Optimal. Leaf size=32 \[ \frac {1}{4} x \left (1+x+x \log ^2\left (e^{\frac {1}{25} e^{10-2 x}-x} x\right )\right ) \]
[Out]
________________________________________________________________________________________
Rubi [F]
time = 0.56, 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 {1}{100} \left (25+50 x+\left (50 x-50 x^2-4 e^{10-2 x} x^2\right ) \log \left (e^{\frac {1}{25} \left (e^{10-2 x}-25 x\right )} x\right )+50 x \log ^2\left (e^{\frac {1}{25} \left (e^{10-2 x}-25 x\right )} x\right )\right ) \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{100} \int \left (25+50 x+\left (50 x-50 x^2-4 e^{10-2 x} x^2\right ) \log \left (e^{\frac {1}{25} \left (e^{10-2 x}-25 x\right )} x\right )+50 x \log ^2\left (e^{\frac {1}{25} \left (e^{10-2 x}-25 x\right )} x\right )\right ) \, dx\\ &=\frac {x}{4}+\frac {x^2}{4}+\frac {1}{100} \int \left (50 x-50 x^2-4 e^{10-2 x} x^2\right ) \log \left (e^{\frac {1}{25} \left (e^{10-2 x}-25 x\right )} x\right ) \, dx+\frac {1}{2} \int x \log ^2\left (e^{\frac {1}{25} \left (e^{10-2 x}-25 x\right )} x\right ) \, dx\\ &=\frac {x}{4}+\frac {x^2}{4}+\frac {1}{100} e^{10-2 x} \log \left (e^{\frac {1}{25} \left (e^{10-2 x}-25 x\right )} x\right )+\frac {1}{50} e^{10-2 x} x \log \left (e^{\frac {1}{25} \left (e^{10-2 x}-25 x\right )} x\right )+\frac {1}{4} x^2 \log \left (e^{\frac {1}{25} \left (e^{10-2 x}-25 x\right )} x\right )+\frac {1}{50} e^{10-2 x} x^2 \log \left (e^{\frac {1}{25} \left (e^{10-2 x}-25 x\right )} x\right )-\frac {1}{6} x^3 \log \left (e^{\frac {1}{25} \left (e^{10-2 x}-25 x\right )} x\right )-\frac {1}{100} \int \frac {e^{-4 x} \left (25 e^{2 x} (-1+x)+2 e^{10} x\right ) \left (25 e^{2 x} x^2 (-3+2 x)-3 e^{10} \left (1+2 x+2 x^2\right )\right )}{75 x} \, dx+\frac {1}{2} \int x \log ^2\left (e^{\frac {1}{25} \left (e^{10-2 x}-25 x\right )} x\right ) \, dx\\ &=\frac {x}{4}+\frac {x^2}{4}+\frac {1}{100} e^{10-2 x} \log \left (e^{\frac {1}{25} \left (e^{10-2 x}-25 x\right )} x\right )+\frac {1}{50} e^{10-2 x} x \log \left (e^{\frac {1}{25} \left (e^{10-2 x}-25 x\right )} x\right )+\frac {1}{4} x^2 \log \left (e^{\frac {1}{25} \left (e^{10-2 x}-25 x\right )} x\right )+\frac {1}{50} e^{10-2 x} x^2 \log \left (e^{\frac {1}{25} \left (e^{10-2 x}-25 x\right )} x\right )-\frac {1}{6} x^3 \log \left (e^{\frac {1}{25} \left (e^{10-2 x}-25 x\right )} x\right )-\frac {\int \frac {e^{-4 x} \left (25 e^{2 x} (-1+x)+2 e^{10} x\right ) \left (25 e^{2 x} x^2 (-3+2 x)-3 e^{10} \left (1+2 x+2 x^2\right )\right )}{x} \, dx}{7500}+\frac {1}{2} \int x \log ^2\left (e^{\frac {1}{25} \left (e^{10-2 x}-25 x\right )} x\right ) \, dx\\ &=\frac {x}{4}+\frac {x^2}{4}+\frac {1}{100} e^{10-2 x} \log \left (e^{\frac {1}{25} \left (e^{10-2 x}-25 x\right )} x\right )+\frac {1}{50} e^{10-2 x} x \log \left (e^{\frac {1}{25} \left (e^{10-2 x}-25 x\right )} x\right )+\frac {1}{4} x^2 \log \left (e^{\frac {1}{25} \left (e^{10-2 x}-25 x\right )} x\right )+\frac {1}{50} e^{10-2 x} x^2 \log \left (e^{\frac {1}{25} \left (e^{10-2 x}-25 x\right )} x\right )-\frac {1}{6} x^3 \log \left (e^{\frac {1}{25} \left (e^{10-2 x}-25 x\right )} x\right )-\frac {\int \left (625 (-1+x) x (-3+2 x)-6 e^{20-4 x} \left (1+2 x+2 x^2\right )+\frac {25 e^{10-2 x} \left (3+3 x-12 x^3+4 x^4\right )}{x}\right ) \, dx}{7500}+\frac {1}{2} \int x \log ^2\left (e^{\frac {1}{25} \left (e^{10-2 x}-25 x\right )} x\right ) \, dx\\ &=\frac {x}{4}+\frac {x^2}{4}+\frac {1}{100} e^{10-2 x} \log \left (e^{\frac {1}{25} \left (e^{10-2 x}-25 x\right )} x\right )+\frac {1}{50} e^{10-2 x} x \log \left (e^{\frac {1}{25} \left (e^{10-2 x}-25 x\right )} x\right )+\frac {1}{4} x^2 \log \left (e^{\frac {1}{25} \left (e^{10-2 x}-25 x\right )} x\right )+\frac {1}{50} e^{10-2 x} x^2 \log \left (e^{\frac {1}{25} \left (e^{10-2 x}-25 x\right )} x\right )-\frac {1}{6} x^3 \log \left (e^{\frac {1}{25} \left (e^{10-2 x}-25 x\right )} x\right )+\frac {\int e^{20-4 x} \left (1+2 x+2 x^2\right ) \, dx}{1250}-\frac {1}{300} \int \frac {e^{10-2 x} \left (3+3 x-12 x^3+4 x^4\right )}{x} \, dx-\frac {1}{12} \int (-1+x) x (-3+2 x) \, dx+\frac {1}{2} \int x \log ^2\left (e^{\frac {1}{25} \left (e^{10-2 x}-25 x\right )} x\right ) \, dx\\ &=\frac {x}{4}+\frac {x^2}{4}+\frac {1}{100} e^{10-2 x} \log \left (e^{\frac {1}{25} \left (e^{10-2 x}-25 x\right )} x\right )+\frac {1}{50} e^{10-2 x} x \log \left (e^{\frac {1}{25} \left (e^{10-2 x}-25 x\right )} x\right )+\frac {1}{4} x^2 \log \left (e^{\frac {1}{25} \left (e^{10-2 x}-25 x\right )} x\right )+\frac {1}{50} e^{10-2 x} x^2 \log \left (e^{\frac {1}{25} \left (e^{10-2 x}-25 x\right )} x\right )-\frac {1}{6} x^3 \log \left (e^{\frac {1}{25} \left (e^{10-2 x}-25 x\right )} x\right )+\frac {\int \left (e^{20-4 x}+2 e^{20-4 x} x+2 e^{20-4 x} x^2\right ) \, dx}{1250}-\frac {1}{300} \int \left (3 e^{10-2 x}+\frac {3 e^{10-2 x}}{x}-12 e^{10-2 x} x^2+4 e^{10-2 x} x^3\right ) \, dx-\frac {1}{12} \int \left (3 x-5 x^2+2 x^3\right ) \, dx+\frac {1}{2} \int x \log ^2\left (e^{\frac {1}{25} \left (e^{10-2 x}-25 x\right )} x\right ) \, dx\\ &=\frac {x}{4}+\frac {x^2}{8}+\frac {5 x^3}{36}-\frac {x^4}{24}+\frac {1}{100} e^{10-2 x} \log \left (e^{\frac {1}{25} \left (e^{10-2 x}-25 x\right )} x\right )+\frac {1}{50} e^{10-2 x} x \log \left (e^{\frac {1}{25} \left (e^{10-2 x}-25 x\right )} x\right )+\frac {1}{4} x^2 \log \left (e^{\frac {1}{25} \left (e^{10-2 x}-25 x\right )} x\right )+\frac {1}{50} e^{10-2 x} x^2 \log \left (e^{\frac {1}{25} \left (e^{10-2 x}-25 x\right )} x\right )-\frac {1}{6} x^3 \log \left (e^{\frac {1}{25} \left (e^{10-2 x}-25 x\right )} x\right )+\frac {\int e^{20-4 x} \, dx}{1250}+\frac {1}{625} \int e^{20-4 x} x \, dx+\frac {1}{625} \int e^{20-4 x} x^2 \, dx-\frac {1}{100} \int e^{10-2 x} \, dx-\frac {1}{100} \int \frac {e^{10-2 x}}{x} \, dx-\frac {1}{75} \int e^{10-2 x} x^3 \, dx+\frac {1}{25} \int e^{10-2 x} x^2 \, dx+\frac {1}{2} \int x \log ^2\left (e^{\frac {1}{25} \left (e^{10-2 x}-25 x\right )} x\right ) \, dx\\ &=-\frac {e^{20-4 x}}{5000}+\frac {1}{200} e^{10-2 x}+\frac {x}{4}-\frac {e^{20-4 x} x}{2500}+\frac {x^2}{8}-\frac {e^{20-4 x} x^2}{2500}-\frac {1}{50} e^{10-2 x} x^2+\frac {5 x^3}{36}+\frac {1}{150} e^{10-2 x} x^3-\frac {x^4}{24}-\frac {1}{100} e^{10} \text {Ei}(-2 x)+\frac {1}{100} e^{10-2 x} \log \left (e^{\frac {1}{25} \left (e^{10-2 x}-25 x\right )} x\right )+\frac {1}{50} e^{10-2 x} x \log \left (e^{\frac {1}{25} \left (e^{10-2 x}-25 x\right )} x\right )+\frac {1}{4} x^2 \log \left (e^{\frac {1}{25} \left (e^{10-2 x}-25 x\right )} x\right )+\frac {1}{50} e^{10-2 x} x^2 \log \left (e^{\frac {1}{25} \left (e^{10-2 x}-25 x\right )} x\right )-\frac {1}{6} x^3 \log \left (e^{\frac {1}{25} \left (e^{10-2 x}-25 x\right )} x\right )+\frac {\int e^{20-4 x} \, dx}{2500}+\frac {\int e^{20-4 x} x \, dx}{1250}-\frac {1}{50} \int e^{10-2 x} x^2 \, dx+\frac {1}{25} \int e^{10-2 x} x \, dx+\frac {1}{2} \int x \log ^2\left (e^{\frac {1}{25} \left (e^{10-2 x}-25 x\right )} x\right ) \, dx\\ &=-\frac {3 e^{20-4 x}}{10000}+\frac {1}{200} e^{10-2 x}+\frac {x}{4}-\frac {3 e^{20-4 x} x}{5000}-\frac {1}{50} e^{10-2 x} x+\frac {x^2}{8}-\frac {e^{20-4 x} x^2}{2500}-\frac {1}{100} e^{10-2 x} x^2+\frac {5 x^3}{36}+\frac {1}{150} e^{10-2 x} x^3-\frac {x^4}{24}-\frac {1}{100} e^{10} \text {Ei}(-2 x)+\frac {1}{100} e^{10-2 x} \log \left (e^{\frac {1}{25} \left (e^{10-2 x}-25 x\right )} x\right )+\frac {1}{50} e^{10-2 x} x \log \left (e^{\frac {1}{25} \left (e^{10-2 x}-25 x\right )} x\right )+\frac {1}{4} x^2 \log \left (e^{\frac {1}{25} \left (e^{10-2 x}-25 x\right )} x\right )+\frac {1}{50} e^{10-2 x} x^2 \log \left (e^{\frac {1}{25} \left (e^{10-2 x}-25 x\right )} x\right )-\frac {1}{6} x^3 \log \left (e^{\frac {1}{25} \left (e^{10-2 x}-25 x\right )} x\right )+\frac {\int e^{20-4 x} \, dx}{5000}+\frac {1}{50} \int e^{10-2 x} \, dx-\frac {1}{50} \int e^{10-2 x} x \, dx+\frac {1}{2} \int x \log ^2\left (e^{\frac {1}{25} \left (e^{10-2 x}-25 x\right )} x\right ) \, dx\\ &=-\frac {7 e^{20-4 x}}{20000}-\frac {1}{200} e^{10-2 x}+\frac {x}{4}-\frac {3 e^{20-4 x} x}{5000}-\frac {1}{100} e^{10-2 x} x+\frac {x^2}{8}-\frac {e^{20-4 x} x^2}{2500}-\frac {1}{100} e^{10-2 x} x^2+\frac {5 x^3}{36}+\frac {1}{150} e^{10-2 x} x^3-\frac {x^4}{24}-\frac {1}{100} e^{10} \text {Ei}(-2 x)+\frac {1}{100} e^{10-2 x} \log \left (e^{\frac {1}{25} \left (e^{10-2 x}-25 x\right )} x\right )+\frac {1}{50} e^{10-2 x} x \log \left (e^{\frac {1}{25} \left (e^{10-2 x}-25 x\right )} x\right )+\frac {1}{4} x^2 \log \left (e^{\frac {1}{25} \left (e^{10-2 x}-25 x\right )} x\right )+\frac {1}{50} e^{10-2 x} x^2 \log \left (e^{\frac {1}{25} \left (e^{10-2 x}-25 x\right )} x\right )-\frac {1}{6} x^3 \log \left (e^{\frac {1}{25} \left (e^{10-2 x}-25 x\right )} x\right )-\frac {1}{100} \int e^{10-2 x} \, dx+\frac {1}{2} \int x \log ^2\left (e^{\frac {1}{25} \left (e^{10-2 x}-25 x\right )} x\right ) \, dx\\ &=-\frac {7 e^{20-4 x}}{20000}+\frac {x}{4}-\frac {3 e^{20-4 x} x}{5000}-\frac {1}{100} e^{10-2 x} x+\frac {x^2}{8}-\frac {e^{20-4 x} x^2}{2500}-\frac {1}{100} e^{10-2 x} x^2+\frac {5 x^3}{36}+\frac {1}{150} e^{10-2 x} x^3-\frac {x^4}{24}-\frac {1}{100} e^{10} \text {Ei}(-2 x)+\frac {1}{100} e^{10-2 x} \log \left (e^{\frac {1}{25} \left (e^{10-2 x}-25 x\right )} x\right )+\frac {1}{50} e^{10-2 x} x \log \left (e^{\frac {1}{25} \left (e^{10-2 x}-25 x\right )} x\right )+\frac {1}{4} x^2 \log \left (e^{\frac {1}{25} \left (e^{10-2 x}-25 x\right )} x\right )+\frac {1}{50} e^{10-2 x} x^2 \log \left (e^{\frac {1}{25} \left (e^{10-2 x}-25 x\right )} x\right )-\frac {1}{6} x^3 \log \left (e^{\frac {1}{25} \left (e^{10-2 x}-25 x\right )} x\right )+\frac {1}{2} \int x \log ^2\left (e^{\frac {1}{25} \left (e^{10-2 x}-25 x\right )} x\right ) \, dx\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 0.20, size = 32, normalized size = 1.00 \begin {gather*} \frac {1}{4} x \left (1+x+x \log ^2\left (e^{\frac {1}{25} e^{10-2 x}-x} x\right )\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [C] Result contains higher order function than in optimal. Order 9 vs. order
3.
