3.100.15 \(\int \frac {300 e^{10} x+216 x^3+510 x^4+300 x^5+e^5 (-510 x^2-600 x^3)+(-100 e^{10} x-72 x^3-160 x^4-100 x^5+e^5 (180 x^2+200 x^3)) \log (\frac {10 e^5 x-9 x^2-10 x^3}{5 e^5-4 x-5 x^2})+(100 e^{10} x+72 x^3+170 x^4+100 x^5+e^5 (-170 x^2-200 x^3)) \log ^2(\frac {10 e^5 x-9 x^2-10 x^3}{5 e^5-4 x-5 x^2})}{450 e^{10}+324 x^2+765 x^3+450 x^4+e^5 (-765 x-900 x^2)+(300 e^{10}+216 x^2+510 x^3+300 x^4+e^5 (-510 x-600 x^2)) \log ^2(\frac {10 e^5 x-9 x^2-10 x^3}{5 e^5-4 x-5 x^2})+(50 e^{10}+36 x^2+85 x^3+50 x^4+e^5 (-85 x-100 x^2)) \log ^4(\frac {10 e^5 x-9 x^2-10 x^3}{5 e^5-4 x-5 x^2})} \, dx\)

Optimal. Leaf size=34 \[ \frac {x^2}{3+\log ^2\left (2 x+\frac {x}{4-5 \left (\frac {e^5}{x}-x\right )}\right )} \]

________________________________________________________________________________________

Rubi [F]  time = 23.84, 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 {300 e^{10} x+216 x^3+510 x^4+300 x^5+e^5 \left (-510 x^2-600 x^3\right )+\left (-100 e^{10} x-72 x^3-160 x^4-100 x^5+e^5 \left (180 x^2+200 x^3\right )\right ) \log \left (\frac {10 e^5 x-9 x^2-10 x^3}{5 e^5-4 x-5 x^2}\right )+\left (100 e^{10} x+72 x^3+170 x^4+100 x^5+e^5 \left (-170 x^2-200 x^3\right )\right ) \log ^2\left (\frac {10 e^5 x-9 x^2-10 x^3}{5 e^5-4 x-5 x^2}\right )}{450 e^{10}+324 x^2+765 x^3+450 x^4+e^5 \left (-765 x-900 x^2\right )+\left (300 e^{10}+216 x^2+510 x^3+300 x^4+e^5 \left (-510 x-600 x^2\right )\right ) \log ^2\left (\frac {10 e^5 x-9 x^2-10 x^3}{5 e^5-4 x-5 x^2}\right )+\left (50 e^{10}+36 x^2+85 x^3+50 x^4+e^5 \left (-85 x-100 x^2\right )\right ) \log ^4\left (\frac {10 e^5 x-9 x^2-10 x^3}{5 e^5-4 x-5 x^2}\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(300*E^10*x + 216*x^3 + 510*x^4 + 300*x^5 + E^5*(-510*x^2 - 600*x^3) + (-100*E^10*x - 72*x^3 - 160*x^4 - 1
00*x^5 + E^5*(180*x^2 + 200*x^3))*Log[(10*E^5*x - 9*x^2 - 10*x^3)/(5*E^5 - 4*x - 5*x^2)] + (100*E^10*x + 72*x^
3 + 170*x^4 + 100*x^5 + E^5*(-170*x^2 - 200*x^3))*Log[(10*E^5*x - 9*x^2 - 10*x^3)/(5*E^5 - 4*x - 5*x^2)]^2)/(4
50*E^10 + 324*x^2 + 765*x^3 + 450*x^4 + E^5*(-765*x - 900*x^2) + (300*E^10 + 216*x^2 + 510*x^3 + 300*x^4 + E^5
*(-510*x - 600*x^2))*Log[(10*E^5*x - 9*x^2 - 10*x^3)/(5*E^5 - 4*x - 5*x^2)]^2 + (50*E^10 + 36*x^2 + 85*x^3 + 5
0*x^4 + E^5*(-85*x - 100*x^2))*Log[(10*E^5*x - 9*x^2 - 10*x^3)/(5*E^5 - 4*x - 5*x^2)]^4),x]

[Out]

