Optimal. Leaf size=548 \[ -\frac{4 i d^{3/2} g p^2 \text{PolyLog}\left (2,1-\frac{2 \sqrt{d}}{\sqrt{d}+i \sqrt{e} x}\right )}{3 e^{3/2}}+\frac{4 i \sqrt{d} f p^2 \text{PolyLog}\left (2,1-\frac{2 \sqrt{d}}{\sqrt{d}+i \sqrt{e} x}\right )}{\sqrt{e}}-\frac{4 d^{3/2} g p \tan ^{-1}\left (\frac{\sqrt{e} x}{\sqrt{d}}\right ) \log \left (c \left (d+e x^2\right )^p\right )}{3 e^{3/2}}+f x \log ^2\left (c \left (d+e x^2\right )^p\right )-4 f p x \log \left (c \left (d+e x^2\right )^p\right )+\frac{4 \sqrt{d} f p \tan ^{-1}\left (\frac{\sqrt{e} x}{\sqrt{d}}\right ) \log \left (c \left (d+e x^2\right )^p\right )}{\sqrt{e}}+\frac{1}{3} g x^3 \log ^2\left (c \left (d+e x^2\right )^p\right )-\frac{4}{9} g p x^3 \log \left (c \left (d+e x^2\right )^p\right )+\frac{4 d g p x \log \left (c \left (d+e x^2\right )^p\right )}{3 e}-\frac{4 i d^{3/2} g p^2 \tan ^{-1}\left (\frac{\sqrt{e} x}{\sqrt{d}}\right )^2}{3 e^{3/2}}+\frac{32 d^{3/2} g p^2 \tan ^{-1}\left (\frac{\sqrt{e} x}{\sqrt{d}}\right )}{9 e^{3/2}}-\frac{8 d^{3/2} g p^2 \log \left (\frac{2 \sqrt{d}}{\sqrt{d}+i \sqrt{e} x}\right ) \tan ^{-1}\left (\frac{\sqrt{e} x}{\sqrt{d}}\right )}{3 e^{3/2}}+\frac{4 i \sqrt{d} f p^2 \tan ^{-1}\left (\frac{\sqrt{e} x}{\sqrt{d}}\right )^2}{\sqrt{e}}-\frac{8 \sqrt{d} f p^2 \tan ^{-1}\left (\frac{\sqrt{e} x}{\sqrt{d}}\right )}{\sqrt{e}}+\frac{8 \sqrt{d} f p^2 \log \left (\frac{2 \sqrt{d}}{\sqrt{d}+i \sqrt{e} x}\right ) \tan ^{-1}\left (\frac{\sqrt{e} x}{\sqrt{d}}\right )}{\sqrt{e}}-\frac{32 d g p^2 x}{9 e}+8 f p^2 x+\frac{8}{27} g p^2 x^3 \]
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Rubi [A] time = 0.719811, antiderivative size = 548, normalized size of antiderivative = 1., number of steps used = 30, number of rules used = 15, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.682, Rules used = {2471, 2450, 2476, 2448, 321, 205, 2470, 12, 4920, 4854, 2402, 2315, 2457, 2455, 302} \[ -\frac{4 i d^{3/2} g p^2 \text{PolyLog}\left (2,1-\frac{2 \sqrt{d}}{\sqrt{d}+i \sqrt{e} x}\right )}{3 e^{3/2}}+\frac{4 i \sqrt{d} f p^2 \text{PolyLog}\left (2,1-\frac{2 \sqrt{d}}{\sqrt{d}+i \sqrt{e} x}\right )}{\sqrt{e}}-\frac{4 d^{3/2} g p \tan ^{-1}\left (\frac{\sqrt{e} x}{\sqrt{d}}\right ) \log \left (c \left (d+e x^2\right )^p\right )}{3 e^{3/2}}+f x \log ^2\left (c \left (d+e x^2\right )^p\right )-4 f p x \log \left (c \left (d+e x^2\right )^p\right )+\frac{4 \sqrt{d} f p \tan ^{-1}\left (\frac{\sqrt{e} x}{\sqrt{d}}\right ) \log \left (c \left (d+e x^2\right )^p\right )}{\sqrt{e}}+\frac{1}{3} g x^3 \log ^2\left (c \left (d+e x^2\right )^p\right )-\frac{4}{9} g