Integrand size = 175, antiderivative size = 28 \[ \int \frac {-1875-675 x+30 x^2+e^6 (-75+3 x)+e^{\frac {2}{3} (-3 x+\log (25-x))} (-75+3 x)+e^3 \left (-750-120 x+6 x^2\right )+e^{\frac {1}{3} (-3 x+\log (25-x))} \left (-750-120 x-70 x^2+3 x^3+e^3 (-150+6 x)\right )}{-1875+75 x+e^6 (-75+3 x)+e^{\frac {2}{3} (-3 x+\log (25-x))} (-75+3 x)+e^3 (-750+30 x)+e^{\frac {1}{3} (-3 x+\log (25-x))} \left (-750+30 x+e^3 (-150+6 x)\right )} \, dx=x+\frac {x^2}{5+e^3+e^{-x} \sqrt [3]{25-x}} \]
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\[ \int \frac {-1875-675 x+30 x^2+e^6 (-75+3 x)+e^{\frac {2}{3} (-3 x+\log (25-x))} (-75+3 x)+e^3 \left (-750-120 x+6 x^2\right )+e^{\frac {1}{3} (-3 x+\log (25-x))} \left (-750-120 x-70 x^2+3 x^3+e^3 (-150+6 x)\right )}{-1875+75 x+e^6 (-75+3 x)+e^{\frac {2}{3} (-3 x+\log (25-x))} (-75+3 x)+e^3 (-750+30 x)+e^{\frac {1}{3} (-3 x+\log (25-x))} \left (-750+30 x+e^3 (-150+6 x)\right )} \, dx=\int \frac {-1875-675 x+30 x^2+e^6 (-75+3 x)+e^{\frac {2}{3} (-3 x+\log (25-x))} (-75+3 x)+e^3 \left (-750-120 x+6 x^2\right )+e^{\frac {1}{3} (-3 x+\log (25-x))} \left (-750-120 x-70 x^2+3 x^3+e^3 (-150+6 x)\right )}{-1875+75 x+e^6 (-75+3 x)+e^{\frac {2}{3} (-3 x+\log (25-x))} (-75+3 x)+e^3 (-750+30 x)+e^{\frac {1}{3} (-3 x+\log (25-x))} \left (-750+30 x+e^3 (-150+6 x)\right )} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {e^{2 x} \left (1875+675 x-30 x^2-e^6 (-75+3 x)-e^{\frac {2}{3} (-3 x+\log (25-x))} (-75+3 x)-e^3 \left (-750-120 x+6 x^2\right )-e^{\frac {1}{3} (-3 x+\log (25-x))} \left (-750-120 x-70 x^2+3 x^3+e^3 (-150+6 x)\right )\right )}{3 \left (5 e^x \left (1+\frac {e^3}{5}\right )+\sqrt [3]{25-x}\right )^2 (25-x)} \, dx \\ & = \frac {1}{3} \int \frac {e^{2 x} \left (1875+675 x-30 x^2-e^6 (-75+3 x)-e^{\frac {2}{3} (-3 x+\log (25-x))} (-75+3 x)-e^3 \left (-750-120 x+6 x^2\right )-e^{\frac {1}{3} (-3 x+\log (25-x))} \left (-750-120 x-70 x^2+3 x^3+e^3 (-150+6 x)\right )\right )}{\left (5 e^x \left (1+\frac {e^3}{5}\right )+\sqrt [3]{25-x}\right )^2 (25-x)} \, dx \\ & = -\text {Subst}\left (\int \frac {3 e^{56} x^3+6 e^{28+x^3} \left (x^3\right )^{4/3}+3 e^{2 x^3} \left (x^3\right )^{5/3}-6 e^{53} x^3 \left (-30+x^3\right )+e^{50} \left (825 x^3-30 x^6\right )+e^{25+x^3} \sqrt [3]{x^3} \left (625+2005 x^3-155 x^6+3 x^9\right )}{x \left (5 e^{25}+e^{28}+e^{x^3} x\right )^2} \, dx,x,\sqrt [3]{25-x}\right ) \\ & = -\text {Subst}\left (\int \frac {3 e^{56} x^3+6 e^{28+x^3} \left (x^3\right )^{4/3}+3 e^{2 x^3} \left (x^3\right )^{5/3}-6 e^{53} x^3 \left (-30+x^3\right )+e^{50} \left (825 x^3-30 x^6\right )+e^{25+x^3} \sqrt [3]{x^3} \left (625+2005 x^3-155 x^6+3 x^9\right )}{x \left (5 e^{25} \left (1+\frac {e^3}{5}\right )+e^{x^3} x\right )^2} \, dx,x,\sqrt [3]{25-x}\right ) \\ & = -\text {Subst}\left (\int \left (3 \left (x^3\right )^{2/3}+\frac {155 e^{25} x^4 \sqrt [3]{x^3}}{-5 e^{25} \left (1+\frac {e^3}{5}\right )-e^{x^3} x}+\frac {30 e^{25} \left (1+\frac {e^3}{5}\right ) \left (x^3\right )^{2/3}}{-5 e^{25} \left (1+\frac {e^3}{5}\right )-e^{x^3} x}-\frac {3125 e^{50} \left (1+\frac {e^3}{5}\right ) \sqrt [3]{x^3}}{x^2 \left (5 e^{25} \left (1+\frac {e^3}{5}\right )+e^{x^3} x\right )^2}-\frac {10025 e^{50} \left (1+\frac {e^3 \left (2035+6 e^3\right )}{10025}\right ) x \sqrt [3]{x^3}}{\left (5 e^{25} \left (1+\frac {e^3}{5}\right )+e^{x^3} x\right )^2}+\frac {775 e^{50} \left (1+\frac {e^3}{5}\right ) x^4 \sqrt [3]{x^3}}{\left (5 e^{25} \left (1+\frac {e^3}{5}\right )+e^{x^3} x\right )^2}-\frac {15 e^{50} \left (1+\frac {e^3}{5}\right ) x^7 \sqrt [3]{x^3}}{\left (5 e^{25} \left (1+\frac {e^3}{5}\right )+e^{x^3} x\right )^2}+\frac {75 e^{50} \left (1+\frac {1}{25} e^3 \left (10+e^3\right )\right ) \left (x^3\right )^{2/3}}{\left (5 e^{25} \left (1+\frac {e^3}{5}\right )+e^{x^3} x\right )^2}+\frac {625 e^{25} \sqrt [3]{x^3}}{x^2 \left (5 e^{25} \left (1+\frac {e^3}{5}\right )+e^{x^3} x\right )}+\frac {2005 e^{25} \left (1+\frac {6 e^3}{2005}\right ) x \sqrt [3]{x^3}}{5 e^{25} \left (1+\frac {e^3}{5}\right )+e^{x^3} x}+\frac {3 e^{25} x^7 \sqrt [3]{x^3}}{5 e^{25} \left (1+\frac {e^3}{5}\right )+e^{x^3} x}+\frac {3 e^{50} \left (5+e^3\right ) x^2 \left (55+e^3-2 x^3\right )}{\left (5 e^{25} \left (1+\frac {e^3}{5}\right )+e^{x^3} x\right )^2}\right ) \, dx,x,\sqrt [3]{25-x}\right ) \\ & = -\left (3 \text {Subst}\left (\int \left (x^3\right )^{2/3} \, dx,x,\sqrt [3]{25-x}\right )\right )-\left (3 e^{25}\right ) \text {Subst}\left (\int \frac {x^7 \sqrt [3]{x^3}}{5 e^{25} \left (1+\frac {e^3}{5}\right )+e^{x^3} x} \, dx,x,\sqrt [3]{25-x}\right )-\left (155 e^{25}\right ) \text {Subst}\left (\int \frac {x^4 \sqrt [3]{x^3}}{-5 e^{25} \left (1+\frac {e^3}{5}\right )-e^{x^3} x} \, dx,x,\sqrt [3]{25-x}\right )-\left (625 e^{25}\right ) \text {Subst}\left (\int \frac {\sqrt [3]{x^3}}{x^2 \left (5 e^{25} \left (1+\frac {e^3}{5}\right )+e^{x^3} x\right )} \, dx,x,\sqrt [3]{25-x}\right )-\left (6 e^{25} \left (5+e^3\right )\right ) \text {Subst}\left (\int \frac {\left (x^3\right )^{2/3}}{-5 e^{25} \left (1+\frac {e^3}{5}\right )-e^{x^3} x} \, dx,x,\sqrt [3]{25-x}\right )+\left (3 e^{50} \left (5+e^3\right )\right ) \text {Subst}\left (\int \frac {x^7 \sqrt [3]{x^3}}{\left (5 e^{25} \left (1+\frac {e^3}{5}\right )+e^{x^3} x\right )^2} \, dx,x,\sqrt [3]{25-x}\right )-\left (3 e^{50} \left (5+e^3\right )\right ) \text {Subst}\left (\int \frac {x^2 \left (55+e^3-2 x^3\right )}{\left (5 e^{25} \left (1+\frac {e^3}{5}\right )+e^{x^3} x\right )^2} \, dx,x,\sqrt [3]{25-x}\right )-\left (155 e^{50} \left (5+e^3\right )\right ) \text {Subst}\left (\int \frac {x^4 \sqrt [3]{x^3}}{\left (5 e^{25} \left (1+\frac {e^3}{5}\right )+e^{x^3} x\right )^2} \, dx,x,\sqrt [3]{25-x}\right )+\left (625 e^{50} \left (5+e^3\right )\right ) \text {Subst}\left (\int \frac {\sqrt [3]{x^3}}{x^2 \left (5 e^{25} \left (1+\frac {e^3}{5}\right )+e^{x^3} x\right )^2} \, dx,x,\sqrt [3]{25-x}\right )-\left (3 e^{50} \left (5+e^3\right )^2\right ) \text {Subst}\left (\int \frac {\left (x^3\right )^{2/3}}{\left (5 e^{25} \left (1+\frac {e^3}{5}\right )+e^{x^3} x\right )^2} \, dx,x,\sqrt [3]{25-x}\right )-\left (e^{25} \left (2005+6 e^3\right )\right ) \text {Subst}\left (\int \frac {x \sqrt [3]{x^3}}{5 e^{25} \left (1+\frac {e^3}{5}\right )+e^{x^3} x} \, dx,x,\sqrt [3]{25-x}\right )+\left (e^{50} \left (10025+2035 e^3+6 e^6\right )\right ) \text {Subst}\left (\int \frac {x \sqrt [3]{x^3}}{\left (5 e^{25} \left (1+\frac {e^3}{5}\right )+e^{x^3} x\right )^2} \, dx,x,\sqrt [3]{25-x}\right ) \\ & = -\left (3 \text {Subst}\left (\int x^2 \, dx,x,\sqrt [3]{25-x}\right )\right )-\left (3 e^{25}\right ) \text {Subst}\left (\int \frac {x^8}{5 e^{25} \left (1+\frac {e^3}{5}\right )+e^{x^3} x} \, dx,x,\sqrt [3]{25-x}\right )-\left (155 e^{25}\right ) \text {Subst}\left (\int \frac {x^5}{-5 e^{25} \left (1+\frac {e^3}{5}\right )-e^{x^3} x} \, dx,x,\sqrt [3]{25-x}\right )-\left (625 e^{25}\right ) \text {Subst}\left (\int \frac {1}{x \left (5 e^{25} \left (1+\frac {e^3}{5}\right )+e^{x^3} x\right )} \, dx,x,\sqrt [3]{25-x}\right )-\left (6 e^{25} \left (5+e^3\right )\right ) \text {Subst}\left (\int \frac {x^2}{-5 e^{25} \left (1+\frac {e^3}{5}\right )-e^{x^3} x} \, dx,x,\sqrt [3]{25-x}\right )+\left (3 e^{50} \left (5+e^3\right )\right ) \text {Subst}\left (\int \frac {x^8}{\left (5 e^{25} \left (1+\frac {e^3}{5}\right )+e^{x^3} x\right )^2} \, dx,x,\sqrt [3]{25-x}\right )-\left (3 e^{50} \left (5+e^3\right )\right ) \text {Subst}\left (\int \left (\frac {\left (55+e^3\right ) x^2}{\left (5 e^{25} \left (1+\frac {e^3}{5}\right )+e^{x^3} x\right )^2}-\frac {2 x^5}{\left (5 e^{25} \left (1+\frac {e^3}{5}\right )+e^{x^3} x\right )^2}\right ) \, dx,x,\sqrt [3]{25-x}\right )-\left (155 e^{50} \left (5+e^3\right )\right ) \text {Subst}\left (\int \frac {x^5}{\left (5 e^{25} \left (1+\frac {e^3}{5}\right )+e^{x^3} x\right )^2} \, dx,x,\sqrt [3]{25-x}\right )+\left (625 e^{50} \left (5+e^3\right )\right ) \text {Subst}\left (\int \frac {1}{x \left (5 e^{25} \left (1+\frac {e^3}{5}\right )+e^{x^3} x\right )^2} \, dx,x,\sqrt [3]{25-x}\right )-\left (3 e^{50} \left (5+e^3\right )^2\right ) \text {Subst}\left (\int \frac {x^2}{\left (5 e^{25} \left (1+\frac {e^3}{5}\right )+e^{x^3} x\right )^2} \, dx,x,\sqrt [3]{25-x}\right )-\left (e^{25} \left (2005+6 e^3\right )\right ) \text {Subst}\left (\int \frac {x^2}{5 e^{25} \left (1+\frac {e^3}{5}\right )+e^{x^3} x} \, dx,x,\sqrt [3]{25-x}\right )+\left (e^{50} \left (10025+2035 e^3+6 e^6\right )\right ) \text {Subst}\left (\int \frac {x^2}{\left (5 e^{25} \left (1+\frac {e^3}{5}\right )+e^{x^3} x\right )^2} \, dx,x,\sqrt [3]{25-x}\right ) \\ & = x-\left (3 e^{25}\right ) \text {Subst}\left (\int \frac {x^8}{5 e^{25} \left (1+\frac {e^3}{5}\right )+e^{x^3} x} \, dx,x,\sqrt [3]{25-x}\right )-\left (155 e^{25}\right ) \text {Subst}\left (\int \frac {x^5}{-5 e^{25} \left (1+\frac {e^3}{5}\right )-e^{x^3} x} \, dx,x,\sqrt [3]{25-x}\right )-\left (625 e^{25}\right ) \text {Subst}\left (\int \frac {1}{x \left (5 e^{25} \left (1+\frac {e^3}{5}\right )+e^{x^3} x\right )} \, dx,x,\sqrt [3]{25-x}\right )-\left (6 e^{25} \left (5+e^3\right )\right ) \text {Subst}\left (\int \frac {x^2}{-5 e^{25} \left (1+\frac {e^3}{5}\right )-e^{x^3} x} \, dx,x,\sqrt [3]{25-x}\right )+\left (3 e^{50} \left (5+e^3\right )\right ) \text {Subst}\left (\int \frac {x^8}{\left (5 e^{25} \left (1+\frac {e^3}{5}\right )+e^{x^3} x\right )^2} \, dx,x,\sqrt [3]{25-x}\right )+\left (6 e^{50} \left (5+e^3\right )\right ) \text {Subst}\left (\int \frac {x^5}{\left (5 e^{25} \left (1+\frac {e^3}{5}\right )+e^{x^3} x\right )^2} \, dx,x,\sqrt [3]{25-x}\right )-\left (155 e^{50} \left (5+e^3\right )\right ) \text {Subst}\left (\int \frac {x^5}{\left (5 e^{25} \left (1+\frac {e^3}{5}\right )+e^{x^3} x\right )^2} \, dx,x,\sqrt [3]{25-x}\right )+\left (625 e^{50} \left (5+e^3\right )\right ) \text {Subst}\left (\int \frac {1}{x \left (5 e^{25} \left (1+\frac {e^3}{5}\right )+e^{x^3} x\right )^2} \, dx,x,\sqrt [3]{25-x}\right )-\left (3 e^{50} \left (5+e^3\right )^2\right ) \text {Subst}\left (\int \frac {x^2}{\left (5 e^{25} \left (1+\frac {e^3}{5}\right )+e^{x^3} x\right )^2} \, dx,x,\sqrt [3]{25-x}\right )-\left (3 e^{50} \left (5+e^3\right ) \left (55+e^3\right )\right ) \text {Subst}\left (\int \frac {x^2}{\left (5 e^{25} \left (1+\frac {e^3}{5}\right )+e^{x^3} x\right )^2} \, dx,x,\sqrt [3]{25-x}\right )-\left (e^{25} \left (2005+6 e^3\right )\right ) \text {Subst}\left (\int \frac {x^2}{5 e^{25} \left (1+\frac {e^3}{5}\right )+e^{x^3} x} \, dx,x,\sqrt [3]{25-x}\right )+\left (e^{50} \left (10025+2035 e^3+6 e^6\right )\right ) \text {Subst}\left (\int \frac {x^2}{\left (5 e^{25} \left (1+\frac {e^3}{5}\right )+e^{x^3} x\right )^2} \, dx,x,\sqrt [3]{25-x}\right ) \\ \end{align*}
Leaf count is larger than twice the leaf count of optimal. \(138\) vs. \(2(28)=56\).
