Optimal. Leaf size=609 \[ -\frac{4 b d^2 e \sqrt{c x-1} \sqrt{c x+1} \left (a+b \cosh ^{-1}(c x)\right )}{3 c^3}-\frac{8 b d e^2 x^2 \sqrt{c x-1} \sqrt{c x+1} \left (a+b \cosh ^{-1}(c x)\right )}{25 c^3}-\frac{16 b d e^2 \sqrt{c x-1} \sqrt{c x+1} \left (a+b \cosh ^{-1}(c x)\right )}{25 c^5}-\frac{12 b e^3 x^4 \sqrt{c x-1} \sqrt{c x+1} \left (a+b \cosh ^{-1}(c x)\right )}{245 c^3}-\frac{16 b e^3 x^2 \sqrt{c x-1} \sqrt{c x+1} \left (a+b \cosh ^{-1}(c x)\right )}{245 c^5}-\frac{32 b e^3 \sqrt{c x-1} \sqrt{c x+1} \left (a+b \cosh ^{-1}(c x)\right )}{245 c^7}+d^2 e x^3 \left (a+b \cosh ^{-1}(c x)\right )^2-\frac{2 b d^2 e x^2 \sqrt{c x-1} \sqrt{c x+1} \left (a+b \cosh ^{-1}(c x)\right )}{3 c}+d^3 x \left (a+b \cosh ^{-1}(c x)\right )^2-\frac{2 b d^3 \sqrt{c x-1} \sqrt{c x+1} \left (a+b \cosh ^{-1}(c x)\right )}{c}+\frac{3}{5} d e^2 x^5 \left (a+b \cosh ^{-1}(c x)\right )^2-\frac{6 b d e^2 x^4 \sqrt{c x-1} \sqrt{c x+1} \left (a+b \cosh ^{-1}(c x)\right )}{25 c}+\frac{1}{7} e^3 x^7 \left (a+b \cosh ^{-1}(c x)\right )^2-\frac{2 b e^3 x^6 \sqrt{c x-1} \sqrt{c x+1} \left (a+b \cosh ^{-1}(c x)\right )}{49 c}+\frac{4 b^2 d^2 e x}{3 c^2}+\frac{8 b^2 d e^2 x^3}{75 c^2}+\frac{16 b^2 d e^2 x}{25 c^4}+\frac{12 b^2 e^3 x^5}{1225 c^2}+\frac{16 b^2 e^3 x^3}{735 c^4}+\frac{32 b^2 e^3 x}{245 c^6}+\frac{2}{9} b^2 d^2 e x^3+2 b^2 d^3 x+\frac{6}{125} b^2 d e^2 x^5+\frac{2}{343} b^2 e^3 x^7 \]
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Rubi [A] time = 2.09912, antiderivative size = 609, normalized size of antiderivative = 1., number of steps used = 26, number of rules used = 7, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.35, Rules used = {5707, 5654, 5718, 8, 5662, 5759, 30} \[ -\frac{4 b d^2 e \sqrt{c x-1} \sqrt{c x+1} \left (a+b \cosh ^{-1}(c x)\right )}{3 c^3}-\frac{8 b d e^2 x^2 \sqrt{c x-1} \sqrt{c x+1} \left (a+b \cosh ^{-1}(c x)\right )}{25 c^3}-\frac{16 b d e^2 \sqrt{c x-1} \sqrt{c x+1} \left (a+b \cosh ^{-1}(c x)\right )}{25 c^5}-\frac{12 b e^3 x^4 \sqrt{c x-1} \sqrt{c x+1} \left (a+b \cosh ^{-1}(c x)\right )}{245 c^3}-\frac{16 b e^3 x^2 \sqrt{c x-1} \sqrt{c x+1} \left (a+b \cosh ^{-1}(c x)\right )}{245 c^5}-\frac{32 b e^3 \sqrt{c x-1} \sqrt{c x+1} \left (a+b \cosh ^{-1}(c x)\right )}{245 c^7}+d^2 e x^3 \left (a+b \cosh ^{-1}(c x)\right )^2-\frac{2 b d^2 e x^2 \sqrt{c x-1} \sqrt{c x+1} \left (a+b \cosh ^{-1}(c x)\right )}{3 c}+d^3 x \left (a+b \cosh ^{-1}(c x)\right )^2-\frac{2 b d^3 \sqrt{c