Defer[Int][Log[(x*(-10*E^5 + 9*x + 10*x^2))/(-5*E^5 + 4*x + 5*x^2)]/(3 + Log[(x*(-10*E^5 + x*(9 + 10*x)))/(-5*
E^5 + x*(4 + 5*x))]^2)^2, x]/5 + ((81 + 200*E^5)*(1 + 9/Sqrt[81 + 400*E^5])*Defer[Int][Log[(x*(-10*E^5 + 9*x +
10*x^2))/(-5*E^5 + 4*x + 5*x^2)]/((-9 - Sqrt[81 + 400*E^5] - 20*x)*(3 + Log[(x*(-10*E^5 + x*(9 + 10*x)))/(-5*
E^5 + x*(4 + 5*x))]^2)^2), x])/5 - (360*E^5*Defer[Int][Log[(x*(-10*E^5 + 9*x + 10*x^2))/(-5*E^5 + 4*x + 5*x^2)
]/((-9 + Sqrt[81 + 400*E^5] - 20*x)*(3 + Log[(x*(-10*E^5 + x*(9 + 10*x)))/(-5*E^5 + x*(4 + 5*x))]^2)^2), x])/S
qrt[81 + 400*E^5] + ((81 + 200*E^5)*(1 - 9/Sqrt[81 + 400*E^5])*Defer[Int][Log[(x*(-10*E^5 + 9*x + 10*x^2))/(-5
*E^5 + 4*x + 5*x^2)]/((-9 + Sqrt[81 + 400*E^5] - 20*x)*(3 + Log[(x*(-10*E^5 + x*(9 + 10*x)))/(-5*E^5 + x*(4 +
5*x))]^2)^2), x])/5 - (4*(8 + 25*E^5)*(1 + 2/Sqrt[4 + 25*E^5])*Defer[Int][Log[(x*(-10*E^5 + 9*x + 10*x^2))/(-5
*E^5 + 4*x + 5*x^2)]/((-4 - 2*Sqrt[4 + 25*E^5] - 10*x)*(3 + Log[(x*(-10*E^5 + x*(9 + 10*x)))/(-5*E^5 + x*(4 +
5*x))]^2)^2), x])/5 + (40*E^5*Defer[Int][Log[(x*(-10*E^5 + 9*x + 10*x^2))/(-5*E^5 + 4*x + 5*x^2)]/((-4 + 2*Sqr
t[4 + 25*E^5] - 10*x)*(3 + Log[(x*(-10*E^5 + x*(9 + 10*x)))/(-5*E^5 + x*(4 + 5*x))]^2)^2), x])/Sqrt[4 + 25*E^5
] - (4*(8 + 25*E^5)*(1 - 2/Sqrt[4 + 25*E^5])*Defer[Int][Log[(x*(-10*E^5 + 9*x + 10*x^2))/(-5*E^5 + 4*x + 5*x^2
)]/((-4 + 2*Sqrt[4 + 25*E^5] - 10*x)*(3 + Log[(x*(-10*E^5 + x*(9 + 10*x)))/(-5*E^5 + x*(4 + 5*x))]^2)^2), x])/
5 - 2*Defer[Int][(x*Log[(x*(-10*E^5 + 9*x + 10*x^2))/(-5*E^5 + 4*x + 5*x^2)])/(3 + Log[(x*(-10*E^5 + x*(9 + 10
*x)))/(-5*E^5 + x*(4 + 5*x))]^2)^2, x] + (40*E^5*Defer[Int][Log[(x*(-10*E^5 + 9*x + 10*x^2))/(-5*E^5 + 4*x + 5
*x^2)]/((4 + 2*Sqrt[4 + 25*E^5] + 10*x)*(3 + Log[(x*(-10*E^5 + x*(9 + 10*x)))/(-5*E^5 + x*(4 + 5*x))]^2)^2), x
])/Sqrt[4 + 25*E^5] - (360*E^5*Defer[Int][Log[(x*(-10*E^5 + 9*x + 10*x^2))/(-5*E^5 + 4*x + 5*x^2)]/((9 + Sqrt[
81 + 400*E^5] + 20*x)*(3 + Log[(x*(-10*E^5 + x*(9 + 10*x)))/(-5*E^5 + x*(4 + 5*x))]^2)^2), x])/Sqrt[81 + 400*E
^5] + 2*Defer[Int][x/(3 + Log[(x*(-10*E^5 + x*(9 + 10*x)))/(-5*E^5 + x*(4 + 5*x))]^2), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {2 x \left (3 \left (50 e^{10}-5 e^5 x (17+20 x)+x^2 \left (36+85 x+50 x^2\right )\right )-2 \left (25 e^{10}-5 e^5 x (9+10 x)+x^2 \left (18+40 x+25 x^2\right )\right ) \log \left (\frac {x \left (-10 e^5+x (9+10 x)\right )}{-5 e^5+x (4+5 x)}\right )+\left (50 e^{10}-5 e^5 x (17+20 x)+x^2 \left (36+85 x+50 x^2\right )\right ) \log ^2\left (\frac {x \left (-10 e^5+x (9+10 x)\right )}{-5 e^5+x (4+5 x)}\right )\right )}{\left (50 e^{10}-85 e^5 x+4 \left (9-25 e^5\right ) x^2+85 x^3+50 x^4\right ) \left (3+\log ^2\left (\frac {x \left (-10 e^5+x (9+10 x)\right )}{-5 e^5+x (4+5 x)}\right )\right )^2} \, dx\\ &=2 \int \frac {x \left (3 \left (50 e^{10}-5 e^5 x (17+20 x)+x^2 \left (36+85 x+50 x^2\right )\right )-2 \left (25 e^{10}-5 e^5 x (9+10 x)+x^2 \left (18+40 x+25 x^2\right )\right ) \log \left (\frac {x \left (-10 e^5+x (9+10 x)\right )}{-5 e^5+x (4+5 x)}\right )+\left (50 e^{10}-5 e^5 x (17+20 x)+x^2 \left (36+85 x+50 x^2\right )\right ) \log ^2\left (\frac {x \left (-10 e^5+x (9+10 x)\right )}{-5 e^5+x (4+5 x)}\right )\right )}{\left (50 e^{10}-85 e^5 x+4 \left (9-25 e^5\right ) x^2+85 x^3+50 x^4\right ) \left (3+\log ^2\left (\frac {x \left (-10 e^5+x (9+10 x)\right )}{-5 e^5+x (4+5 x)}\right )\right )^2} \, dx\\ &=2 \int \left (\frac {2 x \left (-25 e^{10}+45 e^5 x-2 \left (9-25 e^5\right ) x^2-40 x^3-25 x^4\right ) \log \left (\frac {x \left (-10 e^5+9 x+10 x^2\right )}{-5 e^5+4 x+5 x^2}\right )}{\left (10 e^5-9 x-10 x^2\right ) \left (5 e^5-4 x-5 x^2\right ) \left (3+\log ^2\left (\frac {x \left (-10 e^5+x (9+10 x)\right )}{-5 e^5+x (4+5 x)}\right )\right )^2}+\frac {x}{3+\log ^2\left (\frac {x \left (-10 e^5+x (9+10 x)\right )}{-5 e^5+x (4+5 x)}\right )}\right ) \, dx\\ &=2 \int \frac {x}{3+\log ^2\left (\frac {x \left (-10 e^5+x (9+10 x)\right )}{-5 e^5+x (4+5 x)}\right )} \, dx+4 \int \frac {x \left (-25 e^{10}+45 e^5 x-2 \left (9-25 e^5\right ) x^2-40 x^3-25 x^4\right ) \log \left (\frac {x \left (-10 e^5+9 x+10 x^2\right )}{-5 e^5+4 x+5 x^2}\right )}{\left (10 e^5-9 x-10 x^2\right ) \left (5 e^5-4 x-5 x^2\right ) \left (3+\log ^2\left (\frac {x \left (-10 e^5+x (9+10 x)\right )}{-5 e^5+x (4+5 x)}\right )\right )^2} \, dx\\ &=2 \int \frac {x}{3+\log ^2\left (\frac {x \left (-10 e^5+x (9+10 x)\right )}{-5 e^5+x (4+5 x)}\right )} \, dx+4 \int \left (\frac {\log \left (\frac {x \left (-10 e^5+9 x+10 x^2\right )}{-5 e^5+4 x+5 x^2}\right )}{20 \left (3+\log ^2\left (\frac {x \left (-10 e^5+x (9+10 x)\right )}{-5 e^5+x (4+5 x)}\right )\right )^2}-\frac {x \log \left (\frac {x \left (-10 e^5+9 x+10 x^2\right )}{-5 e^5+4 x+5 x^2}\right )}{2 \left (3+\log ^2\left (\frac {x \left (-10 e^5+x (9+10 x)\right )}{-5 e^5+x (4+5 x)}\right )\right )^2}+\frac {\left (-90 e^5+\left (81+200 e^5\right ) x\right ) \log \left (\frac {x \left (-10 e^5+9 x+10 x^2\right )}{-5 e^5+4 x+5 x^2}\right )}{20 \left (10 e^5-9 x-10 x^2\right ) \left (3+\log ^2\left (\frac {x \left (-10 e^5+x (9+10 x)\right )}{-5 e^5+x (4+5 x)}\right )\right )^2}+\frac {\left (10 e^5-\left (8+25 e^5\right ) x\right ) \log \left (\frac {x \left (-10 e^5+9 x+10 x^2\right )}{-5 e^5+4 x+5 x^2}\right )}{5 \left (5 e^5-4 x-5 x^2\right ) \left (3+\log ^2\left (\frac {x \left (-10 e^5+x (9+10 