Optimal. Leaf size=509 \[ -\frac {105 \sqrt {\pi } b^{7/2} e^2 e^{a/b} \text {erf}\left (\frac {\sqrt {a+b \cosh ^{-1}(c+d x)}}{\sqrt {b}}\right )}{128 d}-\frac {35 \sqrt {\frac {\pi }{3}} b^{7/2} e^2 e^{\frac {3 a}{b}} \text {erf}\left (\frac {\sqrt {3} \sqrt {a+b \cosh ^{-1}(c+d x)}}{\sqrt {b}}\right )}{3456 d}+\frac {105 \sqrt {\pi } b^{7/2} e^2 e^{-\frac {a}{b}} \text {erfi}\left (\frac {\sqrt {a+b \cosh ^{-1}(c+d x)}}{\sqrt {b}}\right )}{128 d}+\frac {35 \sqrt {\frac {\pi }{3}} b^{7/2} e^2 e^{-\frac {3 a}{b}} \text {erfi}\left (\frac {\sqrt {3} \sqrt {a+b \cosh ^{-1}(c+d x)}}{\sqrt {b}}\right )}{3456 d}-\frac {35 b^3 e^2 \sqrt {c+d x-1} (c+d x)^2 \sqrt {c+d x+1} \sqrt {a+b \cosh ^{-1}(c+d x)}}{216 d}-\frac {175 b^3 e^2 \sqrt {c+d x-1} \sqrt {c+d x+1} \sqrt {a+b \cosh ^{-1}(c+d x)}}{54 d}+\frac {35 b^2 e^2 (c+d x)^3 \left (a+b \cosh ^{-1}(c+d x)\right )^{3/2}}{108 d}+\frac {35 b^2 e^2 (c+d x) \left (a+b \cosh ^{-1}(c+d x)\right )^{3/2}}{18 d}-\frac {7 b e^2 \sqrt {c+d x-1} (c+d x)^2 \sqrt {c+d x+1} \left (a+b \cosh ^{-1}(c+d x)\right )^{5/2}}{18 d}-\frac {7 b e^2 \sqrt {c+d x-1} \sqrt {c+d x+1} \left (a+b \cosh ^{-1}(c+d x)\right )^{5/2}}{9 d}+\frac {e^2 (c+d x)^3 \left (a+b \cosh ^{-1}(c+d x)\right )^{7/2}}{3 d} \]
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Rubi [A] time = 2.14, antiderivative size = 509, normalized size of antiderivative = 1.00, number of steps used = 35, number of rules used = 13, integrand size = 25, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.520, Rules used = {5866, 12, 5664, 5759, 5718, 5654, 5658, 3308, 2180, 2205, 2204, 5670, 5448} \[ -\frac {105 \sqrt {\pi } b^{7/2} e^2 e^{a/b} \text {Erf}\left (\frac {\sqrt {a+b \cosh ^{-1}(c+d x)}}{\sqrt {b}}\right )}{128 d}-\frac {35 \sqrt {\frac {\pi }{3}} b^{7/2} e^2 e^{\frac {3 a}{b}} \text {Erf}\left (\frac {\sqrt {3} \sqrt {a+b \cosh ^{-1}(c+d x)}}{\sqrt {b}}\right )}{3456 d}+\frac {105 \sqrt {\pi } b^{7/2} e^2 e^{-\frac {a}{b}} \text {Erfi}\left (\frac {\sqrt {a+b \cosh ^{-1}(c+d x)}}{\sqrt {b}}\right )}{128 d}+\frac {35 \sqrt {\frac {\pi }{3}} b^{7/2} e^2 e^{-\frac {3 a}{b}} \text {Erfi}\left (\frac {\sqrt {3} \sqrt {a+b \cosh ^{-1}(c+d x)}}{\sqrt {b}}\right )}{3456 d}-\frac {35 b^3 e^2 \sqrt {c+d x-1} (c+d x)^2 \sqrt {c+d x+1} \sqrt {a+b \cosh ^{-1}(c+d x)}}{216 d}-\frac {175 b^3 e^2 \sqrt {c+d x-1} \sqrt {c+d x+1} \sqrt {a+b \cosh ^{-1}(c+d x)}}{54 d}+\frac {35 b^2 e^2 (c+d x)^3 \left (a+b \cosh ^{-1}(c+d x)\right )^{3/2}}{108 d}+\frac {35 b^2 e^2 (c+d x) \left (a+b \cosh ^{-1}(c+d x)\right )^{3/2}}{18 d}-\frac {7 b e^2 \sqrt {c+d x-1} (c+d x)^2 \sqrt {c+d x+1} \left (a+b \cosh ^{-1}(c+d x)\right )^{5/2}}{18 d}-\frac {7 b e^2 \sqrt {c+d x-1} \sqrt {c+d x+1} \left (a+b \cosh ^{-1}(c+d x)\right )^{5/2}}{9 d}+\frac {e^2 (c+d x)^3 \left (a+b \cosh ^{-1}(c+d x)\right )^{7/2}}{3 d} \]
Antiderivative was successfully verified.