time = 27.90, size = 768, normalized size = 24.00
method | result | size |
risch | \(\frac {x^{2}}{4}+\frac {x}{4}+\frac {x^{2} \ln \left ({\mathrm e}^{\frac {{\mathrm e}^{-2 x +10}}{25}-x}\right )^{2}}{4}+\frac {\left (50 x^{2} \ln \left (x \right )-25 i \pi \,x^{2} \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i {\mathrm e}^{\frac {{\mathrm e}^{-2 x +10}}{25}-x}\right ) \mathrm {csgn}\left (i x \,{\mathrm e}^{\frac {{\mathrm e}^{-2 x +10}}{25}-x}\right )+25 i \pi \,x^{2} \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x \,{\mathrm e}^{\frac {{\mathrm e}^{-2 x +10}}{25}-x}\right )^{2}+25 i \pi \,x^{2} \mathrm {csgn}\left (i {\mathrm e}^{\frac {{\mathrm e}^{-2 x +10}}{25}-x}\right ) \mathrm {csgn}\left (i x \,{\mathrm e}^{\frac {{\mathrm e}^{-2 x +10}}{25}-x}\right )^{2}-25 i \pi \,x^{2} \mathrm {csgn}\left (i x \,{\mathrm e}^{\frac {{\mathrm e}^{-2 x +10}}{25}-x}\right )^{3}\right ) \ln \left ({\mathrm e}^{\frac {{\mathrm e}^{-2 x +10}}{25}-x}\right )}{100}+\frac {x^{2} \ln \left (x \right )^{2}}{4}-\frac {i \pi \,x^{2} \mathrm {csgn}\left (i x \,{\mathrm e}^{\frac {{\mathrm e}^{-2 x +10}}{25}-x}\right )^{3} \ln \left (x \right )}{4}+\frac {i \pi \,x^{2} \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x \,{\mathrm e}^{\frac {{\mathrm e}^{-2 x +10}}{25}-x}\right )^{2} \ln \left (x \right )}{4}+\frac {i \pi \,x^{2} \mathrm {csgn}\left (i {\mathrm e}^{\frac {{\mathrm e}^{-2 x +10}}{25}-x}\right ) \mathrm {csgn}\left (i x \,{\mathrm e}^{\frac {{\mathrm e}^{-2 x +10}}{25}-x}\right )^{2} \ln \left (x \right )}{4}-\frac {i \pi \,x^{2} \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i {\mathrm e}^{\frac {{\mathrm e}^{-2 x +10}}{25}-x}\right ) \mathrm {csgn}\left (i x \,{\mathrm e}^{\frac {{\mathrm e}^{-2 x +10}}{25}-x}\right ) \ln \left (x \right )}{4}-\frac {\pi ^{2} x^{2} \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i {\mathrm e}^{\frac {{\mathrm e}^{-2 x +10}}{25}-x}\right )^{2} \mathrm {csgn}\left (i x \,{\mathrm e}^{\frac {{\mathrm e}^{-2 x +10}}{25}-x}\right )^{2}}{16}+\frac {\pi ^{2} x^{2} \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i {\mathrm e}^{\frac {{\mathrm e}^{-2 x +10}}{25}-x}\right ) \mathrm {csgn}\left (i x \,{\mathrm e}^{\frac {{\mathrm e}^{-2 x +10}}{25}-x}\right )^{3}}{8}-\frac {\pi ^{2} x^{2} \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x \,{\mathrm e}^{\frac {{\mathrm e}^{-2 x +10}}{25}-x}\right )^{4}}{16}+\frac {\pi ^{2} x^{2} \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i {\mathrm e}^{\frac {{\mathrm e}^{-2 x +10}}{25}-x}\right )^{2} \mathrm {csgn}\left (i x \,{\mathrm e}^{\frac {{\mathrm e}^{-2 x +10}}{25}-x}\right )^{3}}{8}-\frac {\pi ^{2} x^{2} \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i {\mathrm e}^{\frac {{\mathrm e}^{-2 x +10}}{25}-x}\right ) \mathrm {csgn}\left (i x \,{\mathrm e}^{\frac {{\mathrm e}^{-2 x +10}}{25}-x}\right )^{4}}{4}+\frac {\pi ^{2} x^{2} \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x \,{\mathrm e}^{\frac {{\mathrm e}^{-2 x +10}}{25}-x}\right )^{5}}{8}-\frac {\pi ^{2} x^{2} \mathrm {csgn}\left (i {\mathrm e}^{\frac {{\mathrm e}^{-2 x +10}}{25}-x}\right )^{2} \mathrm {csgn}\left (i x \,{\mathrm e}^{\frac {{\mathrm e}^{-2 x +10}}{25}-x}\right )^{4}}{16}+\frac {\pi ^{2} x^{2} \mathrm {csgn}\left (i {\mathrm e}^{\frac {{\mathrm e}^{-2 x +10}}{25}-x}\right ) \mathrm {csgn}\left (i x \,{\mathrm e}^{\frac {{\mathrm e}^{-2 x +10}}{25}-x}\right )^{5}}{8}-\frac {\pi ^{2} x^{2} \mathrm {csgn}\left (i x \,{\mathrm e}^{\frac {{\mathrm e}^{-2 x +10}}{25}-x}\right )^{6}}{16}\) | \(768\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 63 vs.
\(2 (26) = 52\).
time = 0.68, size = 63, normalized size = 1.97 \begin {gather*} \frac {1}{4} \, x^{4} - \frac {1}{2} \, x^{3} \log \left (x\right ) + \frac {1}{4} \, x^{2} \log \left (x\right )^{2} + \frac {1}{2500} \, x^{2} e^{\left (-4 \, x + 20\right )} + \frac {1}{4} \, x^{2} - \frac {1}{50} \, {\left (x^{3} e^{10} - x^{2} e^{10} \log \left (x\right )\right )} e^{\left (-2 \, x\right )} + \frac {1}{4} \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.36, size = 32, normalized size = 1.00 \begin {gather*} \frac {1}{4} \, x^{2} \log \left (x e^{\left (-x + \frac {1}{25} \, e^{\left (-2 \, x + 10\right )}\right )}\right )^{2} + \frac {1}{4} \, x^{2} + \frac {1}{4} \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.24, size = 29, normalized size = 0.91 \begin {gather*} \frac {x^{2} \log {\left (x e^{- x + \frac {e^{10 - 2 x}}{25}} \right )}^{2}}{4} + \frac {x^{2}}{4} + \frac {x}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 65 vs.
\(2 (26) = 52\).
time = 0.40, size = 65, normalized size = 2.03 \begin {gather*} \frac {1}{4} \, x^{4} - \frac {1}{50} \, x^{3} e^{\left (-2 \, x + 10\right )} - \frac {1}{2} \, x^{3} \log \left (x\right ) + \frac {1}{50} \, x^{2} e^{\left (-2 \, x + 10\right )} \log \left (x\right ) + \frac {1}{4} \, x^{2} \log \left (x\right )^{2} + \frac {1}{2500} \, x^{2} e^{\left (-4 \, x + 20\right )} + \frac {1}{4} \, x^{2} + \frac {1}{4} \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 3.85, size = 65, normalized size = 2.03 \begin {gather*} \frac {x}{4}-\frac {x^3\,\ln \left (x\right )}{2}+\frac {x^2\,{\ln \left (x\right )}^2}{4}-\frac {x^3\,{\mathrm {e}}^{10-2\,x}}{50}+\frac {x^2\,{\mathrm {e}}^{20-4\,x}}{2500}+\frac {x^2}{4}+\frac {x^4}{4}+\frac {x^2\,{\mathrm {e}}^{10-2\,x}\,\ln \left (x\right )}{50} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________