p x^3 \log \left (c \left (d+e x^2\right )^p\right )+\frac{4 d g p x \log \left (c \left (d+e x^2\right )^p\right )}{3 e}-\frac{4 i d^{3/2} g p^2 \tan ^{-1}\left (\frac{\sqrt{e} x}{\sqrt{d}}\right )^2}{3 e^{3/2}}+\frac{32 d^{3/2} g p^2 \tan ^{-1}\left (\frac{\sqrt{e} x}{\sqrt{d}}\right )}{9 e^{3/2}}-\frac{8 d^{3/2} g p^2 \log \left (\frac{2 \sqrt{d}}{\sqrt{d}+i \sqrt{e} x}\right ) \tan ^{-1}\left (\frac{\sqrt{e} x}{\sqrt{d}}\right )}{3 e^{3/2}}+\frac{4 i \sqrt{d} f p^2 \tan ^{-1}\left (\frac{\sqrt{e} x}{\sqrt{d}}\right )^2}{\sqrt{e}}-\frac{8 \sqrt{d} f p^2 \tan ^{-1}\left (\frac{\sqrt{e} x}{\sqrt{d}}\right )}{\sqrt{e}}+\frac{8 \sqrt{d} f p^2 \log \left (\frac{2 \sqrt{d}}{\sqrt{d}+i \sqrt{e} x}\right ) \tan ^{-1}\left (\frac{\sqrt{e} x}{\sqrt{d}}\right )}{\sqrt{e}}-\frac{32 d g p^2 x}{9 e}+8 f p^2 x+\frac{8}{27} g p^2 x^3 \]
Antiderivative was successfully verified.
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Rule 2471
Rule 2450
Rule 2476
Rule 2448
Rule 321
Rule 205
Rule 2470
Rule 12
Rule 4920
Rule 4854
Rule 2402
Rule 2315
Rule 2457
Rule 2455
Rule 302
Rubi steps
\begin{align*} \int \left (f+g x^2\right ) \log ^2\left (c \left (d+e x^2\right )^p\right ) \, dx &=\int \left (f \log ^2\left (c \left (d+e x^2\right )^p\right )+g x^2 \log ^2\left (c \left (d+e x^2\right )^p\right )\right ) \, dx\\ &=f \int \log ^2\left (c \left (d+e x^2\right )^p\right ) \, dx+g \int x^2 \log ^2\left (c \left (d+e x^2\right )^p\right ) \, dx\\ &=f x \log ^2\left (c \left (d+e x^2\right )^p\right )+\frac{1}{3} g x^3 \log ^2\left (c \left (d+e x^2\right )^p\right )-(4 e f p) \int \frac{x^2 \log \left (c \left (d+e x^2\right )^p\right )}{d+e x^2} \, dx-\frac{1}{3} (4 e g p) \int \frac{x^4 \log \left (c \left (d+e x^2\right )^p\right )}{d+e x^2} \, dx\\ &=f x \log ^2\left (c \left (d+e x^2\right )^p\right )+\frac{1}{3} g x^3 \log ^2\left (c \left (d+e x^2\right )^p\right )-(4 e f p) \int \left (\frac{\log \left (c \left (d+e x^2\right )^p\right )}{e}-\frac{d \log \left (c \left (d+e x^2\right )^p\right )}{e \left (d+e x^2\right )}\right ) \, dx-\frac{1}{3} (4 e g p) \int \left (-\frac{d \log \left (c \left (d+e x^2\right )^p\right )}{e^2}+\frac{x^2 \log \left (c \left (d+e x^2\right )^p\right )}{e}+\frac{d^2 \log \left (c \left (d+e x^2\right )^p\right )}{e^2 \left (d+e x^2\right )}\right ) \, dx\\ &=f x \log ^2\left (c \left (d+e x^2\right )^p\right )+\frac{1}{3} g x^3 \log ^2\left (c \left (d+e x^2\right )^p\right )-(4 f p) \int \log \left (c \left (d+e x^2\right )^p\right ) \, dx+(4 d f p) \int \frac{\log \left (c \left (d+e x^2\right )^p\right )}{d+e x^2} \, dx-\frac{1}{3} (4 g p) \int x^2 \log \left (c \left (d+e x^2\right )^p\right ) \, dx+\frac{(4 d g p) \int \log \left (c \left (d+e x^2\right )^p\right ) \, dx}{3 e}-\frac{\left (4 d^2 g p\right ) \int \frac{\log \left (c \left (d+e x^2\right )^p\right )}{d+e x^2} \, dx}{3 e}\\ &=-4 f p x \log \left (c \left (d+e x^2\right )^p\right )+\frac{4 d g p x \log \left (c \left (d+e x^2\right )^p\right )}{3 e}-\frac{4}{9} g p x^3 \log \left (c \left (d+e x^2\right )^p\right )+\frac{4 \sqrt{d} f p \tan ^{-1}\left (\frac{\sqrt{e} x}{\sqrt{d}}\right ) \log \left (c \left (d+e x^2\right )^p\right )}{\sqrt{e}}-\frac{4 d^{3/2} g p \tan ^{-1}\left (\frac{\sqrt{e} x}{\sqrt{d}}\right ) \log \left (c \left (d+e x^2\right )^p\right )}{3 e^{3/2}}+f x \log ^2\left (c \left (d+e x^2\right )^p\right )+\frac{1}{3} g x^3 \log ^2\left (c \left (d+e x^2\right )^p\right )+\left (8 e f p^2\right ) \int \frac{x^2}{d+e x^2} \, dx-\left (8 d e f p^2\right ) \int \frac{x \tan ^{-1}\left (\frac{\sqrt{e} x}{\sqrt{d}}\right )}{\sqrt{d} \sqrt{e} \left (d+e x^2\right )} \, dx-\frac{1}{3} \left (8 d g p^2\right ) \int \frac{x^2}{d+e x^2} \, dx+\frac{1}{3} \left (8 d^2 g p^2\right ) \int \frac{x \tan ^{-1}\left (\frac{\sqrt{e} x}{\sqrt{d}}\right )}{\sqrt{d} \sqrt{e} \left (d+e x^2\right )} \, dx+\frac{1}{9} \left (8 e g p^2\right ) \int \frac{x^4}{d+e x^2} \, dx\\ &=8 f p^2 x-\frac{8 d g p^2 x}{3 e}-4 f p x \log \left (c \left (d+e x^2\right )^p\right )+\frac{4 d g p x \log \left (c \left (d+e x^2\right )^p\right )}{3 e}-\frac{4}{9} g p x^3 \log \left (c \left (d+e x^2\right )^p\right )+\frac{4 \sqrt{d} f p \tan ^{-1}\left (\frac{\sqrt{e} x}{\sqrt{d}}\right ) \log \left (c \left (d+e x^2\right )^p\right )}{\sqrt{e}}-\frac{4 d^{3/2} g p \tan ^{-1}\left (\frac{\sqrt{e} x}{\sqrt{d}}\right ) \log \left (c \left (d+e x^2\right )^p\right )}{3 e^{3/2}}+f x \log ^2\left (c \left (d+e x^2\right )^p\right )+\frac{1}{3} g x^3 \log ^2\left (c \left (d+e x^2\right )^p\right )-\left (8 d f p^2\right ) \int \frac{1}{d+e x^2} \, dx-\left (8 \sqrt{d} \sqrt{e} f p^2\right ) \int \frac{x \tan ^{-1}\left (\frac{\sqrt{e} x}{\sqrt{d}}\right )}{d+e x^2} \, dx+\frac{\left (8 d^2 g p^2\right ) \int \frac{1}{d+e x^2} \, dx}{3 e}+\frac{\left (8 d^{3/2} g p^2\right ) \int \frac{x \tan ^{-1}\left (\frac{\sqrt{e} x}{\sqrt{d}}\right )}{d+e x^2} \, dx}{3 \sqrt{e}}+\frac{1}{9} \left (8 e g p^2\right ) \int \left (-\frac{d}{e^2}+\frac{x^2}{e}+\frac{d^2}{e^2 \left (d+e x^2\right )}\right ) \, dx\\ &=8 f p^2 x-\frac{32 d g p^2 x}{9 e}+\frac{8}{27} g p^2 x^3-\frac{8 \sqrt{d} f p^2 \tan ^{-1}\left (\frac{\sqrt{e} x}{\sqrt{d}}\right )}{\sqrt{e}}+\frac{8 d^{3/2} g p^2 \tan ^{-1}\left (\frac{\sqrt{e} x}{\sqrt{d}}\right )}{3 e^{3/2}}+\frac{4 i \sqrt{d} f p^2 \tan ^{-1}\left (\frac{\sqrt{e} x}{\sqrt{d}}\right )^2}{\sqrt{e}}-\frac{4 i d^{3/2} g p^2 \tan ^{-1}\left (\frac{\sqrt{e} x}{\sqrt{d}}\right )^2}{3 e^{3/2}}-4 f p x \log \left (c \left (d+e x^2\right )^p\right )+\frac{4 d g p x \log \left (c \left (d+e x^2\right )^p\right )}{3 e}-\frac{4}{9} g p x^3 \log \left (c \left (d+e x^2\right )^p\right )+\frac{4 \sqrt{d} f p \tan ^{-1}\left (\frac{\sqrt{e} x}{\sqrt{d}}\right ) \log \left (c \left (d+e x^2\right )^p\right )}{\sqrt{e}}-\frac{4 d^{3/2} g p \tan ^{-1}\left (\frac{\sqrt{e} x}{\sqrt{d}}\right ) \log \left (c \left (d+e x^2\right )^p\right )}{3 e^{3/2}}+f x \log ^2\left (c \left (d+e x^2\right )^p\right )+\frac{1}{3} g x^3 \log ^2\left (c \left (d+e x^2\right )^p\right )+\left (8 f p^2\right ) \int \frac{\tan ^{-1}\left (\frac{\sqrt{e} x}{\sqrt{d}}\right )}{i-\frac{\sqrt{e} x}{\sqrt{d}}} \, dx-\frac{\left (8 d g p^2\right ) \int \frac{\tan ^{-1}\left (\frac{\sqrt{e} x}{\sqrt{d}}\right )}{i-\frac{\sqrt{e} x}{\sqrt{d}}} \, dx}{3 e}+\frac{\left (8 d^2 g p^2\right ) \int \frac{1}{d+e x^2} \, dx}{9 e}\\ &=8 f p^2 x-\frac{32 d g p^2 x}{9 e}+\frac{8}{27} g p^2 x^3-\frac{8 \sqrt{d} f p^2 \tan ^{-1}\left (\frac{\sqrt{e} x}{\sqrt{d}}\right )}{\sqrt{e}}+\frac{32 d^{3/2} g p^2 \tan ^{-1}\left (\frac{\sqrt{e} x}{\sqrt{d}}\right )}{9 e^{3/2}}+\frac{4 i \sqrt{d} f p^2 \tan ^{-1}\left (\frac{\sqrt{e} x}{\sqrt{d}}\right )^2}{\sqrt{e}}-\frac{4 i d^{3/2} g p^2 \tan ^{-1}\left (\frac{\sqrt{e} x}{\sqrt{d}}\right )^2}{3 e^{3/2}}+\frac{8 \sqrt{d} f p^2 \tan ^{-1}\left (\frac{\sqrt{e} x}{\sqrt{d}}\right ) \log \left (\frac{2 \sqrt{d}}{\sqrt{d}+i \sqrt{e} x}\right )}{\sqrt{e}}-\frac{8 d^{3/2} g p^2 \tan ^{-1}\left (\frac{\sqrt{e} x}{\sqrt{d}}\right ) \log \left (\frac{2 \sqrt{d}}{\sqrt{d}+i \sqrt{e} x}\right )}{3 e^{3/2}}-4 f p x \log \left (c \left (d+e x^2\right )^p\right )+\frac{4 d g p x \log \left (c \left (d+e x^2\right )^p\right )}{3 e}-\frac{4}{9} g p x^3 \log \left (c \left (d+e x^2\right )^p\right )+\frac{4 \sqrt{d} f p \tan ^{-1}\left (\frac{\sqrt{e} x}{\sqrt{d}}\right ) \log \left (c \left (d+e x^2\right )^p\right )}{\sqrt{e}}-\frac{4 d^{3/2} g p \tan ^{-1}\left (\frac{\sqrt{e} x}{\sqrt{d}}\right ) \log \left (c \left (d+e x^2\right )^p\right )}{3 e^{3/2}}+f x \log ^2\left (c \left (d+e x^2\right )^p\right )+\frac{1}{3} g x^3 \log ^2\left (c \left (d+e x^2\right )^p\right )-\left (8 f p^2\right ) \int \frac{\log \left (\frac{2}{1+\frac{i \sqrt{e} x}{\sqrt{d}}}\right )}{1+\frac{e x^2}{d}} \, dx+\frac{\left (8 d g p^2\right ) \int \frac{\log \left (\frac{2}{1+\frac{i \sqrt{e} x}{\sqrt{d}}}\right )}{1+\frac{e x^2}{d}} \, dx}{3 e}\\ &=8 f p^2 x-\frac{32 d g p^2 x}{9 e}+\frac{8}{27} g p^2 x^3-\frac{8 \sqrt{d} f p^2 \tan ^{-1}\left (\frac{\sqrt{e} x}{\sqrt{d}}\right )}{\sqrt{e}}+\frac{32 d^{3/2} g p^2 \tan ^{-1}\left (\frac{\sqrt{e} x}{\sqrt{d}}\right )}{9 e^{3/2}}+\frac{4 i \sqrt{d} f p^2 \tan ^{-1}\left (\frac{\sqrt{e} x}{\sqrt{d}}\right )^2}{\sqrt{e}}-\frac{4 i d^{3/2} g p^2 \tan ^{-1}\left (\frac{\sqrt{e} x}{\sqrt{d}}\right )^2}{3 e^{3/2}}+\frac{8 \sqrt{d} f p^2 \tan ^{-1}\left (\frac{\sqrt{e} x}{\sqrt{d}}\right ) \log \left (\frac{2 \sqrt{d}}{\sqrt{d}+i \sqrt{e} x}\right )}{\sqrt{e}}-\frac{8 d^{3/2} g p^2 \tan ^{-1}\left (\frac{\sqrt{e} x}{\sqrt{d}}\right ) \log \left (\frac{2 \sqrt{d}}{\sqrt{d}+i \sqrt{e} x}\right )}{3 e^{3/2}}-4 f p x \log \left (c \left (d+e x^2\right )^p\right )+\frac{4 d g p x \log \left (c \left (d+e x^2\right )^p\right )}{3 e}-\frac{4}{9} g p x^3 \log \left (c \left (d+e x^2\right )^p\right )+\frac{4 \sqrt{d} f p \tan ^{-1}\left (\frac{\sqrt{e} x}{\sqrt{d}}\right ) \log \left (c \left (d+e x^2\right )^p\right )}{\sqrt{e}}-\frac{4 d^{3/2} g p \tan ^{-1}\left (\frac{\sqrt{e} x}{\sqrt{d}}\right ) \log \left (c \left (d+e x^2\right )^p\right )}{3 e^{3/2}}+f x \log ^2\left (c \left (d+e x^2\right )^p\right )+\frac{1}{3} g x^3 \log ^2\left (c \left (d+e x^2\right )^p\right )+\frac{\left (8 i \sqrt{d} f p^2\right ) \operatorname{Subst}\left (\int \frac{\log (2 x)}{1-2 x} \, dx,x,\frac{1}{1+\frac{i \sqrt{e} x}{\sqrt{d}}}\right )}{\sqrt{e}}-\frac{\left (8 i d^{3/2} g p^2\right ) \operatorname{Subst}\left (\int \frac{\log (2 x)}{1-2 x} \, dx,x,\frac{1}{1+\frac{i \sqrt{e} x}{\sqrt{d}}}\right )}{3 e^{3/2}}\\ &=8 f p^2 x-\frac{32 d g p^2 x}{9 e}+\frac{8}{27} g p^2 x^3-\frac{8 \sqrt{d} f p^2 \tan ^{-1}\left (\frac{\sqrt{e} x}{\sqrt{d}}\right )}{\sqrt{e}}+\frac{32 d^{3/2} g p^2 \tan ^{-1}\left (\frac{\sqrt{e} x}{\sqrt{d}}\right )}{9 e^{3/2}}+\frac{4 i \sqrt{d} f p^2 \tan ^{-1}\left (\frac{\sqrt{e} x}{\sqrt{d}}\right )^2}{\sqrt{e}}-\frac{4 i d^{3/2} g p^2 \tan ^{-1}\left (\frac{\sqrt{e} x}{\sqrt{d}}\right )^2}{3 e^{3/2}}+\frac{8 \sqrt{d} f p^2 \tan ^{-1}\left (\frac{\sqrt{e} x}{\sqrt{d}}\right ) \log \left (\frac{2 \sqrt{d}}{\sqrt{d}+i \sqrt{e} x}\right )}{\sqrt{e}}-\frac{8 d^{3/2} g p^2 \tan ^{-1}\left (\frac{\sqrt{e} x}{\sqrt{d}}\right ) \log \left (\frac{2 \sqrt{d}}{\sqrt{d}+i \sqrt{e} x}\right )}{3 