x-1} \sqrt{c x+1} \left (a+b \cosh ^{-1}(c x)\right )}{c}+\frac{3}{5} d e^2 x^5 \left (a+b \cosh ^{-1}(c x)\right )^2-\frac{6 b d e^2 x^4 \sqrt{c x-1} \sqrt{c x+1} \left (a+b \cosh ^{-1}(c x)\right )}{25 c}+\frac{1}{7} e^3 x^7 \left (a+b \cosh ^{-1}(c x)\right )^2-\frac{2 b e^3 x^6 \sqrt{c x-1} \sqrt{c x+1} \left (a+b \cosh ^{-1}(c x)\right )}{49 c}+\frac{4 b^2 d^2 e x}{3 c^2}+\frac{8 b^2 d e^2 x^3}{75 c^2}+\frac{16 b^2 d e^2 x}{25 c^4}+\frac{12 b^2 e^3 x^5}{1225 c^2}+\frac{16 b^2 e^3 x^3}{735 c^4}+\frac{32 b^2 e^3 x}{245 c^6}+\frac{2}{9} b^2 d^2 e x^3+2 b^2 d^3 x+\frac{6}{125} b^2 d e^2 x^5+\frac{2}{343} b^2 e^3 x^7 \]
Antiderivative was successfully verified.
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Rule 5707
Rule 5654
Rule 5718
Rule 8
Rule 5662
Rule 5759
Rule 30
Rubi steps
\begin{align*} \int \left (d+e x^2\right )^3 \left (a+b \cosh ^{-1}(c x)\right )^2 \, dx &=\int \left (d^3 \left (a+b \cosh ^{-1}(c x)\right )^2+3 d^2 e x^2 \left (a+b \cosh ^{-1}(c x)\right )^2+3 d e^2 x^4 \left (a+b \cosh ^{-1}(c x)\right )^2+e^3 x^6 \left (a+b \cosh ^{-1}(c x)\right )^2\right ) \, dx\\ &=d^3 \int \left (a+b \cosh ^{-1}(c x)\right )^2 \, dx+\left (3 d^2 e\right ) \int x^2 \left (a+b \cosh ^{-1}(c x)\right )^2 \, dx+\left (3 d e^2\right ) \int x^4 \left (a+b \cosh ^{-1}(c x)\right )^2 \, dx+e^3 \int x^6 \left (a+b \cosh ^{-1}(c x)\right )^2 \, dx\\ &=d^3 x \left (a+b \cosh ^{-1}(c x)\right )^2+d^2 e x^3 \left (a+b \cosh ^{-1}(c x)\right )^2+\frac{3}{5} d e^2 x^5 \left (a+b \cosh ^{-1}(c x)\right )^2+\frac{1}{7} e^3 x^7 \left (a+b \cosh ^{-1}(c x)\right )^2-\left (2 b c d^3\right ) \int \frac{x \left (a+b \cosh ^{-1}(c x)\right )}{\sqrt{-1+c x} \sqrt{1+c x}} \, dx-\left (2 b c d^2 e\right ) \int \frac{x^3 \left (a+b \cosh ^{-1}(c x)\right )}{\sqrt{-1+c x} \sqrt{1+c x}} \, dx-\frac{1}{5} \left (6 b c d e^2\right ) \int \frac{x^5 \left (a+b \cosh ^{-1}(c x)\right )}{\sqrt{-1+c x} \sqrt{1+c x}} \, dx-\frac{1}{7} \left (2 b c e^3\right ) \int \frac{x^7 \left (a+b \cosh ^{-1}(c x)\right )}{\sqrt{-1+c x} \sqrt{1+c x}} \, dx\\ &=-\frac{2 b d^3 \sqrt{-1+c x} \sqrt{1+c x} \left (a+b \cosh ^{-1}(c x)\right )}{c}-\frac{2 b d^2 e x^2 \sqrt{-1+c x} \sqrt{1+c x} \left (a+b \cosh ^{-1}(c x)\right )}{3 c}-\frac{6 b d e^2 x^4 \sqrt{-1+c x} \sqrt{1+c x} \left (a+b \cosh ^{-1}(c x)\right )}{25 c}-\frac{2 b e^3 x^6 \sqrt{-1+c x} \sqrt{1+c x} \left (a+b \cosh ^{-1}(c x)\right )}{49 c}+d^3 x \left (a+b \cosh ^{-1}(c