x)\right )}{-5 e^5+x (4+5 x)}\right )\right )^2}\right ) \, dx\\ &=\frac {1}{5} \int \frac {\log \left (\frac {x \left (-10 e^5+9 x+10 x^2\right )}{-5 e^5+4 x+5 x^2}\right )}{\left (3+\log ^2\left (\frac {x \left (-10 e^5+x (9+10 x)\right )}{-5 e^5+x (4+5 x)}\right )\right )^2} \, dx+\frac {1}{5} \int \frac {\left (-90 e^5+\left (81+200 e^5\right ) x\right ) \log \left (\frac {x \left (-10 e^5+9 x+10 x^2\right )}{-5 e^5+4 x+5 x^2}\right )}{\left (10 e^5-9 x-10 x^2\right ) \left (3+\log ^2\left (\frac {x \left (-10 e^5+x (9+10 x)\right )}{-5 e^5+x (4+5 x)}\right )\right )^2} \, dx+\frac {4}{5} \int \frac {\left (10 e^5-\left (8+25 e^5\right ) x\right ) \log \left (\frac {x \left (-10 e^5+9 x+10 x^2\right )}{-5 e^5+4 x+5 x^2}\right )}{\left (5 e^5-4 x-5 x^2\right ) \left (3+\log ^2\left (\frac {x \left (-10 e^5+x (9+10 x)\right )}{-5 e^5+x (4+5 x)}\right )\right )^2} \, dx-2 \int \frac {x \log \left (\frac {x \left (-10 e^5+9 x+10 x^2\right )}{-5 e^5+4 x+5 x^2}\right )}{\left (3+\log ^2\left (\frac {x \left (-10 e^5+x (9+10 x)\right )}{-5 e^5+x (4+5 x)}\right )\right )^2} \, dx+2 \int \frac {x}{3+\log ^2\left (\frac {x \left (-10 e^5+x (9+10 x)\right )}{-5 e^5+x (4+5 x)}\right )} \, dx\\ &=\frac {1}{5} \int \frac {\log \left (\frac {x \left (-10 e^5+9 x+10 x^2\right )}{-5 e^5+4 x+5 x^2}\right )}{\left (3+\log ^2\left (\frac {x \left (-10 e^5+x (9+10 x)\right )}{-5 e^5+x (4+5 x)}\right )\right )^2} \, dx+\frac {1}{5} \int \left (\frac {\left (81+200 e^5\right ) x \log \left (\frac {x \left (-10 e^5+9 x+10 x^2\right )}{-5 e^5+4 x+5 x^2}\right )}{\left (10 e^5-9 x-10 x^2\right ) \left (3+\log ^2\left (\frac {x \left (-10 e^5+x (9+10 x)\right )}{-5 e^5+x (4+5 x)}\right )\right )^2}+\frac {90 e^5 \log \left (\frac {x \left (-10 e^5+9 x+10 x^2\right )}{-5 e^5+4 x+5 x^2}\right )}{\left (-10 e^5+9 x+10 x^2\right ) \left (3+\log ^2\left (\frac {x \left (-10 e^5+x (9+10 x)\right )}{-5 e^5+x (4+5 x)}\right )\right )^2}\right ) \, dx+\frac {4}{5} \int \left (\frac {10 e^5 \log \left (\frac {x \left (-10 e^5+9 x+10 x^2\right )}{-5 e^5+4 x+5 x^2}\right )}{\left (5 e^5-4 x-5 x^2\right ) \left (3+\log ^2\left (\frac {x \left (-10 e^5+x (9+10 x)\right )}{-5 e^5+x (4+5 x)}\right )\right )^2}+\frac {\left (-8-25 e^5\right ) x \log \left (\frac {x \left (-10 e^5+9 x+10 x^2\right )}{-5 e^5+4 x+5 x^2}\right )}{\left (5 e^5-4 x-5 x^2\right ) \left (3+\log ^2\left (\frac {x \left (-10 e^5+x (9+10 x)\right )}{-5 e^5+x (4+5 x)}\right )\right )^2}\right ) \, dx-2 \int \frac {x \log \left (\frac {x \left (-10 e^5+9 x+10 x^2\right )}{-5 e^5+4 x+5 x^2}\right )}{\left (3+\log ^2\left (\frac {x \left (-10 e^5+x (9+10 x)\right )}{-5 e^5+x (4+5 x)}\right )\right )^2} \, dx+2 \int \frac {x}{3+\log ^2\left (\frac {x \left (-10 e^5+x (9+10 x)\right )}{-5 e^5+x (4+5 x)}\right )} \, dx\\ &=\frac {1}{5} \int \frac {\log \left (\frac {x \left (-10 e^5+9 x+10 x^2\right )}{-5 e^5+4 x+5 x^2}\right )}{\left (3+\log ^2\left (\frac {x \left (-10 e^5+x (9+10 x)\right )}{-5 e^5+x (4+5 x)}\right )\right )^2} \, dx-2 \int \frac {x \log \left (\frac {x \left (-10 e^5+9 x+10 x^2\right )}{-5 e^5+4 x+5 x^2}\right )}{\left (3+\log ^2\left (\frac {x \left (-10 e^5+x (9+10 x)\right )}{-5 e^5+x (4+5 x)}\right )\right )^2} \, dx+2 \int \frac {x}{3+\log ^2\left (\frac {x \left (-10 e^5+x (9+10 x)\right )}{-5 e^5+x (4+5 x)}\right )} \, dx+\left (8 e^5\right ) \int \frac {\log \left (\frac {x \left (-10 e^5+9 x+10 x^2\right )}{-5 e^5+4 x+5 x^2}\right )}{\left (5 e^5-4 x-5 x^2\right ) \left (3+\log ^2\left (\frac {x \left (-10 e^5+x (9+10 x)\right )}{-5 e^5+x (4+5 x)}\right )\right )^2} \, dx+\left (18 e^5\right ) \int \frac {\log \left (\frac {x \left (-10 e^5+9 x+10 x^2\right )}{-5 e^5+4 x+5 x^2}\right )}{\left (-10 e^5+9 x+10 x^2\right ) \left (3+\log ^2\left (\frac {x \left (-10 e^5+x (9+10 x)\right )}{-5 e^5+x (4+5 x)}\right )\right )^2} \, dx-\frac {1}{5} \left (4 \left (8+25 e^5\right )\right ) \int \frac {x \log \left (\frac {x \left (-10 e^5+9 x+10 x^2\right )}{-5 e^5+4 x+5 x^2}\right )}{\left (5 e^5-4 x-5 x^2\right ) \left (3+\log ^2\left (\frac {x \left (-10 e^5+x (9+10 x)\right )}{-5 e^5+x (4+5 x)}\right )\right )^2} \, dx+\frac {1}{5} \left (81+200 e^5\right ) \int \frac {x \log \left (\frac {x \left (-10 e^5+9 x+10 x^2\right )}{-5 e^5+4 x+5 x^2}\right )}{\left (10 e^5-9 x-10 x^2\right ) \left (3+\log ^2\left (\frac {x \left (-10 e^5+x (9+10 x)\right )}{-5 e^5+x (4+5 x)}\right )\right )^2} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [A]  time = 0.18, size = 41, normalized size = 1.21 \begin {gather*} \frac {x^2}{3+\log ^2\left (\frac {x \left (-10 e^5+x (9+10 x)\right )}{-5 e^5+x (4+5 x)}\right )} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(300*E^10*x + 216*x^3 + 510*x^4 + 300*x^5 + E^5*(-510*x^2 - 600*x^3) + (-100*E^10*x - 72*x^3 - 160*x
^4 - 100*x^5 + E^5*(180*x^2 + 200*x^3))*Log[(10*E^5*x - 9*x^2 - 10*x^3)/(5*E^5 - 4*x - 5*x^2)] + (100*E^10*x +
72*x^3 + 170*x^4 + 100*x^5 + E^5*(-170*x^2 - 200*x^3))*Log[(10*E^5*x - 9*x^2 - 10*x^3)/(5*E^5 - 4*x - 5*x^2)]
^2)/(450*E^10 + 324*x^2 + 765*x^3 + 450*x^4 + E^5*(-765*x - 900*x^2) + (300*E^10 + 216*x^2 + 510*x^3 + 300*x^4
+ E^5*(-510*x - 600*x^2))*Log[(10*E^5*x - 9*x^2 - 10*x^3)/(5*E^5 - 4*x - 5*x^2)]^2 + (50*E^10 + 36*x^2 + 85*x
^3 + 50*x^4 + E^5*(-85*x - 100*x^2))*Log[(10*E^5*x - 9*x^2 - 10*x^3)/(5*E^5 - 4*x - 5*x^2)]^4),x]

