21409 x}{691488 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^7}+\frac {5 (21409+47471 x)}{6453888 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^6}+\frac {41 (47471+92875 x)}{90354432 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^5}+\frac {41 (3436375+5677637 x)}{5059848192 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^4}+\frac {451 (811091+998691 x)}{10119696384 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^3}+\frac {451 (28962039+14627273 x)}{283351498752 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^2}+\frac {11275 (14627273-35058731 x)}{3966920982528 (3-2 x)^{19/2} \left (1+x+2 x^2\right )}+\frac {\int \frac {-1091470402720759789622974464000-1241341767917511174480513024000 x}{(3-2 x)^{13/2} \left (1+x+2 x^2\right )} \, dx}{95213778554088965806386504007680}\\ &=\frac {4718120139975}{351733660450816 (3-2 x)^{19/2}}-\frac {815900548375}{629418129227776 (3-2 x)^{17/2}}-\frac {3029508823715}{1555033025150976 (3-2 x)^{15/2}}-\frac {13515743021825}{13476952884641792 (3-2 x)^{13/2}}-\frac {5846828446875}{14513641568075776 (3-2 x)^{11/2}}+\frac {x}{63 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^9}+\frac {53+173 x}{7056 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^8}+\frac {8477+21409 x}{691488 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^7}+\frac {5 (21409+47471 x)}{6453888 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^6}+\frac {41 (47471+92875 x)}{90354432 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^5}+\frac {41 (3436375+5677637 x)}{5059848192 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^4}+\frac {451 (811091+998691 x)}{10119696384 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^3}+\frac {451 (28962039+14627273 x)}{283351498752 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^2}+\frac {11275 (14627273-35058731 x)}{3966920982528 (3-2 x)^{19/2} \left (1+x+2 x^2\right )}+\frac {\int \frac {-6249079685931055968022769664000-11813932218388106205374976000000 x}{(3-2 x)^{11/2} \left (1+x+2 x^2\right )} \, dx}{2665985799514491042578822112215040}\\ &=\frac {4718120139975}{351733660450816 (3-2 x)^{19/2}}-\frac {815900548375}{629418129227776 (3-2 x)^{17/2}}-\frac {3029508823715}{1555033025150976 (3-2 x)^{15/2}}-\frac {13515743021825}{13476952884641792 (3-2 x)^{13/2}}-\frac {5846828446875}{14513641568075776 (3-2 x)^{11/2}}-\frac {37283626871975}{261245548225363968 (3-2 x)^{9/2}}+\frac {x}{63 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^9}+\frac {53+173 x}{7056 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^8}+\frac {8477+21409 x}{691488 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^7}+\frac {5 (21409+47471 x)}{6453888 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^6}+\frac {41 (47471+92875 x)}{90354432 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^5}+\frac {41 (3436375+5677637 x)}{5059848192 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^4}+\frac {451 (811091+998691 x)}{10119696384 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^3}+\frac {451 (28962039+14627273 x)}{283351498752 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^2}+\frac {11275 (14627273-35058731 x)}{3966920982528 (3-2 x)^{19/2} \left (1+x+2 x^2\right )}+\frac {\int \frac {-26364773050672235333432205312000-95879912054052861104340934656000 x}{(3-2 x)^{9/2} \left (1+x+2 x^2\right )} \, dx}{74647602386405749192207019142021120}\\ &=\frac {4718120139975}{351733660450816 (3-2 x)^{19/2}}-\frac {815900548375}{629418129227776 (3-2 x)^{17/2}}-\frac {3029508823715}{1555033025150976 (3-2 x)^{15/2}}-\frac {13515743021825}{13476952884641792 (3-2 x)^{13/2}}-\frac {5846828446875}{14513641568075776 (3-2 x)^{11/2}}-\frac {37283626871975}{261245548225363968 (3-2 x)^{9/2}}-\frac {132355162272575}{2844673747342852096 (3-2 x)^{7/2}}+\frac {x}{63 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^9}+\frac {53+173 