x)\right )^2+d^2 e x^3 \left (a+b \cosh ^{-1}(c x)\right )^2+\frac{3}{5} d e^2 x^5 \left (a+b \cosh ^{-1}(c x)\right )^2+\frac{1}{7} e^3 x^7 \left (a+b \cosh ^{-1}(c x)\right )^2+\left (2 b^2 d^3\right ) \int 1 \, dx+\frac{1}{3} \left (2 b^2 d^2 e\right ) \int x^2 \, dx-\frac{\left (4 b d^2 e\right ) \int \frac{x \left (a+b \cosh ^{-1}(c x)\right )}{\sqrt{-1+c x} \sqrt{1+c x}} \, dx}{3 c}+\frac{1}{25} \left (6 b^2 d e^2\right ) \int x^4 \, dx-\frac{\left (24 b d e^2\right ) \int \frac{x^3 \left (a+b \cosh ^{-1}(c x)\right )}{\sqrt{-1+c x} \sqrt{1+c x}} \, dx}{25 c}+\frac{1}{49} \left (2 b^2 e^3\right ) \int x^6 \, dx-\frac{\left (12 b e^3\right ) \int \frac{x^5 \left (a+b \cosh ^{-1}(c x)\right )}{\sqrt{-1+c x} \sqrt{1+c x}} \, dx}{49 c}\\ &=2 b^2 d^3 x+\frac{2}{9} b^2 d^2 e x^3+\frac{6}{125} b^2 d e^2 x^5+\frac{2}{343} b^2 e^3 x^7-\frac{2 b d^3 \sqrt{-1+c x} \sqrt{1+c x} \left (a+b \cosh ^{-1}(c x)\right )}{c}-\frac{4 b d^2 e \sqrt{-1+c x} \sqrt{1+c x} \left (a+b \cosh ^{-1}(c x)\right )}{3 c^3}-\frac{2 b d^2 e x^2 \sqrt{-1+c x} \sqrt{1+c x} \left (a+b \cosh ^{-1}(c x)\right )}{3 c}-\frac{8 b d e^2 x^2 \sqrt{-1+c x} \sqrt{1+c x} \left (a+b \cosh ^{-1}(c x)\right )}{25 c^3}-\frac{6 b d e^2 x^4 \sqrt{-1+c x} \sqrt{1+c x} \left (a+b \cosh ^{-1}(c x)\right )}{25 c}-\frac{12 b e^3 x^4 \sqrt{-1+c x} \sqrt{1+c x} \left (a+b \cosh ^{-1}(c x)\right )}{245 c^3}-\frac{2 b e^3 x^6 \sqrt{-1+c x} \sqrt{1+c x} \left (a+b \cosh ^{-1}(c x)\right )}{49 c}+d^3 x \left (a+b \cosh ^{-1}(c x)\right )^2+d^2 e x^3 \left (a+b \cosh ^{-1}(c x)\right )^2+\frac{3}{5} d e^2 x^5 \left (a+b \cosh ^{-1}(c x)\right )^2+\frac{1}{7} e^3 x^7 \left (a+b \cosh ^{-1}(c x)\right )^2+\frac{\left (4 b^2 d^2 e\right ) \int 1 \, dx}{3 c^2}-\frac{\left (16 b d e^2\right ) \int \frac{x \left (a+b \cosh ^{-1}(c x)\right )}{\sqrt{-1+c x} \sqrt{1+c x}} \, dx}{25 c^3}+\frac{\left (8 b^2 d e^2\right ) \int x^2 \, dx}{25 c^2}-\frac{\left (48 b e^3\right ) \int \frac{x^3 \left (a+b \cosh ^{-1}(c x)\right )}{\sqrt{-1+c x} \sqrt{1+c x}} \, dx}{245 c^3}+\frac{\left (12 b^2 e^3\right ) \int x^4 \, dx}{245 c^2}\\ &=2 b^2 d^3 x+\frac{4 b^2 d^2 e x}{3 c^2}+\frac{2}{9} b^2 d^2 e x^3+\frac{8 b^2 d e^2 x^3}{75 c^2}+\frac{6}{125} b^2 d e^2 x^5+\frac{12 b^2 e^3 x^5}{1225 c^2}+\frac{2}{343} b^2 e^3 x^7-\frac{2 b d^3 \sqrt{-1+c x} \sqrt{1+c x} \left (a+b \cosh ^{-1}(c x)\right )}{c}-\frac{4 b d^2 e \sqrt{-1+c x} \sqrt{1+c x} \left (a+b \cosh ^{-1}(c x)\right )}{3 