[Out]

x^2/(3 + Log[(x*(-10*E^5 + x*(9 + 10*x)))/(-5*E^5 + x*(4 + 5*x))]^2)

________________________________________________________________________________________

fricas [A]  time = 0.89, size = 43, normalized size = 1.26 \begin {gather*} \frac {x^{2}}{\log \left (\frac {10 \, x^{3} + 9 \, x^{2} - 10 \, x e^{5}}{5 \, x^{2} + 4 \, x - 5 \, e^{5}}\right )^{2} + 3} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((100*x*exp(5)^2+(-200*x^3-170*x^2)*exp(5)+100*x^5+170*x^4+72*x^3)*log((10*x*exp(5)-10*x^3-9*x^2)/(5
*exp(5)-5*x^2-4*x))^2+(-100*x*exp(5)^2+(200*x^3+180*x^2)*exp(5)-100*x^5-160*x^4-72*x^3)*log((10*x*exp(5)-10*x^
3-9*x^2)/(5*exp(5)-5*x^2-4*x))+300*x*exp(5)^2+(-600*x^3-510*x^2)*exp(5)+300*x^5+510*x^4+216*x^3)/((50*exp(5)^2
+(-100*x^2-85*x)*exp(5)+50*x^4+85*x^3+36*x^2)*log((10*x*exp(5)-10*x^3-9*x^2)/(5*exp(5)-5*x^2-4*x))^4+(300*exp(
5)^2+(-600*x^2-510*x)*exp(5)+300*x^4+510*x^3+216*x^2)*log((10*x*exp(5)-10*x^3-9*x^2)/(5*exp(5)-5*x^2-4*x))^2+4
50*exp(5)^2+(-900*x^2-765*x)*exp(5)+450*x^4+765*x^3+324*x^2),x, algorithm="fricas")

[Out]

x^2/(log((10*x^3 + 9*x^2 - 10*x*e^5)/(5*x^2 + 4*x - 5*e^5))^2 + 3)

________________________________________________________________________________________

giac [A]  time = 9.17, size = 44, normalized size = 1.29 \begin {gather*} \frac {2 \, x^{2}}{\log \left (\frac {10 \, x^{3} + 9 \, x^{2} - 10 \, x e^{5}}{5 \, x^{2} + 4 \, x - 5 \, e^{5}}\right )^{2} + 3} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((100*x*exp(5)^2+(-200*x^3-170*x^2)*exp(5)+100*x^5+170*x^4+72*x^3)*log((10*x*exp(5)-10*x^3-9*x^2)/(5
*exp(5)-5*x^2-4*x))^2+(-100*x*exp(5)^2+(200*x^3+180*x^2)*exp(5)-100*x^5-160*x^4-72*x^3)*log((10*x*exp(5)-10*x^
3-9*x^2)/(5*exp(5)-5*x^2-4*x))+300*x*exp(5)^2+(-600*x^3-510*x^2)*exp(5)+300*x^5+510*x^4+216*x^3)/((50*exp(5)^2
+(-100*x^2-85*x)*exp(5)+50*x^4+85*x^3+36*x^2)*log((10*x*exp(5)-10*x^3-9*x^2)/(5*exp(5)-5*x^2-4*x))^4+(300*exp(
5)^2+(-600*x^2-510*x)*exp(5)+300*x^4+510*x^3+216*x^2)*log((10*x*exp(5)-10*x^3-9*x^2)/(5*exp(5)-5*x^2-4*x))^2+4
50*exp(5)^2+(-900*x^2-765*x)*exp(5)+450*x^4+765*x^3+324*x^2),x, algorithm="giac")

