Optimal. Leaf size=158 \[ -2 \sqrt [4]{d} \tan ^{-1}\left (\frac {\sqrt [4]{d} \sqrt [4]{x \left (2 a b+b^2\right )-a b^2+x^2 (-a-2 b)+x^3}}{a-x}\right )+2 \sqrt [4]{d} \tanh ^{-1}\left (\frac {\sqrt [4]{d} \sqrt [4]{x \left (2 a b+b^2\right )-a b^2+x^2 (-a-2 b)+x^3}}{a-x}\right )+\frac {4 \left (-a b^2+2 a b x-a x^2+b^2 x-2 b x^2+x^3\right )^{3/4}}{(b-x)^2} \]
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Rubi [F] time = 28.42, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {(2 a-3 b+x) \left (-a^3+3 a^2 x-3 a x^2+x^3\right )}{(-b+x) \sqrt [4]{(-a+x) (-b+x)^2} \left (-a^3-b^2 d+\left (3 a^2+2 b d\right ) x-(3 a+d) x^2+x^3\right )} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {(2 a-3 b+x) \left (-a^3+3 a^2 x-3 a x^2+x^3\right )}{(-b+x) \sqrt [4]{(-a+x) (-b+x)^2} \left (-a^3-b^2 d+\left (3 a^2+2 b d\right ) x-(3 a+d) x^2+x^3\right )} \, dx &=\frac {\left (\sqrt [4]{-a+x} \sqrt {-b+x}\right ) \int \frac {(2 a-3 b+x) \left (-a^3+3 a^2 x-3 a x^2+x^3\right )}{\sqrt [4]{-a+x} (-b+x)^{3/2} \left (-a^3-b^2 d+\left (3 a^2+2 b d\right ) x-(3 a+d) x^2+x^3\right )} \, dx}{\sqrt [4]{(-a+x) (-b+x)^2}}\\ &=\frac {\left (\sqrt [4]{-a+x} \sqrt {-b+x}\right ) \int \frac {(-a+x)^{3/4} (2 a-3 b+x) \left (a^2-2 a x+x^2\right )}{(-b+x)^{3/2} \left (-a^3-b^2 d+\left (3 a^2+2 b d\right ) x-(3 a+d) x^2+x^3\right )} \, dx}{\sqrt [4]{(-a+x) (-b+x)^2}}\\ &=\frac {\left (\sqrt [4]{-a+x} \sqrt {-b+x}\right ) \int \frac {(-a+x)^{11/4} (2 a-3 b+x)}{(-b+x)^{3/2} \left (-a^3-b^2 d+\left (3 a^2+2 b d\right ) x-(3 a+d) x^2+x^3\right )} \, dx}{\sqrt [4]{(-a+x) (-b+x)^2}}\\ &=\frac {\left (\sqrt [4]{-a+x} \sqrt {-b+x}\right ) \int \left (\frac {3 \left (1-\frac {2 a}{3 b}\right ) b (-a+x)^{11/4}}{(-b+x)^{3/2} \left (a^3+b^2 d-\left (3 a^2+2 b d\right ) x+(3 a+d) x^2-x^3\right )}+\frac {x (-a+x)^{11/4}}{(-b+x)^{3/2} \left (-a^3-b^2 d+\left (3 a^2+2 b d\right ) x-(3 a+d) x^2+x^3\right )}\right ) \, dx}{\sqrt [4]{(-a+x) (-b+x)^2}}\\ &=\frac {\left (\sqrt [4]{-a+x} \sqrt {-b+x}\right ) \int \frac {x (-a+x)^{11/4}}{(-b+x)^{3/2} \left (-a^3-b^2 d+\left (3 a^2+2 b d\right ) x-(3 a+d) x^2+x^3\right )} \, dx}{\sqrt [4]{(-a+x) (-b+x)^2}}+\frac {\left ((-2 a+3 b) \sqrt [4]{-a+x} \sqrt {-b+x}\right ) \int \frac {(-a+x)^{11/4}}{(-b+x)^{3/2} \left (a^3+b^2 d-\left (3 a^2+2 b d\right ) x+(3 a+d) x^2-x^3\right )} \, dx}{\sqrt [4]{(-a+x) (-b+x)^2}}\\ &=-\frac {\left (4 \sqrt [4]{-a+x} \sqrt {-b+x}\right ) \operatorname {Subst}\left (\int \frac {x^{14} \left (a+x^4\right )}{\left (a-b+x^4\right )^{3/2} \left (a^2 d+b^2 d-2 b d x^4+x^8 \left (d-x^4\right )+2 a d \left (-b+x^4\right )\right )} \, dx,x,\sqrt [4]{-a+x}\right )}{\sqrt [4]{(-a+x) (-b+x)^2}}+\frac {\left (4 (-2 a+3 b) \sqrt [4]{-a+x} \sqrt {-b+x}\right ) \operatorname {Subst}\left (\int \frac {x^{14}}{\left (a-b+x^4\right )^{3/2} \left (a^2 d+b^2 d-2 b d x^4+x^8 \left (d-x^4\right )+2 a d \left (-b+x^4\right )\right )} \, dx,x,\sqrt [4]{-a+x}\right )}{\sqrt [4]{(-a+x) (-b+x)^2}}\\ &=-\frac {\left (4 \sqrt [4]{-a+x} \sqrt {-b+x}\right ) \operatorname {Subst}\left (\int \frac {x^{14} \left (a+x^4\right )}{\left (a-b+x^4\right )^{3/2} \left (a^2 \left (1+\frac {b^2}{a^2}\right ) d-2 b d x^4+x^8 \left (d-x^4\right )+2 a d \left (-b+x^4\right )\right )} \, dx,x,\sqrt [4]{-a+x}\right )}{\sqrt [4]{(-a+x) (-b+x)^2}}+\frac {\left (4 (-2 a+3 b) \sqrt [4]{-a+x} \sqrt {-b+x}\right ) \operatorname {Subst}\left (\int \frac {x^{14}}{\left (a-b+x^4\right )^{3/2} \left (a^2 \left (1+\frac {b^2}{a^2}\right ) d-2 b d x^4+x^8 \left (d-x^4\right )+2 a d \left (-b+x^4\right )\right )} \, dx,x,\sqrt [4]{-a+x}\right )}{\sqrt [4]{(-a+x) (-b+x)^2}}\\ &=-\frac {\left (4 \sqrt [4]{-a+x} \sqrt {-b+x}\right ) \operatorname {Subst}\left (\int \left (-\frac {(a+d) x^2}{\left (a-b+x^4\right )^{3/2}}-\frac {x^6}{\left (a-b+x^4\right )^{3/2}}+\frac {x^2 \left ((a-b)^2 d (a+d)+(a-b) d (3 a-b+2 d) x^4+d (3 a-2 b+d) x^8\right )}{\left (a-b+x^4\right )^{3/2} \left (a^2 \left (1+\frac {b^2}{a^2}\right ) d-2 b d x^4+x^8 \left (d-x^4\right )+2 a d \left (-b+x^4\right )\right )}\right ) \, dx,x,\sqrt [4]{-a+x}\right )}{\sqrt [4]{(-a+x) (-b+x)^2}}+\frac {\left (4 (-2 a+3 b) \sqrt [4]{-a+x} \sqrt {-b+x}\right ) \operatorname {Subst}\left (\int \left (-\frac {x^2}{\left (a-b+x^4\right )^{3/2}}+\frac {x^2 \left ((a-b)^2 d+2 (a-b) d x^4+d x^8\right )}{\left (a-b+x^4\right )^{3/2} \left (a^2 \left (1+\frac {b^2}{a^2}\right ) d-2 b d x^4+x^8 \left (d-x^4\right )+2 a d \left (-b+x^4\right )\right )}\right ) \, dx,x,\sqrt [4]{-a+x}\right )}{\sqrt [4]{(-a+x) (-b+x)^2}}\\ &=\frac {\left (4 \sqrt [4]{-a+x} \sqrt {-b+x}\right ) \operatorname {Subst}\left (\int \frac {x^6}{\left (a-b+x^4\right )^{3/2}} \, dx,x,\sqrt [4]{-a+x}\right )}{\sqrt [4]{(-a+x) (-b+x)^2}}-\frac {\left (4 \sqrt [4]{-a+x} \sqrt {-b+x}\right ) \operatorname {Subst}\left (\int \frac {x^2 \left ((a-b)^2 d (a+d)+(a-b) d (3 a-b+2 d) x^4+d (3 a-2 b+d) x^8\right )}{\left (a-b+x^4\right )^{3/2} \left (a^2 \left (1+\frac {b^2}{a^2}\right ) d-2 b d x^4+x^8 \left (d-x^4\right )+2 a d \left (-b+x^4\right )\right )} \, dx,x,\sqrt [4]{-a+x}\right )}{\sqrt [4]{(-a+x) (-b+x)^2}}-\frac {\left (4 (-2 a+3 b) \sqrt [4]{-a+x} \sqrt {-b+x}\right ) \operatorname {Subst}\left (\int \frac {x^2}{\left (a-b+x^4\right )^{3/2}} \, dx,x,\sqrt [4]{-a+x}\right )}{\sqrt [4]{(-a+x) (-b+x)^2}}+\frac {\left (4 (-2 a+3 b) \sqrt [4]{-a+x} \sqrt {-b+x}\right ) \operatorname {Subst}\left (\int \frac {x^2 \left ((a-b)^2 d+2 (a-b) d x^4+d x^8\right )}{\left (a-b+x^4\right )^{3/2} \left (a^2 \left (1+\frac {b^2}{a^2}\right ) d-2 b d x^4+x^8 \left (d-x^4\right )+2 a d \left (-b+x^4\right )\right )} \, dx,x,\sqrt [4]{-a+x}\right )}{\sqrt [4]{(-a+x) (-b+x)^2}}-\frac {\left (4 (-a-d) \sqrt [4]{-a+x} \sqrt {-b+x}\right ) \operatorname {Subst}\left (\int \frac {x^2}{\left (a-b+x^4\right )^{3/2}} \, dx,x,\sqrt [4]{-a+x}\right )}{\sqrt [4]{(-a+x) (-b+x)^2}}\\ &=\frac {2 (a-x)}{\sqrt [4]{-\left ((a-x) (b-x)^2\right )}}-\frac {2 (2 a-3 b) (a-x)}{(a-b) \sqrt [4]{-\left ((a-x) (b-x)^2\right )}}-\frac {2 (a+d) (a-x)}{(a-b) \sqrt [4]{-\left ((a-x) (b-x)^2\right )}}-\frac {\left (4 \sqrt [4]{-a+x} \sqrt {-b+x}\right ) \operatorname {Subst}\left (\int \left (\frac {(a-b)^2 d (a+d) x^2}{\left (a-b+x^4\right )^{3/2} \left (a^2 \left (1+\frac {b (-2 a+b)}{a^2}\right ) d+2 a \left (1-\frac {b}{a}\right ) d x^4+d x^8-x^{12}\right )}+\frac {(a-b) d (3 a-b+2 d) x^6}{\left (a-b+x^4\right )^{3/2} \left (a^2 \left (1+\frac {b (-2 a+b)}{a^2}\right ) d+2 a \left (1-\frac {b}{a}\right ) d x^4+d x^8-x^{12}\right )}+\frac {d (3 a-2 b+d) x^{10}}{\left (a-b+x^4\right )^{3/2} \left (a^2 \left (1+\frac {b (-2 a+b)}{a^2}\right ) d+2 a \left (1-\frac {b}{a}\right ) d x^4+d x^8-x^{12}\right )}\right ) \, dx,x,\sqrt [4]{-a+x}\right )}{\sqrt [4]{(-a+x) (-b+x)^2}}+\frac {\left (6 \sqrt [4]{-a+x} \sqrt {-b+x}\right ) \operatorname {Subst}\left (\int \frac {x^2}{\sqrt {a-b+x^4}} \, dx,x,\sqrt [4]{-a+x}\right )}{\sqrt [4]{(-a+x) (-b+x)^2}}+\frac {\left (2 (-2 a+3 b) \sqrt [4]{-a+x} \sqrt {-b+x}\right ) \operatorname {Subst}\left (\int \frac {x^2}{\sqrt {a-b+x^4}} \, dx,x,\sqrt [4]{-a+x}\right )}{(a-b) \sqrt [4]{(-a+x) (-b+x)^2}}+\frac {\left (2 (-a-d) \sqrt [4]{-a+x} \sqrt {-b+x}\right ) \operatorname {Subst}\left (\int \frac {x^2}{\sqrt {a-b+x^4}} \, dx,x,\sqrt [4]{-a+x}\right )}{(a-b) \sqrt [4]{(-a+x) (-b+x)^2}}+\frac {\left (4 (-2 a+3 b) \sqrt [4]{-a+x} \sqrt {-b+x}\right ) \operatorname {Subst}\left (\int \frac {x^2 \left ((a-b) d+d x^4\right )^2}{\left (a-b+x^4\right )^{3/2} \left (a^2 \left (1+\frac {b^2}{a^2}\right ) d-2 b d x^4+x^8 \left (d-x^4\right )+2 a d \left (-b+x^4\right )\right )} \, dx,x,\sqrt [4]{-a+x}\right )}{d \sqrt [4]{(-a+x) (-b+x)^2}}\\ &=\frac {2 (a-x)}{\sqrt [4]{-\left ((a-x) (b-x)^2\right )}}-\frac {2 (2 a-3 b) (a-x)}{(a-b) \sqrt [4]{-\left ((a-x) (b-x)^2\right )}}-\frac {2 (a+d) (a-x)}{(a-b) \sqrt [4]{-\left ((a-x) (b-x)^2\right )}}+\frac {\left (6 \sqrt {a-b} \sqrt [4]{-a+x} \sqrt {-b+x}\right ) \operatorname {Subst}\left (\int \frac {1}{\sqrt {a-b+x^4}} \, dx,x,\sqrt [4]{-a+x}\right )}{\sqrt [4]{(-a+x) (-b+x)^2}}-\frac {\left (6 \sqrt {a-b} \sqrt [4]{-a+x} \sqrt {-b+x}\right ) \operatorname {Subst}\left (\int \frac {1-\frac {x^2}{\sqrt {a-b}}}{\sqrt {a-b+x^4}} \, dx,x,\sqrt [4]{-a+x}\right )}{\sqrt [4]{(-a+x) (-b+x)^2}}+\frac {\left (2 (-2 a+3 b) \sqrt [4]{-a+x} \sqrt {-b+x}\right ) \operatorname {Subst}\left (\int \frac {1}{\sqrt {a-b+x^4}} \, dx,x,\sqrt [4]{-a+x}\right )}{\sqrt {a-b} \sqrt [4]{(-a+x) (-b+x)^2}}-\frac {\left (2 (-2 a+3 b) \sqrt [4]{-a+x} \sqrt {-b+x}\right ) \operatorname {Subst}\left (\int \frac {1-\frac {x^2}{\sqrt {a-b}}}{\sqrt {a-b+x^4}} \, dx,x,\sqrt [4]{-a+x}\right )}{\sqrt {a-b} \sqrt [4]{(-a+x) (-b+x)^2}}+\frac {\left (2 (-a-d) \sqrt [4]{-a+x} \sqrt {-b+x}\right ) \operatorname {Subst}\left (\int \frac {1}{\sqrt {a-b+x^4}} \, dx,x,\sqrt [4]{-a+x}\right )}{\sqrt {a-b} \sqrt [4]{(-a+x) (-b+x)^2}}-\frac {\left (2 (-a-d) \sqrt [4]{-a+x} \sqrt {-b+x}\right ) \operatorname {Subst}\left (\int \frac {1-\frac {x^2}{\sqrt {a-b}}}{\sqrt {a-b+x^4}} \, dx,x,\sqrt [4]{-a+x}\right )}{\sqrt {a-b} \sqrt [4]{(-a+x) (-b+x)^2}}+\frac {\left (4 (-2 a+3 b) d \sqrt [4]{-a+x} \sqrt {-b+x}\right ) \operatorname {Subst}\left (\int \frac {x^2 \sqrt {a-b+x^4}}{a^2 \left (1+\frac {b^2}{a^2}\right ) d-2 b d x^4+x^8 \left (d-x^4\right )+2 a d \left (-b+x^4\right )} \, dx,x,\sqrt [4]{-a+x}\right )}{\sqrt [4]{(-a+x) (-b+x)^2}}-\frac {\left (4 (a-b)^2 d (a+d) \sqrt [4]{-a+x} \sqrt {-b+x}\right ) \operatorname {Subst}\left (\int \frac {x^2}{\left (a-b+x^4\right )^{3/2} \left (a^2 \left (1+\frac {b (-2 a+b)}{a^2}\right ) d+2 a \left (1-\frac {b}{a}\right ) d x^4+d x^8-x^{12}\right )} \, dx,x,\sqrt [4]{-a+x}\right )}{\sqrt [4]{(-a+x) (-b+x)^2}}-\frac {\left (4 d (3 a-2 b+d) \sqrt [4]{-a+x} \sqrt {-b+x}\right ) \operatorname {Subst}\left (\int \frac {x^{10}}{\left (a-b+x^4\right )^{3/2} \left (a^2 \left (1+\frac {b (-2 a+b)}{a^2}\right ) d+2 a \left (1-\frac {b}{a}\right ) d x^4+d x^8-x^{12}\right )} \, dx,x,\sqrt [4]{-a+x}\right )}{\sqrt [4]{(-a+x) (-b+x)^2}}-\frac {\left (4 (a-b) d (3 a-b+2 d) \sqrt [4]{-a+x} \sqrt {-b+x}\right ) \operatorname {Subst}\left (\int \frac {x^6}{\left (a-b+x^4\right )^{3/2} \left (a^2 \left (1+\frac {b (-2 a+b)}{a^2}\right ) d+2 a \left (1-\frac {b}{a}\right ) d x^4+d x^8-x^{12}\right )} \, dx,x,\sqrt [4]{-a+x}\right )}{\sqrt [4]{(-a+x) (-b+x)^2}}\\ &=\frac {2 (a-x)}{\sqrt [4]{-\left ((a-x) (b-x)^2\right )}}-\frac {2 (2 a-3 b) (a-x)}{(a-b) \sqrt [4]{-\left ((a-x) (b-x)^2\right )}}-\frac {2 (a+d) (a-x)}{(a-b) \sqrt [4]{-\left ((a-x) (b-x)^2\right )}}+\frac {2 (2 a-3 b) (b-x) \sqrt {-a+x}}{(a-b)^{3/2} \sqrt [4]{-\left ((a-x) (b-x)^2\right )} \left (1+\frac {\sqrt {-a+x}}{\sqrt {a-b}}\right )}-\frac {6 (b-x) \sqrt {-a+x}}{\sqrt {a-b} \sqrt [4]{-\left ((a-x) (b-x)^2\right )} \left (1+\frac {\sqrt {-a+x}}{\sqrt {a-b}}\right )}+\frac {2 (a+d) (b-x) \sqrt {-a+x}}{(a-b)^{3/2} \sqrt [4]{-\left ((a-x) (b-x)^2\right )} \left (1+\frac {\sqrt {-a+x}}{\sqrt {a-b}}\right )}+\frac {2 (2 a-3 b) \sqrt [4]{-a+x} \sqrt {-\frac {b-x}{(a-b) \left (1+\frac {\sqrt {-a+x}}{\sqrt {a-b}}\right )^2}} \left (1+\frac {\sqrt {-a+x}}{\sqrt {a-b}}\right ) E\left (2 \tan ^{-1}\left (\frac {\sqrt [4]{-a+x}}{\sqrt [4]{a-b}}\right )|\frac {1}{2}\right )}{\sqrt [4]{a-b} \sqrt [4]{-\left ((a-x) (b-x)^2\right )}}-\frac {6 (a-b)^{3/4} \sqrt [4]{-a+x} \sqrt {-\frac {b-x}{(a-b) \left (1+\frac {\sqrt {-a+x}}{\sqrt {a-b}}\right )^2}} \left (1+\frac {\sqrt {-a+x}}{\sqrt {a-b}}\right ) E\left (2 \tan ^{-1}\left (\frac {\sqrt [4]{-a+x}}{\sqrt [4]{a-b}}\right )|\frac {1}{2}\right )}{\sqrt [4]{-\left ((a-x) (b-x)^2\right )}}+\frac {2 (a+d) \sqrt [4]{-a+x} \sqrt {-\frac {b-x}{(a-b) \left (1+\frac {\sqrt {-a+x}}{\sqrt {a-b}}\right )^2}} \left (1+\frac {\sqrt {-a+x}}{\sqrt {a-b}}\right ) E\left (2 \tan ^{-1}\left (\frac {\sqrt [4]{-a+x}}{\sqrt [4]{a-b}}\right )|\frac {1}{2}\right )}{\sqrt [4]{a-b} \sqrt [4]{-\left ((a-x) (b-x)^2\right )}}-\frac {(2 a-3 b) \sqrt [4]{-a+x} \sqrt {-\frac {b-x}{(a-b) \left (1+\frac {\sqrt {-a+x}}{\sqrt {a-b}}\right )^2}} \left (1+\frac {\sqrt {-a+x}}{\sqrt {a-b}}\right ) F\left (2 \tan ^{-1}\left (\frac {\sqrt [4]{-a+x}}{\sqrt [4]{a-b}}\right )|\frac {1}{2}\right )}{\sqrt [4]{a-b} \sqrt [4]{-\left ((a-x) (b-x)^2\right )}}+\frac {3 (a-b)^{3/4} \sqrt [4]{-a+x} \sqrt {-\frac {b-x}{(a-b) \left (1+\frac {\sqrt {-a+x}}{\sqrt {a-b}}\right )^2}} \left (1+\frac {\sqrt {-a+x}}{\sqrt {a-b}}\right ) F\left (2 \tan ^{-1}\left (\frac {\sqrt [4]{-a+x}}{\sqrt [4]{a-b}}\right )|\frac {1}{2}\right )}{\sqrt [4]{-\left ((a-x) (b-x)^2\right )}}-\frac {(a+d) \sqrt [4]{-a+x} \sqrt {-\frac {b-x}{(a-b) \left (1+\frac {\sqrt {-a+x}}{\sqrt {a-b}}\right )^2}} \left (1+\frac {\sqrt {-a+x}}{\sqrt {a-b}}\right ) F\left (2 \tan ^{-1}\left (\frac {\sqrt [4]{-a+x}}{\sqrt [4]{a-b}}\right )|\frac {1}{2}\right )}{\sqrt [4]{a-b} \sqrt [4]{-\left ((a-x) (b-x)^2\right )}}+\frac {\left (4 (-2 a+3 b) d \sqrt [4]{-a+x} \sqrt {-b+x}\right ) \operatorname {Subst}\left (\int \frac {x^2 \sqrt {a-b+x^4}}{a^2 \left (1+\frac {b^2}{a^2}\right ) d-2 b d x^4+x^8 \left (d-x^4\right )+2 a d \left (-b+x^4\right )} \, dx,x,\sqrt [4]{-a+x}\right )}{\sqrt [4]{(-a+x) (-b+x)^2}}-\frac {\left (4 (a-b)^2 d (a+d) \sqrt [4]{-a+x} \sqrt {-b+x}\right ) \operatorname {Subst}\left (\int \frac {x^2}{\left (a-b+x^4\right )^{3/2} \left (a^2 \left (1+\frac {b (-2 a+b)}{a^2}\right ) d+2 a \left (1-\frac {b}{a}\right ) d x^4+d x^8-x^{12}\right )} \, dx,x,\sqrt [4]{-a+x}\right )}{\sqrt [4]{(-a+x) (-b+x)^2}}-\frac {\left (4 d (3 a-2 b+d) \sqrt [4]{-a+x} \sqrt {-b+x}\right ) \operatorname {Subst}\left (\int \frac {x^{10}}{\left (a-b+x^4\right )^{3/2} \left (a^2 \left (1+\frac {b (-2 a+b)}{a^2}\right ) d+2 a \left (1-\frac {b}{a}\right ) d x^4+d x^8-x^{12}\right )} \, dx,x,\sqrt [4]{-a+x}\right )}{\sqrt [4]{(-a+x) (-b+x)^2}}-\frac {\left (4 (a-b) d (3 a-b+2 d) \sqrt [4]{-a+x} \sqrt {-b+x}\right ) \operatorname {Subst}\left (\int \frac {x^6}{\left (a-b+x^4\right )^{3/2} \left (a^2 \left (1+\frac {b (-2 a+b)}{a^2}\right ) d+2 a \left (1-\frac {b}{a}\right ) d x^4+d x^8-x^{12}\right )} \, dx,x,\sqrt [4]{-a+x}\right )}{\sqrt [4]{(-a+x) (-b+x)^2}}\\ \end {align*}