x}{7056 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^8}+\frac {8477+21409 x}{691488 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^7}+\frac {5 (21409+47471 x)}{6453888 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^6}+\frac {41 (47471+92875 x)}{90354432 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^5}+\frac {41 (3436375+5677637 x)}{5059848192 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^4}+\frac {451 (811091+998691 x)}{10119696384 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^3}+\frac {451 (28962039+14627273 x)}{283351498752 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^2}+\frac {11275 (14627273-35058731 x)}{3966920982528 (3-2 x)^{19/2} \left (1+x+2 x^2\right )}+\frac {\int \frac {-19158360297272160458775773184000-680738564527006107959774429184000 x}{(3-2 x)^{7/2} \left (1+x+2 x^2\right )} \, dx}{2090132866819360977381796535976591360}\\ &=\frac {4718120139975}{351733660450816 (3-2 x)^{19/2}}-\frac {815900548375}{629418129227776 (3-2 x)^{17/2}}-\frac {3029508823715}{1555033025150976 (3-2 x)^{15/2}}-\frac {13515743021825}{13476952884641792 (3-2 x)^{13/2}}-\frac {5846828446875}{14513641568075776 (3-2 x)^{11/2}}-\frac {37283626871975}{261245548225363968 (3-2 x)^{9/2}}-\frac {132355162272575}{2844673747342852096 (3-2 x)^{7/2}}-\frac {11557581705725}{812763927812243456 (3-2 x)^{5/2}}+\frac {x}{63 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^9}+\frac {53+173 x}{7056 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^8}+\frac {8477+21409 x}{691488 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^7}+\frac {5 (21409+47471 x)}{6453888 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^6}+\frac {41 (47471+92875 x)}{90354432 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^5}+\frac {41 (3436375+5677637 x)}{5059848192 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^4}+\frac {451 (811091+998691 x)}{10119696384 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^3}+\frac {451 (28962039+14627273 x)}{283351498752 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^2}+\frac {11275 (14627273-35058731 x)}{3966920982528 (3-2 x)^{19/2} \left (1+x+2 x^2\right )}+\frac {\int \frac {1208210246675834932249342672896000-4161064828351125289593749667840000 x}{(3-2 x)^{5/2} \left (1+x+2 x^2\right )} \, dx}{58523720270942107366690303007344558080}\\ &=\frac {4718120139975}{351733660450816 (3-2 x)^{19/2}}-\frac {815900548375}{629418129227776 (3-2 x)^{17/2}}-\frac {3029508823715}{1555033025150976 (3-2 x)^{15/2}}-\frac {13515743021825}{13476952884641792 (3-2 x)^{13/2}}-\frac {5846828446875}{14513641568075776 (3-2 x)^{11/2}}-\frac {37283626871975}{261245548225363968 (3-2 x)^{9/2}}-\frac {132355162272575}{2844673747342852096 (3-2 x)^{7/2}}-\frac {11557581705725}{812763927812243456 (3-2 x)^{5/2}}-\frac {46601678385075}{11378694989371408384 (3-2 x)^{3/2}}+\frac {x}{63 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^9}+\frac {53+173 x}{7056 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^8}+\frac {8477+21409 x}{691488 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^7}+\frac {5 (21409+47471 x)}{6453888 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^6}+\frac {41 (47471+92875 x)}{90354432 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^5}+\frac {41 (3436375+5677637 x)}{5059848192 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^4}+\frac {451 (811091+998691 x)}{10119696384 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^3}+\frac {451 (28962039+14627273 x)}{283351498752 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^2}+\frac {11275 (14627273-35058731 x)}{3966920982528 (3-2 x)^{19/2} \left (1+x+2 x^2\right )}+\frac {\int \frac {17987811630108930037182240718848000-20133547983403412008565127315456000 x}{(3-2 x)^{3/2} \left (1+x+2 x^2\right )} \, dx}{1638664167586379006267328484205647626240}\\ &=\frac {4718120139975}{351733660450816 (3-2 x)^{19/2}}-\frac {815900548375}{629418129227776 (3-2 x)^{17/2}}-\frac {3029508823715}{1555033025150976 (3-2 x)^{15/2}}-\frac {13515743021825}{13476952884641792 (3-2 x)^{13/2}}-\frac {5846828446875}{14513641568075776 (3-2 x)^{11/2}}-\frac {37283626871975}{261245548225363968 (3-2 x)^{9/2}}-\frac {132355162272575}{2844673747342852096 (3-2 x)^{7/2}}-\frac {11557581705725}{812763927812243456 (3-2 x)^{5/2}}-\frac {46601678385075}{11378694989371408384 (3-2 x)^{3/2}}-\frac {24229218097975}{22757389978742816768 \sqrt {3-2 x}}+\frac {x}{63 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^9}+\frac {53+173 x}{7056 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^8}+\frac {8477+21409 x}{691488 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^7}+\frac {5 (21409+47471 x)}{6453888 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^6}+\frac {41 (47471+92875 x)}{90354432 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^5}+\frac {41 (3436375+5677637 x)}{5059848192 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^4}+\frac {451 (811091+998691 x)}{10119696384 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^3}+\frac {451 (28962039+14627273 x)}{283351498752 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^2}+\frac {11275 (14627273-35058731 x)}{3966920982528 (3-2 x)^{19/2} \left (1+x+2 x^2\right )}+\frac {\int \frac {184169589007678264314588180381696000-48850041379984751902661801017344000 x}{\sqrt {3-2 x} \left (1+x+2 x^2\right )} \, dx}{45882596692418612175485197557758133534720}\\ &=\frac {4718120139975}{351733660450816 (3-2 x)^{19/2}}-\frac {815900548375}{629418129227776 (3-2 x)^{17/2}}-\frac {3029508823715}{1555033025150976 (3-2 x)^{15/2}}-\frac {13515743021825}{13476952884641792 (3-2 x)^{13/2}}-\frac {5846828446875}{14513641568075776 (3-2 x)^{11/2}}-\frac {37283626871975}{261245548225363968 (3-2 x)^{9/2}}-\frac {132355162272575}{2844673747342852096 (3-2 x)^{7/2}}-\frac {11557581705725}{812763927812243456 (3-2 x)^{5/2}}-\frac {46601678385075}{11378694989371408384 (3-2 x)^{3/2}}-\frac {24229218097975}{22757389978742816768 \sqrt {3-2 x}}+\frac {x}{63 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^9}+\frac {53+173 x}{7056 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^8}+\frac {8477+21409 x}{691488 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^7}+\frac {5 (21409+47471 x)}{6453888 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^6}+\frac {41 (47471+92875 x)}{90354432 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^5}+\frac {41 (3436375+5677637 x)}{5059848192 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^4}+\frac {451 (811091+998691 x)}{10119696384 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^3}+\frac {451 (28962039+14627273 x)}{283351498752 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^2}+\frac {11275 (14627273-35058731 x)}{3966920982528 (3-2 x)^{19/2} \left (1+x+2 x^2\right )}+\frac {\operatorname {Subst}\left (\int \frac {-221789053875402272921190957711360000-48850041379984751902661801017344000 x^2}{28-14 x^2+2 x^4} \, dx,x,\sqrt {3-2 x}\right )}{22941298346209306087742598778879066767360}\\ &=\frac {4718120139975}{351733660450816 (3-2 x)^{19/2}}-\frac {815900548375}{629418129227776 (3-2 x)^{17/2}}-\frac {3029508823715}{1555033025150976 (3-2 x)^{15/2}}-\frac {13515743021825}{13476952884641792 (3-2 x)^{13/2}}-\frac {5846828446875}{14513641568075776 (3-2 x)^{11/2}}-\frac {37283626871975}{261245548225363968 (3-2 x)^{9/2}}-\frac {132355162272575}{2844673747342852096 (3-2 x)^{7/2}}-\frac {11557581705725}{812763927812243456 (3-2 x)^{5/2}}-\frac {46601678385075}{11378694989371408384 (3-2 x)^{3/2}}-\frac {24229218097975}{22757389978742816768 \sqrt {3-2 x}}+\frac {x}{63 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^9}+\frac {53+173 x}{7056 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^8}+\frac {8477+21409 x}{691488 