[Out]

2*x^2/(log((10*x^3 + 9*x^2 - 10*x*e^5)/(5*x^2 + 4*x - 5*e^5))^2 + 3)

________________________________________________________________________________________

maple [A]  time = 0.07, size = 44, normalized size = 1.29

method	result	size
risch	\(\frac {x^{2}}{\ln \left (\frac {10 x \,{\mathrm e}^{5}-10 x^{3}-9 x^{2}}{5 \,{\mathrm e}^{5}-5 x^{2}-4 x}\right )^{2}+3}\)	\(44\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((100*x*exp(5)^2+(-200*x^3-170*x^2)*exp(5)+100*x^5+170*x^4+72*x^3)*ln((10*x*exp(5)-10*x^3-9*x^2)/(5*exp(5)
-5*x^2-4*x))^2+(-100*x*exp(5)^2+(200*x^3+180*x^2)*exp(5)-100*x^5-160*x^4-72*x^3)*ln((10*x*exp(5)-10*x^3-9*x^2)
/(5*exp(5)-5*x^2-4*x))+300*x*exp(5)^2+(-600*x^3-510*x^2)*exp(5)+300*x^5+510*x^4+216*x^3)/((50*exp(5)^2+(-100*x
^2-85*x)*exp(5)+50*x^4+85*x^3+36*x^2)*ln((10*x*exp(5)-10*x^3-9*x^2)/(5*exp(5)-5*x^2-4*x))^4+(300*exp(5)^2+(-60
0*x^2-510*x)*exp(5)+300*x^4+510*x^3+216*x^2)*ln((10*x*exp(5)-10*x^3-9*x^2)/(5*exp(5)-5*x^2-4*x))^2+450*exp(5)^
2+(-900*x^2-765*x)*exp(5)+450*x^4+765*x^3+324*x^2),x,method=_RETURNVERBOSE)

[Out]

x^2/(ln((10*x*exp(5)-10*x^3-9*x^2)/(5*exp(5)-5*x^2-4*x))^2+3)

________________________________________________________________________________________

maxima [B]  time = 0.51, size = 104, normalized size = 3.06 \begin {gather*} -\frac {x^{2}}{2 \, {\left (\log \left (5 \, x^{2} + 4 \, x - 5 \, e^{5}\right ) - \log \relax (x)\right )} \log \left (10 \, x^{2} + 9 \, x - 10 \, e^{5}\right ) - \log \left (10 \, x^{2} + 9 \, x - 10 \, e^{5}\right )^{2} - \log \left (5 \, x^{2} + 4 \, x - 5 \, e^{5}\right )^{2} + 2 \, \log \left (5 \, x^{2} + 4 \, x - 5 \, e^{5}\right ) \log \relax (x) - \log \relax (x)^{2} - 3} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((100*x*exp(5)^2+(-200*x^3-170*x^2)*exp(5)+100*x^5+170*x^4+72*x^3)*log((10*x*exp(5)-10*x^3-9*x^2)/(5
*exp(5)-5*x^2-4*x))^2+(-100*x*exp(5)^2+(200*x^3+180*x^2)*exp(5)-100*x^5-160*x^4-72*x^3)*log((10*x*exp(5)-10*x^
3-9*x^2)/(5*exp(5)-5*x^2-4*x))+300*x*exp(5)^2+(-600*x^3-510*x^2)*exp(5)+300*x^5+510*x^4+216*x^3)/((50*exp(5)^2
+(-100*x^2-85*x)*exp(5)+50*x^4+85*x^3+36*x^2)*log((10*x*exp(5)-10*x^3-9*x^2)/(5*exp(5)-5*x^2-4*x))^4+(300*exp(
5)^2+(-600*x^2-510*x)*exp(5)+300*x^4+510*x^3+216*x^2)*log((10*x*exp(5)-10*x^3-9*x^2)/(5*exp(5)-5*x^2-4*x))^2+4
50*exp(5)^2+(-900*x^2-765*x)*exp(5)+450*x^4+765*x^3+324*x^2),x, algorithm="maxima")