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Rule 12
Rule 2180
Rule 2204
Rule 2205
Rule 3308
Rule 5448
Rule 5654
Rule 5658
Rule 5664
Rule 5670
Rule 5718
Rule 5759
Rule 5866
Rubi steps
\begin {align*} \int (c e+d e x)^2 \left (a+b \cosh ^{-1}(c+d x)\right )^{7/2} \, dx &=\frac {\operatorname {Subst}\left (\int e^2 x^2 \left (a+b \cosh ^{-1}(x)\right )^{7/2} \, dx,x,c+d x\right )}{d}\\ &=\frac {e^2 \operatorname {Subst}\left (\int x^2 \left (a+b \cosh ^{-1}(x)\right )^{7/2} \, dx,x,c+d x\right )}{d}\\ &=\frac {e^2 (c+d x)^3 \left (a+b \cosh ^{-1}(c+d x)\right )^{7/2}}{3 d}-\frac {\left (7 b e^2\right ) \operatorname {Subst}\left (\int \frac {x^3 \left (a+b \cosh ^{-1}(x)\right )^{5/2}}{\sqrt {-1+x} \sqrt {1+x}} \, dx,x,c+d x\right )}{6 d}\\ &=-\frac {7 b e^2 \sqrt {-1+c+d x} (c+d x)^2 \sqrt {1+c+d x} \left (a+b \cosh ^{-1}(c+d x)\right )^{5/2}}{18 d}+\frac {e^2 (c+d x)^3 \left (a+b \cosh ^{-1}(c+d x)\right )^{7/2}}{3 d}-\frac {\left (7 b e^2\right ) \operatorname {Subst}\left (\int \frac {x \left (a+b \cosh ^{-1}(x)\right )^{5/2}}{\sqrt {-1+x} \sqrt {1+x}} \, dx,x,c+d x\right )}{9 d}+\frac {\left (35 b^2 e^2\right ) \operatorname {Subst}\left (\int x^2 \left (a+b \cosh ^{-1}(x)\right )^{3/2} \, dx,x,c+d x\right )}{36 d}\\ &=\frac {35 b^2 e^2 (c+d x)^3 \left (a+b \cosh ^{-1}(c+d x)\right )^{3/2}}{108 d}-\frac {7 b e^2 \sqrt {-1+c+d x} \sqrt {1+c+d x} \left (a+b \cosh ^{-1}(c+d x)\right )^{5/2}}{9 d}-\frac {7 b e^2 \sqrt {-1+c+d x} (c+d x)^2 \sqrt {1+c+d x} \left (a+b \cosh ^{-1}(c+d x)\right )^{5/2}}{18 d}+\frac {e^2 (c+d x)^3 \left (a+b \cosh ^{-1}(c+d x)\right )^{7/2}}{3 d}+\frac {\left (35 b^2 e^2\right ) \operatorname {Subst}\left (\int \left (a+b \cosh ^{-1}(x)\right )^{3/2} \, dx,x,c+d x\right )}{18 d}-\frac {\left (35 b^3 e^2\right ) \operatorname {Subst}\left (\int \frac {x^3 \sqrt {a+b \cosh ^{-1}(x)}}{\sqrt {-1+x} \sqrt {1+x}} \, dx,x,c+d x\right )}{72 d}\\ &=-\frac {35 b^3 e^2 \sqrt {-1+c+d x} (c+d x)^2 \sqrt {1+c+d x} \sqrt {a+b \cosh ^{-1}(c+d x)}}{216 d}+\frac {35 b^2 e^2 (c+d x) \left (a+b \cosh ^{-1}(c+d x)\right )^{3/2}}{18 d}+\frac {35 b^2 e^2 (c+d x)^3 \left (a+b \cosh ^{-1}(c+d x)\right )^{3/2}}{108 d}-\frac {7 b e^2 \sqrt {-1+c+d x} \sqrt {1+c+d x} \left (a+b \cosh ^{-1}(c+d x)\right )^{5/2}}{9 d}-\frac {7 b e^2 \sqrt {-1+c+d x} (c+d x)^2 \sqrt {1+c+d x} \left (a+b \cosh ^{-1}(c+d x)\right )^{5/2}}{18 d}+\frac {e^2 (c+d x)^3 \left (a+b \cosh ^{-1}(c+d x)\right )^{7/2}}{3 d}-\frac {\left (35 b^3 e^2\right ) \operatorname {Subst}\left (\int \frac {x \sqrt {a+b \cosh ^{-1}(x)}}{\sqrt {-1+x} \sqrt {1+x}} \, dx,x,c+d x\right )}{108 d}-\frac {\left (35 b^3 e^2\right ) \operatorname {Subst}\left (\int \frac {x \sqrt {a+b \cosh ^{-1}(x)}}{\sqrt {-1+x} \sqrt {1+x}} \, dx,x,c+d x\right )}{12 d}+\frac {\left (35 b^4 e^2\right ) \operatorname {Subst}\left (\int \frac {x^2}{\sqrt {a+b \cosh ^{-1}(x)}} \, dx,x,c+d x\right )}{432 d}\\ &=-\frac {175 b^3 e^2 \sqrt {-1+c+d x} \sqrt {1+c+d x} \sqrt {a+b \cosh ^{-1}(c+d x)}}{54 d}-\frac {35 b^3 e^2 \sqrt {-1+c+d x} (c+d x)^2 \sqrt {1+c+d x} \sqrt {a+b \cosh ^{-1}(c+d x)}}{216 d}+\frac {35 b^2 e^2 (c+d x) \left (a+b \cosh ^{-1}(c+d x)\right )^{3/2}}{18 d}+\frac {35 b^2 e^2 (c+d x)^3 \left (a+b \cosh ^{-1}(c+d x)\right )^{3/2}}{108 d}-\frac {7 b e^2 \sqrt {-1+c+d x} \sqrt {1+c+d x} \left (a+b \cosh ^{-1}(c+d x)\right )^{5/2}}{9 d}-\frac {7 b e^2 \sqrt {-1+c+d x} (c+d x)^2 \sqrt {1+c+d x} \left (a+b \cosh ^{-1}(c+d x)\right )^{5/2}}{18 d}+\frac {e^2 (c+d x)^3 \left (a+b \cosh ^{-1}(c+d x)\right )^{7/2}}{3 d}+\frac {\left (35 b^4 e^2\right ) \operatorname {Subst}\left (\int \frac {\cosh ^2(x) \sinh (x)}{\sqrt {a+b x}} \, dx,x,\cosh ^{-1}(c+d x)\right )}{432 d}+\frac {\left (35 b^4 e^2\right ) \operatorname {Subst}\left (\int \frac {1}{\sqrt {a+b \cosh ^{-1}(x)}} \, dx,x,c+d x\right )}{216 d}+\frac {\left (35 b^4 e^2\right ) \operatorname {Subst}\left (\int \frac {1}{\sqrt {a+b \cosh ^{-1}(x)}} \, dx,x,c+d x\right )}{24 d}\\ &=-\frac {175 b^3 e^2 \sqrt {-1+c+d x} \sqrt {1+c+d x} \sqrt {a+b \cosh ^{-1}(c+d x)}}{54 d}-\frac {35 b^3 e^2 \sqrt {-1+c+d x} (c+d x)^2 \sqrt {1+c+d x} \sqrt {a+b \cosh ^{-1}(c+d x)}}{216 d}+\frac {35 b^2 e^2 (c+d x) \left (a+b \cosh ^{-1}(c+d x)\right )^{3/2}}{18 d}+\frac {35 b^2 e^2 (c+d x)^3 \left (a+b \cosh ^{-1}(c+d x)\right )^{3/2}}{108 d}-\frac {7 b e^2 \sqrt {-1+c+d x} \sqrt {1+c+d x} \left (a+b \cosh ^{-1}(c+d x)\right )^{5/2}}{9 d}-\frac {7 b e^2 \sqrt {-1+c+d x} (c+d x)^2 \sqrt {1+c+d x} \left (a+b \cosh ^{-1}(c+d x)\right )^{5/2}}{18 d}+\frac {e^2 (c+d x)^3 \left (a+b \cosh ^{-1}(c+d x)\right )^{7/2}}{3 d}-\frac {\left (35 b^3 e^2\right ) \operatorname {Subst}\left (\int \frac {\sinh \left (\frac {a}{b}-\frac {x}{b}\right )}{\sqrt {x}} \, dx,x,a+b \cosh ^{-1}(c+d x)\right )}{216 d}-\frac {\left (35 b^3 e^2\right ) \operatorname {Subst}\left (\int \frac {\sinh \left (\frac {a}{b}-\frac {x}{b}\right )}{\sqrt {x}} \, dx,x,a+b \cosh ^{-1}(c+d x)\right )}{24 d}+\frac {\left (35 b^4 e^2\right ) \operatorname {Subst}\left (\int \left (\frac {\sinh (x)}{4 \sqrt {a+b x}}+\frac {\sinh (3 x)}{4 \sqrt {a+b x}}\right ) \, dx,x,\cosh ^{-1}(c+d x)\right )}{432 d}\\ &=-\frac {175 b^3 e^2 \sqrt {-1+c+d x} \sqrt {1+c+d x} \sqrt {a+b \cosh ^{-1}(c+d x)}}{54 d}-\frac {35 b^3 e^2 \sqrt {-1+c+d x} (c+d x)^2 \sqrt {1+c+d x} \sqrt {a+b \cosh ^{-1}(c+d x)}}{216 d}+\frac {35 b^2 e^2 (c+d x) \left (a+b \cosh ^{-1}(c+d x)\right )^{3/2}}{18 d}+\frac {35 b^2 e^2 (c+d x)^3 \left (a+b \cosh ^{-1}(c+d x)\right )^{3/2}}{108 d}-\frac {7 b e^2 \sqrt {-1+c+d x} \sqrt {1+c+d x} \left (a+b \cosh ^{-1}(c+d x)\right )^{5/2}}{9 d}-\frac {7 b e^2 \sqrt {-1+c+d x} (c+d x)^2 \sqrt {1+c+d x} \left (a+b \cosh ^{-1}(c+d x)\right )^{5/2}}{18 d}+\frac {e^2 (c+d x)^3 \left (a+b \cosh ^{-1}(c+d x)\right )^{7/2}}{3 d}-\frac {\left (35 b^3 e^2\right ) \operatorname {Subst}\left (\int \frac {e^{-i \left (\frac {i a}{b}-\frac {i x}{b}\right )}}{\sqrt {x}} \, dx,x,a+b \cosh ^{-1}(c+d x)\right )}{432 d}+\frac {\left (35 b^3 e^2\right ) \operatorname {Subst}\left (\int \frac {e^{i \left (\frac {i a}{b}-\frac {i x}{b}\right )}}{\sqrt {x}} \, dx,x,a+b \cosh ^{-1}(c+d x)\right )}{432 d}-\frac {\left (35 b^3 e^2\right ) \operatorname {Subst}\left (\int \frac {e^{-i \left (\frac {i a}{b}-\frac {i x}{b}\right )}}{\sqrt {x}} \, dx,x,a+b \cosh ^{-1}(c+d x)\right )}{48 d}+\frac {\left (35 b^3 e^2\right ) \operatorname {Subst}\left (\int \frac {e^{i \left (\frac {i a}{b}-\frac {i x}{b}\right )}}{\sqrt {x}} \, dx,x,a+b \cosh ^{-1}(c+d x)\right )}{48 d}+\frac {\left (35 b^4 e^2\right ) \operatorname {Subst}\left (\int \frac {\sinh (x)}{\sqrt {a+b x}} \, dx,x,\cosh ^{-1}(c+d x)\right )}{1728 d}+\frac {\left (35 b^4 e^2\right ) \operatorname {Subst}\left (\int \frac {\sinh (3 x)}{\sqrt {a+b x}} \, dx,x,\cosh ^{-1}(c+d x)\right )}{1728 d}\\ &=-\frac {175 b^3 e^2 \sqrt {-1+c+d x} \sqrt {1+c+d x} \sqrt {a+b \cosh ^{-1}(c+d x)}}{54 d}-\frac {35 b^3 e^2 \sqrt {-1+c+d x} (c+d x)^2 \sqrt {1+c+d x} \sqrt {a+b \cosh ^{-1}(c+d x)}}{216 d}+\frac {35 b^2 e^2 (c+d x) \left (a+b \cosh ^{-1}(c+d x)\right )^{3/2}}{18 d}+\frac {35 b^2 e^2 (c+d x)^3 \left (a+b \cosh ^{-1}(c+d x)\right )^{3/2}}{108 d}-\frac {7 b e^2 \sqrt {-1+c+d x} \sqrt {1+c+d x} \left (a+b \cosh ^{-1}(c+d x)\right )^{5/2}}{9 d}-\frac {7 b e^2 \sqrt {-1+c+d x} (c+d x)^2 \sqrt {1+c+d x} \left (a+b \cosh ^{-1}(c+d x)\right )^{5/2}}{18 d}+\frac {e^2 (c+d x)^3 \left (a+b \cosh ^{-1}(c+d x)\right )^{7/2}}{3 d}-\frac {\left (35 b^3 e^2\right ) \operatorname {Subst}\left (\int e^{\frac {a}{b}-\frac {x^2}{b}} \, dx,x,\sqrt {a+b \cosh ^{-1}(c+d x)}\right )}{216 d}+\frac {\left (35 b^3 e^2\right ) \operatorname {Subst}\left (\int e^{-\frac {a}{b}+\frac {x^2}{b}} \, dx,x,\sqrt {a+b \cosh ^{-1}(c+d x)}\right )}{216 d}-\frac {\left (35 b^3 e^2\right ) \operatorname {Subst}\left (\int e^{\frac {a}{b}-\frac {x^2}{b}} \, dx,x,\sqrt {a+b \cosh ^{-1}(c+d x)}\right )}{24 d}+\frac {\left (35 b^3 e^2\right ) \operatorname {Subst}\left (\int e^{-\frac {a}{b}+\frac {x^2}{b}} \, dx,x,\sqrt {a+b \cosh ^{-1}(c+d x)}\right )}{24 d}-\frac {\left (35 b^4 e^2\right ) \operatorname {Subst}\left (\int \frac {e^{-3 x}}{\sqrt {a+b x}} \, dx,x,\cosh ^{-1}(c+d x)\right )}{3456 d}-\frac {\left (35 b^4 e^2\right ) \operatorname {Subst}\left (\int \frac {e^{-x}}{\sqrt {a+b x}} \, dx,x,\cosh ^{-1}(c+d x)\right )}{3456 d}+\frac {\left (35 b^4 e^2\right ) \operatorname {Subst}\left (\int \frac {e^x}{\sqrt {a+b x}} \, dx,x,\cosh ^{-1}(c+d x)\right )}{3456 d}+\frac {\left (35 b^4 e^2\right ) \operatorname {Subst}\left (\int \frac {e^{3 x}}{\sqrt {a+b x}} \, dx,x,\cosh ^{-1}(c+d x)\right )}{3456 d}\\ &=-\frac {175 b^3 e^2 \sqrt {-1+c+d x} \sqrt {1+c+d x} \sqrt {a+b \cosh ^{-1}(c+d x)}}{54 d}-\frac {35 b^3 e^2 \sqrt {-1+c+d x} (c+d x)^2 \sqrt {1+c+d x} \sqrt {a+b \cosh ^{-1}(c+d x)}}{216 d}+\frac {35 b^2 e^2 (c+d x) \left (a+b \cosh ^{-1}(c+d x)\right )^{3/2}}{18 d}+\frac {35 b^2 e^2 (c+d x)^3 \left (a+b \cosh ^{-1}(c+d x)\right )^{3/2}}{108 d}-\frac {7 b e^2 \sqrt {-1+c+d x} \sqrt {1+c+d x} \left (a+b \cosh ^{-1}(c+d x)\right )^{5/2}}{9 d}-\frac {7 b e^2 \sqrt {-1+c+d x} (c+d x)^2 \sqrt {1+c+d x} \left (a+b \cosh ^{-1}(c+d x)\right )^{5/2}}{18 d}+\frac {e^2 (c+d x)^3 \left (a+b \cosh ^{-1}(c+d x)\right )^{7/2}}{3 d}-\frac {175 b^{7/2} e^2 e^{a/b} \sqrt {\pi } \text {erf}\left (\frac {\sqrt {a+b \cosh ^{-1}(c+d x)}}{\sqrt {b}}\right )}{216 d}+\frac {175 b^{7/2} e^2 e^{-\frac {a}{b}} \sqrt {\pi } \text {erfi}\left (\frac {\sqrt {a+b \cosh ^{-1}(c+d x)}}{\sqrt {b}}\right )}{216 d}-\frac {\left (35 b^3 e^2\right ) \operatorname {Subst}\left (\int e^{\frac {3 a}{b}-\frac {3 x^2}{b}} \, dx,x,\sqrt {a+b \cosh ^{-1}(c+d x)}\right )}{1728 d}-\frac {\left (35 b^3 e^2\right ) \operatorname {Subst}\left (\int e^{\frac {a}{b}-\frac {x^2}{b}} \, dx,x,\sqrt {a+b \cosh ^{-1}(c+d x)}\right )}{1728 d}+\frac {\left (35 b^3 e^2\right ) \operatorname {Subst}\left (\int e^{-\frac {a}{b}+\frac {x^2}{b}} \, dx,x,\sqrt {a+b \cosh ^{-1}(c+d x)}\right )}{1728 d}+\frac {\left (35 b^3 e^2\right ) \operatorname {Subst}\left (\int e^{-\frac {3 a}{b}+\frac {3 x^2}{b}} \, dx,x,\sqrt {a+b \cosh ^{-1}(c+d x)}\right )}{1728 d}\\ &=-\frac {175 b^3 e^2 \sqrt {-1+c+d x} \sqrt {1+c+d x} \sqrt {a+b \cosh ^{-1}(c+d x)}}{54 d}-\frac {35 b^3 e^2 \sqrt {-1+c+d x} (c+d x)^2 \sqrt {1+c+d x} \sqrt {a+b \cosh ^{-1}(c+d x)}}{216 d}+\frac {35 b^2 e^2 (c+d x) \left (a+b \cosh ^{-1}(c+d x)\right )^{3/2}}{18 d}+\frac {35 b^2 e^2 (c+d x)^3 \left (a+b \cosh ^{-1}(c+d x)\right )^{3/2}}{108 d}-\frac {7 b e^2 \sqrt {-1+c+d x} \sqrt {1+c+d x} \left (a+b \cosh ^{-1}(c+d x)\right )^{5/2}}{9 d}-\frac {7 b e^2 \sqrt {-1+c+d x} (c+d x)^2 \sqrt {1+c+d x} \left (a+b \cosh ^{-1}(c+d x)\right )^{5/2}}{18 d}+\frac {e^2 (c+d x)^3 \left (a+b \cosh ^{-1}(c+d x)\right )^{7/2}}{3 d}-\frac {105 b^{7/2} e^2 e^{a/b} \sqrt {\pi } \text {erf}\left (\frac {\sqrt {a+b \cosh ^{-1}(c+d x)}}{\sqrt {b}}\right )}{128 d}-\frac {35 b^{7/2} e^2 e^{\frac {3 a}{b}} \sqrt {\frac {\pi }{3}} \text {erf}\left (\frac {\sqrt {3} \sqrt {a+b \cosh ^{-1}(c+d x)}}{\sqrt {b}}\right )}{3456 d}+\frac {105 b^{7/2} e^2 e^{-\frac {a}{b}} \sqrt {\pi } \text {erfi}\left (\frac {\sqrt {a+b \cosh ^{-1}(c+d x)}}{\sqrt {b}}\right )}{128 d}+\frac {35 b^{7/2} e^2 e^{-\frac {3 a}{b}} \sqrt {\frac {\pi }{3}} \text {erfi}\left (\frac {\sqrt {3} \sqrt {a+b \cosh ^{-1}(c+d x)}}{\sqrt {b}}\right )}{3456 d}\\ \end {align*}
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Mathematica [B] time = 14.07, size = 1523, normalized size = 2.99 \[ \text {result too large to display} \]
Warning: Unable to verify antiderivative.
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fricas [F(-2)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Exception raised: TypeError} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [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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maple [F(-2)] time = 180.00, size = 0, normalized size = 0.00 \[ \int \left (d e x +c e \right )^{2} \left (a +b \,\mathrm {arccosh}\left (d x +c \right )\right )^{\frac {7}{2}}\, dx \]
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 \[ \int {\left (d e x + c e\right )}^{2} {\left (b \operatorname {arcosh}\left (d x + c\right ) + a\right )}^{\frac {7}{2}}\,{d x} \]
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 \[ \int {\left (c\,e+d\,e\,x\right )}^2\,{\left (a+b\,\mathrm {acosh}\left (c+d\,x\right )\right )}^{7/2} \,d x \]
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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