Time = 11.22 (sec) , antiderivative size = 138, normalized size of antiderivative = 4.93 \[ \int \frac {-1875-675 x+30 x^2+e^6 (-75+3 x)+e^{\frac {2}{3} (-3 x+\log (25-x))} (-75+3 x)+e^3 \left (-750-120 x+6 x^2\right )+e^{\frac {1}{3} (-3 x+\log (25-x))} \left (-750-120 x-70 x^2+3 x^3+e^3 (-150+6 x)\right )}{-1875+75 x+e^6 (-75+3 x)+e^{\frac {2}{3} (-3 x+\log (25-x))} (-75+3 x)+e^3 (-750+30 x)+e^{\frac {1}{3} (-3 x+\log (25-x))} \left (-750+30 x+e^3 (-150+6 x)\right )} \, dx=\frac {x \left (25+e^{9+3 x}-x-5 e^{2 x} \sqrt [3]{25-x} x-e^{3+2 x} \sqrt [3]{25-x} x+e^x (25-x)^{2/3} x+25 e^{3 x} (5+x)+e^{6+3 x} (15+x)+5 e^{3+3 x} (15+2 x)\right )}{25+125 e^{3 x}+75 e^{3+3 x}+15 e^{6+3 x}+e^{9+3 x}-x} \]
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Time = 2.35 (sec) , antiderivative size = 25, normalized size of antiderivative = 0.89
method | result | size |
risch | \(\frac {x^{2}}{\left (-x +25\right )^{\frac {1}{3}} {\mathrm e}^{-x}+{\mathrm e}^{3}+5}+x\) | \(25\) |
norman | \(\frac {x^{2}+\left ({\mathrm e}^{3}+5\right ) x +{\mathrm e}^{\frac {\ln \left (-x +25\right )}{3}-x} x}{{\mathrm e}^{\frac {\ln \left (-x +25\right )}{3}-x}+{\mathrm e}^{3}+5}\) | \(46\) |
parallelrisch | \(\frac {750+3 x \,{\mathrm e}^{3}+3 x^{2}+3 \,{\mathrm e}^{\frac {\ln \left (-x +25\right )}{3}-x} x +150 \,{\mathrm e}^{3}+15 x +150 \,{\mathrm e}^{\frac {\ln \left (-x +25\right )}{3}-x}}{3 \,{\mathrm e}^{\frac {\ln \left (-x +25\right )}{3}-x}+3 \,{\mathrm e}^{3}+15}\) | \(72\) |
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Time = 0.27 (sec) , antiderivative size = 46, normalized size of antiderivative = 1.64 \[ \int \frac {-1875-675 x+30 x^2+e^6 (-75+3 x)+e^{\frac {2}{3} (-3 x+\log (25-x))} (-75+3 x)+e^3 \left (-750-120 x+6 x^2\right )+e^{\frac {1}{3} (-3 x+\log (25-x))} \left (-750-120 x-70 x^2+3 x^3+e^3 (-150+6 x)\right )}{-1875+75 x+e^6 (-75+3 x)+e^{\frac {2}{3} (-3 x+\log (25-x))} (-75+3 x)+e^3 (-750+30 x)+e^{\frac {1}{3} (-3 x+\log (25-x))} \left (-750+30 x+e^3 (-150+6 x)\right )} \, dx=\frac {x^{2} + x e^{3} + x e^{\left (-x + \frac {1}{3} \, \log \left (-x + 25\right )\right )} + 5 \, x}{e^{3} + e^{\left (-x + \frac {1}{3} \, \log \left (-x + 25\right )\right )} + 5} \]
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Timed out. \[ \int \frac {-1875-675 x+30 x^2+e^6 (-75+3 x)+e^{\frac {2}{3} (-3 x+\log (25-x))} (-75+3 x)+e^3 \left (-750-120 x+6 x^2\right )+e^{\frac {1}{3} (-3 x+\log (25-x))} \left (-750-120 x-70 x^2+3 x^3+e^3 (-150+6 x)\right )}{-1875+75 x+e^6 (-75+3 x)+e^{\frac {2}{3} (-3 x+\log (25-x))} (-75+3 x)+e^3 (-750+30 x)+e^{\frac {1}{3} (-3 x+\log (25-x))} \left (-750+30 x+e^3 (-150+6 x)\right )} \, dx=\text {Timed out} \]
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Leaf count of result is larger than twice the leaf count of optimal. 63 vs. \(2 (25) = 50\).