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^7}+\frac {5 (21409+47471 x)}{6453888 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^6}+\frac {41 (47471+92875 x)}{90354432 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^5}+\frac {41 (3436375+5677637 x)}{5059848192 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^4}+\frac {451 (811091+998691 x)}{10119696384 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^3}+\frac {451 (28962039+14627273 x)}{283351498752 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^2}+\frac {11275 (14627273-35058731 x)}{3966920982528 (3-2 x)^{19/2} \left (1+x+2 x^2\right )}+\frac {\operatorname {Subst}\left (\int \frac {-221789053875402272921190957711360000 \sqrt {7+2 \sqrt {14}}-\left (-221789053875402272921190957711360000+48850041379984751902661801017344000 \sqrt {14}\right ) x}{\sqrt {14}-\sqrt {7+2 \sqrt {14}} x+x^2} \, dx,x,\sqrt {3-2 x}\right )}{91765193384837224350970395115516267069440 \sqrt {14 \left (7+2 \sqrt {14}\right )}}+\frac {\operatorname {Subst}\left (\int \frac {-221789053875402272921190957711360000 \sqrt {7+2 \sqrt {14}}+\left (-221789053875402272921190957711360000+48850041379984751902661801017344000 \sqrt {14}\right ) x}{\sqrt {14}+\sqrt {7+2 \sqrt {14}} x+x^2} \, dx,x,\sqrt {3-2 x}\right )}{91765193384837224350970395115516267069440 \sqrt {14 \left (7+2 \sqrt {14}\right )}}\\ &=\frac {4718120139975}{351733660450816 (3-2 x)^{19/2}}-\frac {815900548375}{629418129227776 (3-2 x)^{17/2}}-\frac {3029508823715}{1555033025150976 (3-2 x)^{15/2}}-\frac {13515743021825}{13476952884641792 (3-2 x)^{13/2}}-\frac {5846828446875}{14513641568075776 (3-2 x)^{11/2}}-\frac {37283626871975}{261245548225363968 (3-2 x)^{9/2}}-\frac {132355162272575}{2844673747342852096 (3-2 x)^{7/2}}-\frac {11557581705725}{812763927812243456 (3-2 x)^{5/2}}-\frac {46601678385075}{11378694989371408384 (3-2 x)^{3/2}}-\frac {24229218097975}{22757389978742816768 \sqrt {3-2 x}}+\frac {x}{63 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^9}+\frac {53+173 x}{7056 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^8}+\frac {8477+21409 x}{691488 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^7}+\frac {5 (21409+47471 x)}{6453888 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^6}+\frac {41 (47471+92875 x)}{90354432 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^5}+\frac {41 (3436375+5677637 x)}{5059848192 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^4}+\frac {451 (811091+998691 x)}{10119696384 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^3}+\frac {451 (28962039+14627273 x)}{283351498752 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^2}+\frac {11275 (14627273-35058731 x)}{3966920982528 (3-2 x)^{19/2} \left (1+x+2 x^2\right )}+\frac {\left (11275 \left (9756589235-2148932869 \sqrt {14}\right )\right ) \operatorname {Subst}\left (\int \frac {-\sqrt {7+2 \sqrt {14}}+2 x}{\sqrt {14}-\sqrt {7+2 \sqrt {14}} x+x^2} \, dx,x,\sqrt {3-2 x}\right )}{91029559914971267072 \sqrt {14 \left (7+2 \sqrt {14}\right )}}-\frac {\left (11275 \left (9756589235-2148932869 \sqrt {14}\right )\right ) \operatorname {Subst}\left (\int \frac {\sqrt {7+2 \sqrt {14}}+2 x}{\sqrt {14}+\sqrt {7+2 \sqrt {14}} x+x^2} \, dx,x,\sqrt {3-2 x}\right )}{91029559914971267072 \sqrt {14 \left (7+2 \sqrt {14}\right )}}-\frac {\left (11275 \left (30085060166+9756589235 \sqrt {14}\right )\right ) \operatorname {Subst}\left (\int \frac {1}{\sqrt {14}-\sqrt {7+2 \sqrt {14}} x+x^2} \, dx,x,\sqrt {3-2 x}\right )}{1274413838809597739008}-\frac {\left (11275 \left (30085060166+9756589235 \sqrt {14}\right )\right ) \operatorname {Subst}\left (\int \frac {1}{\sqrt {14}+\sqrt {7+2 \sqrt {14}} x+x^2} \, dx,x,\sqrt {3-2 x}\right )}{1274413838809597739008}\\ &=\frac {4718120139975}{351733660450816 (3-2 x)^{19/2}}-\frac {815900548375}{629418129227776 (3-2 x)^{17/2}}-\frac {3029508823715}{1555033025150976 (3-2 x)^{15/2}}-\frac {13515743021825}{13476952884641792 (3-2 x)^{13/2}}-\frac {5846828446875}{14513641568075776 (3-2 x)^{11/2}}-\frac {37283626871975}{261245548225363968 (3-2 x)^{9/2}}-\frac {132355162272575}{2844673747342852096 (3-2 x)^{7/2}}-\frac {11557581705725}{812763927812243456 (3-2 x)^{5/2}}-\frac {46601678385075}{11378694989371408384 (3-2 x)^{3/2}}-\frac {24229218097975}{22757389978742816768 \sqrt {3-2 x}}+\frac {x}{63 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^9}+\frac {53+173 x}{7056 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^8}+\frac {8477+21409 x}{691488 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^7}+\frac {5 (21409+47471 x)}{6453888 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^6}+\frac {41 (47471+92875 x)}{90354432 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^5}+\frac {41 (3436375+5677637 x)}{5059848192 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^4}+\frac {451 (811091+998691 x)}{10119696384 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^3}+\frac {451 (28962039+14627273 x)}{283351498752 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^2}+\frac {11275 (14627273-35058731 x)}{3966920982528 (3-2 x)^{19/2} \left (1+x+2 x^2\right )}+\frac {11275 \left (9756589235-2148932869 \sqrt {14}\right ) \log \left (3+\sqrt {14}-\sqrt {7+2 \sqrt {14}} \sqrt {3-2 x}-2 x\right )}{91029559914971267072 \sqrt {14 \left (7+2 \sqrt {14}\right )}}-\frac {11275 \left (9756589235-2148932869 \sqrt {14}\right ) \log \left (3+\sqrt {14}+\sqrt {7+2 \sqrt {14}} \sqrt {3-2 x}-2 x\right )}{91029559914971267072 \sqrt {14 \left (7+2 \sqrt {14}\right )}}+\frac {\left (11275 \left (30085060166+9756589235 \sqrt {14}\right )\right ) \operatorname {Subst}\left (\int \frac {1}{7-2 \sqrt {14}-x^2} \, dx,x,-\sqrt {7+2 \sqrt {14}}+2 \sqrt {3-2 x}\right )}{637206919404798869504}+\frac {\left (11275 \left (30085060166+9756589235 \sqrt {14}\right )\right ) \operatorname {Subst}\left (\int \frac {1}{7-2 \sqrt {14}-x^2} \, dx,x,\sqrt {7+2 \sqrt {14}}+2 \sqrt {3-2 x}\right )}{637206919404798869504}\\ &=\frac {4718120139975}{351733660450816 (3-2 x)^{19/2}}-\frac {815900548375}{629418129227776 (3-2 x)^{17/2}}-\frac {3029508823715}{1555033025150976 (3-2 x)^{15/2}}-\frac {13515743021825}{13476952884641792 (3-2 x)^{13/2}}-\frac {5846828446875}{14513641568075776 (3-2 x)^{11/2}}-\frac {37283626871975}{261245548225363968 (3-2 x)^{9/2}}-\frac {132355162272575}{2844673747342852096 (3-2 x)^{7/2}}-\frac {11557581705725}{812763927812243456 (3-2 x)^{5/2}}-\frac {46601678385075}{11378694989371408384 (3-2 x)^{3/2}}-\frac {24229218097975}{22757389978742816768 \sqrt {3-2 x}}+\frac {x}{63 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^9}+\frac {53+173 x}{7056 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^8}+\frac {8477+21409 x}{691488 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^7}+\frac {5 (21409+47471 x)}{6453888 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^6}+\frac {41 (47471+92875 x)}{90354432 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^5}+\frac {41 (3436375+5677637 x)}{5059848192 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^4}+\frac {451 (811091+998691 x)}{10119696384 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^3}+\frac {451 (28962039+14627273 x)}{283351498752 (3-2 x)^{19/2} \left (1+x+2 x^2\right )^2}+\frac {11275 (14627273-35058731 x)}{3966920982528 (3-2 x)^{19/2} \left (1+x+2 x^2\right )}+\frac {11275 \sqrt {\frac {1}{2} \left (7+2 \sqrt {14}\right )} \left (9756589235+2148932869 \sqrt {14}\right ) \tan ^{-1}\left (\frac {\sqrt {7+2 \sqrt {14}}-2 \sqrt {3-2 x}}{\sqrt {-7+2 \sqrt {14}}}\right )}{318603459702399434752}-\frac {11275 \sqrt {\frac {1}{2} \left (7+2 \sqrt {14}\right )} \left (9756589235+2148932869 \sqrt {14}\right ) \tan ^{-1}\left (\frac {\sqrt {7+2 \sqrt {14}}+2 \sqrt {3-2 x}}{\sqrt {-7+2 \sqrt {14}}}\right )}{318603459702399434752}+\frac {11275 \left (9756589235-2148932869 \sqrt {14}\right ) \log \left (3+\sqrt {14}-\sqrt {7+2 \sqrt {14}} \sqrt {3-2 x}-2 x\right )}{91029559914971267072 \sqrt {14 \left (7+2 \sqrt {14}\right )}}-\frac {11275 \left (9756589235-2148932869 \sqrt {14}\right ) \log \left (3+\sqrt {14}+\sqrt {7+2 \sqrt {14}} \sqrt {3-2 x}-2 x\right )}{91029559914971267072 \sqrt {14 \left (7+2 \sqrt {14}\right )}}\\ \end {align*}