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Mathematica [C] time = 12.48, size = 2491, normalized size = 15.77 \begin {gather*} \text {Result too large to show} \end {gather*}
Warning: Unable to verify antiderivative.
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IntegrateAlgebraic [F] time = 180.00, size = 0, normalized size = 0.00 \begin {gather*} \text {\$Aborted} \end {gather*}
Verification is not applicable to the result.
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fricas [F(-1)] 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*} \int -\frac {{\left (a^{3} - 3 \, a^{2} x + 3 \, a x^{2} - x^{3}\right )} {\left (2 \, a - 3 \, b + x\right )}}{{\left (a^{3} + b^{2} d + {\left (3 \, a + d\right )} x^{2} - x^{3} - {\left (3 \, a^{2} + 2 \, b d\right )} x\right )} \left (-{\left (a - x\right )} {\left (b - x\right )}^{2}\right )^{\frac {1}{4}} {\left (b - x\right )}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [F] time = 0.04, size = 0, normalized size = 0.00 \[\int \frac {\left (2 a -3 b +x \right ) \left (-a^{3}+3 a^{2} x -3 a \,x^{2}+x^{3}\right )}{\left (-b +x \right ) \left (\left (-a +x \right ) \left (-b +x \right )^{2}\right )^{\frac {1}{4}} \left (-a^{3}-b^{2} d +\left (3 a^{2}+2 b d \right ) x -\left (3 a +d \right ) x^{2}+x^{3}\right )}\, dx\]
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*} -\int \frac {{\left (a^{3} - 3 \, a^{2} x + 3 \, a x^{2} - x^{3}\right )} {\left (2 \, a - 3 \, b + x\right )}}{{\left (a^{3} + b^{2} d + {\left (3 \, a + d\right )} x^{2} - x^{3} - {\left (3 \, a^{2} + 2 \, b d\right )} x\right )} \left (-{\left (a - x\right )} {\left (b - x\right )}^{2}\right )^{\frac {1}{4}} {\left (b - x\right )}}\,{d x} \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 = -0.01 \begin {gather*} -\int \frac {\left (2\,a-3\,b+x\right )\,\left (a^3-3\,a^2\,x+3\,a\,x^2-x^3\right )}{\left (b-x\right )\,{\left (-\left (a-x\right )\,{\left (b-x\right )}^2\right )}^{1/4}\,\left (b^2\,d-x\,\left (3\,a^2+2\,b\,d\right )+x^2\,\left (3\,a+d\right )+a^3-x^3\right )} \,d x \end {gather*}
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 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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