Time = 0.24 (sec) , antiderivative size = 63, normalized size of antiderivative = 2.25 \[ \int \frac {-1875-675 x+30 x^2+e^6 (-75+3 x)+e^{\frac {2}{3} (-3 x+\log (25-x))} (-75+3 x)+e^3 \left (-750-120 x+6 x^2\right )+e^{\frac {1}{3} (-3 x+\log (25-x))} \left (-750-120 x-70 x^2+3 x^3+e^3 (-150+6 x)\right )}{-1875+75 x+e^6 (-75+3 x)+e^{\frac {2}{3} (-3 x+\log (25-x))} (-75+3 x)+e^3 (-750+30 x)+e^{\frac {1}{3} (-3 x+\log (25-x))} \left (-750+30 x+e^3 (-150+6 x)\right )} \, dx=\frac {{\left (x - 25\right )}^{2} e^{25} - {\left (-x + 25\right )}^{\frac {4}{3}} e^{\left (-x + 25\right )} + {\left (x - 25\right )} {\left (e^{28} + 55 \, e^{25}\right )} + 625 \, e^{25}}{{\left (-x + 25\right )}^{\frac {1}{3}} e^{\left (-x + 25\right )} + e^{28} + 5 \, e^{25}} \]
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\[ \int \frac {-1875-675 x+30 x^2+e^6 (-75+3 x)+e^{\frac {2}{3} (-3 x+\log (25-x))} (-75+3 x)+e^3 \left (-750-120 x+6 x^2\right )+e^{\frac {1}{3} (-3 x+\log (25-x))} \left (-750-120 x-70 x^2+3 x^3+e^3 (-150+6 x)\right )}{-1875+75 x+e^6 (-75+3 x)+e^{\frac {2}{3} (-3 x+\log (25-x))} (-75+3 x)+e^3 (-750+30 x)+e^{\frac {1}{3} (-3 x+\log (25-x))} \left (-750+30 x+e^3 (-150+6 x)\right )} \, dx=\int { \frac {30 \, x^{2} + 3 \, {\left (x - 25\right )} e^{6} + 6 \, {\left (x^{2} - 20 \, x - 125\right )} e^{3} + {\left (3 \, x^{3} - 70 \, x^{2} + 6 \, {\left (x - 25\right )} e^{3} - 120 \, x - 750\right )} e^{\left (-x + \frac {1}{3} \, \log \left (-x + 25\right )\right )} + 3 \, {\left (x - 25\right )} e^{\left (-2 \, x + \frac {2}{3} \, \log \left (-x + 25\right )\right )} - 675 \, x - 1875}{3 \, {\left ({\left (x - 25\right )} e^{6} + 10 \, {\left (x - 25\right )} e^{3} + 2 \, {\left ({\left (x - 25\right )} e^{3} + 5 \, x - 125\right )} e^{\left (-x + \frac {1}{3} \, \log \left (-x + 25\right )\right )} + {\left (x - 25\right )} e^{\left (-2 \, x + \frac {2}{3} \, \log \left (-x + 25\right )\right )} + 25 \, x - 625\right )}} \,d x } \]
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Time = 15.13 (sec) , antiderivative size = 60, normalized size of antiderivative = 2.14 \[ \int \frac {-1875-675 x+30 x^2+e^6 (-75+3 x)+e^{\frac {2}{3} (-3 x+\log (25-x))} (-75+3 x)+e^3 \left (-750-120 x+6 x^2\right )+e^{\frac {1}{3} (-3 x+\log (25-x))} \left (-750-120 x-70 x^2+3 x^3+e^3 (-150+6 x)\right )}{-1875+75 x+e^6 (-75+3 x)+e^{\frac {2}{3} (-3 x+\log (25-x))} (-75+3 x)+e^3 (-750+30 x)+e^{\frac {1}{3} (-3 x+\log (25-x))} \left (-750+30 x+e^3 (-150+6 x)\right )} \, dx=x-\frac {76\,x^2\,{\mathrm {e}}^3-3\,x^3\,{\mathrm {e}}^3+380\,x^2-15\,x^3}{\left (3\,x-76\right )\,\left ({\mathrm {e}}^3+5\right )\,\left ({\mathrm {e}}^3+{\mathrm {e}}^{-x}\,{\left (25-x\right )}^{1/3}+5\right )} \]
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