c^3}-\frac{16 b d e^2 \sqrt{-1+c x} \sqrt{1+c x} \left (a+b \cosh ^{-1}(c x)\right )}{25 c^5}-\frac{2 b d^2 e x^2 \sqrt{-1+c x} \sqrt{1+c x} \left (a+b \cosh ^{-1}(c x)\right )}{3 c}-\frac{8 b d e^2 x^2 \sqrt{-1+c x} \sqrt{1+c x} \left (a+b \cosh ^{-1}(c x)\right )}{25 c^3}-\frac{16 b e^3 x^2 \sqrt{-1+c x} \sqrt{1+c x} \left (a+b \cosh ^{-1}(c x)\right )}{245 c^5}-\frac{6 b d e^2 x^4 \sqrt{-1+c x} \sqrt{1+c x} \left (a+b \cosh ^{-1}(c x)\right )}{25 c}-\frac{12 b e^3 x^4 \sqrt{-1+c x} \sqrt{1+c x} \left (a+b \cosh ^{-1}(c x)\right )}{245 c^3}-\frac{2 b e^3 x^6 \sqrt{-1+c x} \sqrt{1+c x} \left (a+b \cosh ^{-1}(c x)\right )}{49 c}+d^3 x \left (a+b \cosh ^{-1}(c x)\right )^2+d^2 e x^3 \left (a+b \cosh ^{-1}(c x)\right )^2+\frac{3}{5} d e^2 x^5 \left (a+b \cosh ^{-1}(c x)\right )^2+\frac{1}{7} e^3 x^7 \left (a+b \cosh ^{-1}(c x)\right )^2+\frac{\left (16 b^2 d e^2\right ) \int 1 \, dx}{25 c^4}-\frac{\left (32 b e^3\right ) \int \frac{x \left (a+b \cosh ^{-1}(c x)\right )}{\sqrt{-1+c x} \sqrt{1+c x}} \, dx}{245 c^5}+\frac{\left (16 b^2 e^3\right ) \int x^2 \, dx}{245 c^4}\\ &=2 b^2 d^3 x+\frac{4 b^2 d^2 e x}{3 c^2}+\frac{16 b^2 d e^2 x}{25 c^4}+\frac{2}{9} b^2 d^2 e x^3+\frac{8 b^2 d e^2 x^3}{75 c^2}+\frac{16 b^2 e^3 x^3}{735 c^4}+\frac{6}{125} b^2 d e^2 x^5+\frac{12 b^2 e^3 x^5}{1225 c^2}+\frac{2}{343} b^2 e^3 x^7-\frac{2 b d^3 \sqrt{-1+c x} \sqrt{1+c x} \left (a+b \cosh ^{-1}(c x)\right )}{c}-\frac{4 b d^2 e \sqrt{-1+c x} \sqrt{1+c x} \left (a+b \cosh ^{-1}(c x)\right )}{3 c^3}-\frac{16 b d e^2 \sqrt{-1+c x} \sqrt{1+c x} \left (a+b \cosh ^{-1}(c x)\right )}{25 c^5}-\frac{32 b e^3 \sqrt{-1+c x} \sqrt{1+c x} \left (a+b \cosh ^{-1}(c x)\right )}{245 c^7}-\frac{2 b d^2 e x^2 \sqrt{-1+c x} \sqrt{1+c x} \left (a+b \cosh ^{-1}(c x)\right )}{3 c}-\frac{8 b d e^2 x^2 \sqrt{-1+c x} \sqrt{1+c x} \left (a+b \cosh ^{-1}(c x)\right )}{25 c^3}-\frac{16 b e^3 x^2 \sqrt{-1+c x} \sqrt{1+c x} \left (a+b \cosh ^{-1}(c x)\right )}{245 c^5}-\frac{6 b d e^2 x^4 \sqrt{-1+c x} \sqrt{1+c x} \left (a+b \cosh ^{-1}(c x)\right )}{25 c}-\frac{12 b e^3 x^4 \sqrt{-1+c x} \sqrt{1+c x} \left (a+b \cosh ^{-1}(c x)\right )}{245 c^3}-\frac{2 b e^3 x^6 \sqrt{-1+c x} \sqrt{1+c x} \left (a+b \cosh ^{-1}(c x)\right )}{49 c}+d^3 x \left (a+b \cosh ^{-1}(c x)\right )^2+d^2 e x^3 \left (a+b \cosh ^{-1}(c x)\right )^2+\frac{3}{5} d e^2 x^5 \left (a+b \cosh ^{-1}(c x)\right )^2+\frac{1}{7} e^3 x^7 \left (a+b \cosh ^{-1}(c x)\right )^2+\frac{\left (32 b^2 e^3\right ) \int 1 \, dx}{245 c^6}\\ &=2 b^2 d^3 x+\frac{4 b^2 d^2 e x}{3 c^2}+\frac{16 b^2 d e^2 x}{25 c^4}+\frac{32 b^2 e^3 x}{245 c^6}+\frac{2}{9} b^2 d^2 e x^3+\frac{8 b^2 d e^2 x^3}{75 c^2}+\frac{16 b^2 e^3 x^3}{735 c^4}+\frac{6}{125} b^2 d e^2 x^5+\frac{12 b^2 e^3 x^5}{1225 c^2}+\frac{2}{343} b^2 e^3 x^7-\frac{2 b d^3 \sqrt{-1+c x} \sqrt{1+c x} \left (a+b \cosh ^{-1}(c x)\right )}{c}-\frac{4 b d^2 e \sqrt{-1+c x} \sqrt{1+c x} \left (a+b \cosh ^{-1}(c x)\right )}{3 c^3}-\frac{16 b d e^2 \sqrt{-1+c x} \sqrt{1+c x} \left (a+b \cosh ^{-1}(c x)\right )}{25 c^5}-\frac{32 b e^3 \sqrt{-1+c x} \sqrt{1+c x} \left (a+b \cosh ^{-1}(c x)\right )}{245 c^7}-\frac{2 b d^2 e x^2 \sqrt{-1+c x} \sqrt{1+c x} \left (a+b \cosh ^{-1}(c x)\right )}{3 c}-\frac{8 b d e^2 x^2 \sqrt{-1+c x} \sqrt{1+c x} \left (a+b \cosh ^{-1}(c x)\right )}{25 c^3}-\frac{16 b e^3 x^2 \sqrt{-1+c x} \sqrt{1+c x} \left (a+b \cosh ^{-1}(c x)\right )}{245 c^5}-\frac{6 b d e^2 x^4 \sqrt{-1+c x} \sqrt{1+c x} \left (a+b \cosh ^{-1}(c x)\right )}{25 c}-\frac{12 b e^3 x^4 \sqrt{-1+c x} \sqrt{1+c x} \left (a+b \cosh ^{-1}(c x)\right )}{245 c^3}-\frac{2 b e^3 x^6 \sqrt{-1+c x} \sqrt{1+c x} \left (a+b \cosh ^{-1}(c x)\right )}{49 c}+d^3 x \left (a+b \cosh ^{-1}(c x)\right )^2+d^2 e x^3 \left (a+b \cosh ^{-1}(c x)\right )^2+\frac{3}{5} d e^2 x^5 \left (a+b \cosh ^{-1}(c x)\right )^2+\frac{1}{7} e^3 x^7 \left (a+b \cosh ^{-1}(c x)\right )^2\\ \end{align*}
Mathematica [A] time = 0.842717, size = 453, normalized size = 0.74 \[ \frac{11025 a^2 c^7 x \left (35 d^2 e x^2+35 d^3+21 d e^2 x^4+5 e^3 x^6\right )-210 a b \sqrt{c x-1} \sqrt{c x+1} \left (c^6 \left (1225 d^2 e x^2+3675 d^3+441 d e^2 x^4+75 e^3 x^6\right )+2 c^4 e \left (1225 d^2+294 d e x^2+45 e^2 x^4\right )+24 c^2 e^2 \left (49 d+5 e x^2\right )+240 e^3\right )-210 b \cosh ^{-1}(c x) \left (b \sqrt{c x-1} \sqrt{c x+1} \left (c^6 \left (1225 d^2 e x^2+3675 d^3+441 d e^2 x^4+75 e^3 x^6\right )+2 c^4 e \left (1225 d^2+294 d e x^2+45 e^2 x^4\right )+24 c^2 e^2 \left (49 d+5 e x^2\right )+240 e^3\right )-105 a c^7 x \left (35 d^2 e x^2+35 d^3+21 d e^2 x^4+5 e^3 x^6\right )\right )+2 b^2 c x \left (c^6 \left (42875 d^2 e x^2+385875 d^3+9261 d e^2 x^4+1125 e^3 x^6\right )+210 c^4 e \left (1225 d^2+98 d e x^2+9 e^2 x^4\right )+840 c^2 e^2 \left (147 d+5 e x^2\right )+25200 e^3\right )+11025 b^2 c^7 x \cosh ^{-1}(c x)^2 \left (35 d^2 e x^2+35 d^3+21 d e^2 x^4+5 e^3 x^6\right )}{385875 