e^{3/2}}-4 f p x \log \left (c \left (d+e x^2\right )^p\right )+\frac{4 d g p x \log \left (c \left (d+e x^2\right )^p\right )}{3 e}-\frac{4}{9} g p x^3 \log \left (c \left (d+e x^2\right )^p\right )+\frac{4 \sqrt{d} f p \tan ^{-1}\left (\frac{\sqrt{e} x}{\sqrt{d}}\right ) \log \left (c \left (d+e x^2\right )^p\right )}{\sqrt{e}}-\frac{4 d^{3/2} g p \tan ^{-1}\left (\frac{\sqrt{e} x}{\sqrt{d}}\right ) \log \left (c \left (d+e x^2\right )^p\right )}{3 e^{3/2}}+f x \log ^2\left (c \left (d+e x^2\right )^p\right )+\frac{1}{3} g x^3 \log ^2\left (c \left (d+e x^2\right )^p\right )+\frac{4 i \sqrt{d} f p^2 \text{Li}_2\left (1-\frac{2 \sqrt{d}}{\sqrt{d}+i \sqrt{e} x}\right )}{\sqrt{e}}-\frac{4 i d^{3/2} g p^2 \text{Li}_2\left (1-\frac{2 \sqrt{d}}{\sqrt{d}+i \sqrt{e} x}\right )}{3 e^{3/2}}\\ \end{align*}
Mathematica [A] time = 0.264454, size = 281, normalized size = 0.51 \[ \frac{-36 i \sqrt{d} p^2 (d g-3 e f) \text{PolyLog}\left (2,\frac{\sqrt{e} x+i \sqrt{d}}{\sqrt{e} x-i \sqrt{d}}\right )+\sqrt{e} x \left (9 e \left (3 f+g x^2\right ) \log ^2\left (c \left (d+e x^2\right )^p\right )-12 p \left (-3 d g+9 e f+e g x^2\right ) \log \left (c \left (d+e x^2\right )^p\right )+8 p^2 \left (-12 d g+27 e f+e g x^2\right )\right )-12 \sqrt{d} p \tan ^{-1}\left (\frac{\sqrt{e} x}{\sqrt{d}}\right ) \left ((3 d g-9 e f) \log \left (c \left (d+e x^2\right )^p\right )+6 p (d g-3 e f) \log \left (\frac{2 \sqrt{d}}{\sqrt{d}+i \sqrt{e} x}\right )+2 p (9 e f-4 d g)\right )-36 i \sqrt{d} p^2 (d g-3 e f) \tan ^{-1}\left (\frac{\sqrt{e} x}{\sqrt{d}}\right )^2}{27 e^{3/2}} \]
Antiderivative was successfully verified.
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Maple [F] time = 1.481, size = 0, normalized size = 0. \begin{align*} \int \left ( g{x}^{2}+f \right ) \left ( \ln \left ( c \left ( e{x}^{2}+d \right ) ^{p} \right ) \right ) ^{2}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F(-2)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: ValueError} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [F] time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left ({\left (g x^{2} + f\right )} \log \left ({\left (e x^{2} + d\right )}^{p} c\right )^{2}, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \left (f + g x^{2}\right ) \log{\left (c \left (d + e x^{2}\right )^{p} \right )}^{2}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int{\left (g x^{2} + f\right )} \log \left ({\left (e x^{2} + d\right )}^{p} c\right )^{2}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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