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Mathematica [C] time = 6.09, size = 610, normalized size = 0.94 \[ \frac {x}{63 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^9}+\frac {\frac {67816 x+20776}{1568 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^8}+\frac {\frac {117492592 x+46521776}{1372 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^7}+\frac {\frac {164128134240 x+74020332960}{1176 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^6}+\frac {\frac {184316990760000 x+94209549053760}{980 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^5}+\frac {1}{980} \left (\frac {157747397367934080 x+95476201213680000}{784 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^4}+\frac {1}{784} \left (\frac {89735798552133000960 x+72879297583985544960}{588 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^3}+\frac {1}{588} \left (\frac {18400346379541577848320 x+36432734212165998389760}{392 (3-2 x)^{19/2} \left (2 x^2+x+1\right )^2}+\frac {1}{392} \left (\frac {6440121232839552246912000-15435719146659136558464000 x}{196 (3-2 x)^{19/2} \left (2 x^2+x+1\right )}+\frac {1}{196} \left (\frac {39479926882545221954112000}{19 (3-2 x)^{19/2}}+\frac {1}{266} \left (-\frac {908021664138480966930240000}{17 (3-2 x)^{17/2}}+\frac {1}{238} \left (-\frac {19105520493023248582746201600}{(3-2 x)^{15/2}}+\frac {1}{210} \left (-\frac {26849557435537239465884310720000}{13 (3-2 x)^{13/2}}+\frac {1}{182} \left (-\frac {150994423858598796539274120000000}{(3-2 x)^{11/2}}+\frac {1}{154} \left (-\frac {8237718113587514139784976619840000}{(3-2 x)^{9/2}}+\frac {1}{126} \left (-\frac {338389312036560466460044072847040000}{(3-2 x)^{7/2}}+\frac {1}{98} \left (-\frac {10135305528576510550836394515648960000}{(3-2 x)^{5/2}}+\frac {1}{70} \left (-\frac {204334375738495648812805956791073600000}{(3-2 x)^{3/2}}+\frac {1}{42} \left (-\frac {2230994866519889796828561036406228800000}{\sqrt {3-2 x}}+\frac {1}{7} \left (\frac {\sqrt {\frac {1}{2} \left (7-i \sqrt {7}\right )} \left (-31233928131278457155599854509687203200000-71750597240923349846054347713013891200000 i \sqrt {7}\right ) \tanh ^{-1}\left (\frac {\sqrt {2} \sqrt {3-2 x}}{\sqrt {7-i \sqrt {7}}}\right )}{-14+2 i \sqrt {7}}+\frac {\sqrt {\frac {1}{2} \left (7+i \sqrt {7}\right )} \left (-31233928131278457155599854509687203200000+71750597240923349846054347713013891200000 i \sqrt {7}\right ) \tanh ^{-1}\left (\frac {\sqrt {2} \sqrt {3-2 x}}{\sqrt {7+i \sqrt {7}}}\right )}{-14-2 i \sqrt {7}}\right )\right )\right )\right )\right )\right )\right )\right )\right )\right )\right )\right )\right )\right )\right )}{1176}}{1372}}{1568}}{1764} \]
Antiderivative was successfully verified.
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fricas [B] time = 1.72, size = 1563, normalized size = 2.41 \[ \text {result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 4.19, size = 972, normalized size = 1.50 \[ \text {result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.07, size = 719, normalized size = 1.11 \[ \text {result too large to display} \]
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 \[ \int \frac {1}{{\left (2 \, x^{2} + x + 1\right )}^{10} {\left (-2 \, x + 3\right )}^{\frac {21}{2}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.56, size = 567, normalized size = 0.88 \[ \text {result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
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