c^7} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.085, size = 632, normalized size = 1. \begin{align*} \text{result too large to display} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.15874, size = 923, normalized size = 1.52 \begin{align*} \text{result too large to display} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.93084, size = 1338, normalized size = 2.2 \begin{align*} \frac{1125 \,{\left (49 \, a^{2} + 2 \, b^{2}\right )} c^{7} e^{3} x^{7} + 189 \,{\left (49 \,{\left (25 \, a^{2} + 2 \, b^{2}\right )} c^{7} d e^{2} + 20 \, b^{2} c^{5} e^{3}\right )} x^{5} + 35 \,{\left (1225 \,{\left (9 \, a^{2} + 2 \, b^{2}\right )} c^{7} d^{2} e + 1176 \, b^{2} c^{5} d e^{2} + 240 \, b^{2} c^{3} e^{3}\right )} x^{3} + 11025 \,{\left (5 \, b^{2} c^{7} e^{3} x^{7} + 21 \, b^{2} c^{7} d e^{2} x^{5} + 35 \, b^{2} c^{7} d^{2} e x^{3} + 35 \, b^{2} c^{7} d^{3} x\right )} \log \left (c x + \sqrt{c^{2} x^{2} - 1}\right )^{2} + 105 \,{\left (3675 \,{\left (a^{2} + 2 \, b^{2}\right )} c^{7} d^{3} + 4900 \, b^{2} c^{5} d^{2} e + 2352 \, b^{2} c^{3} d e^{2} + 480 \, b^{2} c e^{3}\right )} x + 210 \,{\left (525 \, a b c^{7} e^{3} x^{7} + 2205 \, a b c^{7} d e^{2} x^{5} + 3675 \, a b c^{7} d^{2} e x^{3} + 3675 \, a b c^{7} d^{3} x -{\left (75 \, b^{2} c^{6} e^{3} x^{6} + 3675 \, b^{2} c^{6} d^{3} + 2450 \, b^{2} c^{4} d^{2} e + 1176 \, b^{2} c^{2} d e^{2} + 240 \, b^{2} e^{3} + 9 \,{\left (49 \, b^{2} c^{6} d e^{2} + 10 \, b^{2} c^{4} e^{3}\right )} x^{4} +{\left (1225 \, b^{2} c^{6} d^{2} e + 588 \, b^{2} c^{4} d e^{2} + 120 \, b^{2} c^{2} e^{3}\right )} x^{2}\right )} \sqrt{c^{2} x^{2} - 1}\right )} \log \left (c x + \sqrt{c^{2} x^{2} - 1}\right ) - 210 \,{\left (75 \, a b c^{6} e^{3} x^{6} + 3675 \, a b c^{6} d^{3} + 2450 \, a b c^{4} d^{2} e + 1176 \, a b c^{2} d e^{2} + 240 \, a b e^{3} + 9 \,{\left (49 \, a b c^{6} d e^{2} + 10 \, a b c^{4} e^{3}\right )} x^{4} +{\left (1225 \, a b c^{6} d^{2} e + 588 \, a b c^{4} d e^{2} + 120 \, a b c^{2} e^{3}\right )} x^{2}\right )} \sqrt{c^{2} x^{2} - 1}}{385875 \, c^{7}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 20.429, size = 996, normalized size = 1.64 \begin{align*} \text{result too large to display} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.57134, size = 986, normalized size = 1.62 \begin{align*} \text{result too large to display} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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