[Out]

-x^2/(2*(log(5*x^2 + 4*x - 5*e^5) - log(x))*log(10*x^2 + 9*x - 10*e^5) - log(10*x^2 + 9*x - 10*e^5)^2 - log(5*
x^2 + 4*x - 5*e^5)^2 + 2*log(5*x^2 + 4*x - 5*e^5)*log(x) - log(x)^2 - 3)

________________________________________________________________________________________

mupad [B]  time = 7.56, size = 43, normalized size = 1.26 \begin {gather*} \frac {x^2}{{\ln \left (\frac {10\,x^3+9\,x^2-10\,{\mathrm {e}}^5\,x}{5\,x^2+4\,x-5\,{\mathrm {e}}^5}\right )}^2+3} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((300*x*exp(10) - exp(5)*(510*x^2 + 600*x^3) - log((9*x^2 - 10*x*exp(5) + 10*x^3)/(4*x - 5*exp(5) + 5*x^2))
*(100*x*exp(10) - exp(5)*(180*x^2 + 200*x^3) + 72*x^3 + 160*x^4 + 100*x^5) + 216*x^3 + 510*x^4 + 300*x^5 + log
((9*x^2 - 10*x*exp(5) + 10*x^3)/(4*x - 5*exp(5) + 5*x^2))^2*(100*x*exp(10) - exp(5)*(170*x^2 + 200*x^3) + 72*x
^3 + 170*x^4 + 100*x^5))/(450*exp(10) + log((9*x^2 - 10*x*exp(5) + 10*x^3)/(4*x - 5*exp(5) + 5*x^2))^4*(50*exp
(10) - exp(5)*(85*x + 100*x^2) + 36*x^2 + 85*x^3 + 50*x^4) + log((9*x^2 - 10*x*exp(5) + 10*x^3)/(4*x - 5*exp(5
) + 5*x^2))^2*(300*exp(10) - exp(5)*(510*x + 600*x^2) + 216*x^2 + 510*x^3 + 300*x^4) - exp(5)*(765*x + 900*x^2
) + 324*x^2 + 765*x^3 + 450*x^4),x)

[Out]

x^2/(log((9*x^2 - 10*x*exp(5) + 10*x^3)/(4*x - 5*exp(5) + 5*x^2))^2 + 3)

________________________________________________________________________________________

sympy [A]  time = 0.61, size = 37, normalized size = 1.09 \begin {gather*} \frac {x^{2}}{\log {\left (\frac {- 10 x^{3} - 9 x^{2} + 10 x e^{5}}{- 5 x^{2} - 4 x + 5 e^{5}} \right )}^{2} + 3} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((100*x*exp(5)**2+(-200*x**3-170*x**2)*exp(5)+100*x**5+170*x**4+72*x**3)*ln((10*x*exp(5)-10*x**3-9*x
**2)/(5*exp(5)-5*x**2-4*x))**2+(-100*x*exp(5)**2+(200*x**3+180*x**2)*exp(5)-100*x**5-160*x**4-72*x**3)*ln((10*
x*exp(5)-10*x**3-9*x**2)/(5*exp(5)-5*x**2-4*x))+300*x*exp(5)**2+(-600*x**3-510*x**2)*exp(5)+300*x**5+510*x**4+
216*x**3)/((50*exp(5)**2+(-100*x**2-85*x)*exp(5)+50*x**4+85*x**3+36*x**2)*ln((10*x*exp(5)-10*x**3-9*x**2)/(5*e
xp(5)-5*x**2-4*x))**4+(300*exp(5)**2+(-600*x**2-510*x)*exp(5)+300*x**4+510*x**3+216*x**2)*ln((10*x*exp(5)-10*x
**3-9*x**2)/(5*exp(5)-5*x**2-4*x))**2+450*exp(5)**2+(-900*x**2-765*x)*exp(5)+450*x**4+765*x**3+324*x**2),x)

[Out]

x**2/(log((-10*x**3 - 9*x**2 + 10*x*exp(5))/(-5*x**2 - 4*x + 5*exp(5)))**2 + 3)

________________________________________________________________________________________