3.2.40 \(\int \frac {e^{\frac {1}{9} (144-96 x+160 x^2-96 x^3+16 x^4+(72-24 x+72 x^2-24 x^3) \log (7-x^2)+(9+9 x^2) \log ^2(7-x^2))} (672-2096 x+1872 x^2+16 x^3-336 x^4+64 x^5+(168-972 x+480 x^2+180 x^3-72 x^4) \log (7-x^2)+(-126 x+18 x^3) \log ^2(7-x^2))}{-63+9 x^2} \, dx\)

Optimal. Leaf size=25 \[ e^{\left (1+x^2\right ) \left (4-\frac {4 x}{3}+\log \left (7-x^2\right )\right )^2} \]

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Rubi [F]  time = 11.58, 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 {\exp \left (\frac {1}{9} \left (144-96 x+160 x^2-96 x^3+16 x^4+\left (72-24 x+72 x^2-24 x^3\right ) \log \left (7-x^2\right )+\left (9+9 x^2\right ) \log ^2\left (7-x^2\right )\right )\right ) \left (672-2096 x+1872 x^2+16 x^3-336 x^4+64 x^5+\left (168-972 x+480 x^2+180 x^3-72 x^4\right ) \log \left (7-x^2\right )+\left (-126 x+18 x^3\right ) \log ^2\left (7-x^2\right )\right )}{-63+9 x^2} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^((144 - 96*x + 160*x^2 - 96*x^3 + 16*x^4 + (72 - 24*x + 72*x^2 - 24*x^3)*Log[7 - x^2] + (9 + 9*x^2)*Log
[7 - x^2]^2)/9)*(672 - 2096*x + 1872*x^2 + 16*x^3 - 336*x^4 + 64*x^5 + (168 - 972*x + 480*x^2 + 180*x^3 - 72*x
^4)*Log[7 - x^2] + (-126*x + 18*x^3)*Log[7 - x^2]^2))/(-63 + 9*x^2),x]

[Out]

(-160*Defer[Int][E^(((1 + x^2)*(-12 + 4*x - 3*Log[7 - x^2])^2)/9), x])/3 - (64*(3 - Sqrt[7])*Defer[Int][E^(((1
+ x^2)*(-12 + 4*x - 3*Log[7 - x^2])^2)/9)/(Sqrt[7] - x), x])/3 + (464*Defer[Int][E^(((1 + x^2)*(-12 + 4*x - 3
*Log[7 - x^2])^2)/9)*x, x])/9 - (112*Defer[Int][E^(((1 + x^2)*(-12 + 4*x - 3*Log[7 - x^2])^2)/9)*x^2, x])/3 +
(64*Defer[Int][E^(((1 + x^2)*(-12 + 4*x - 3*Log[7 - x^2])^2)/9)*x^3, x])/9 + (64*(3 + Sqrt[7])*Defer[Int][E^((
(1 + x^2)*(-12 + 4*x - 3*Log[7 - x^2])^2)/9)/(Sqrt[7] + x), x])/3 - (8*Defer[Int][E^(((1 + x^2)*(-12 + 4*x - 3
*Log[7 - x^2])^2)/9)*Log[7 - x^2], x])/3 - 16*Defer[Int][(E^(((1 + x^2)*(-12 + 4*x - 3*Log[7 - x^2])^2)/9)*Log
[7 - x^2])/(Sqrt[7] - x), x] + 20*Defer[Int][E^(((1 + x^2)*(-12 + 4*x - 3*Log[7 - x^2])^2)/9)*x*Log[7 - x^2],
x] - 8*Defer[Int][E^(((1 + x^2)*(-12 + 4*x - 3*Log[7 - x^2])^2)/9)*x^2*Log[7 - x^2], x] + 16*Defer[Int][(E^(((
1 + x^2)*(-12 + 4*x - 3*Log[7 - x^2])^2)/9)*Log[7 - x^2])/(Sqrt[7] + x), x] + 2*Defer[Int][E^(((1 + x^2)*(-12
+ 4*x - 3*Log[7 - x^2])^2)/9)*x*Log[7 - x^2]^2, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {16 \exp \left (\frac {1}{9} \left (1+x^2\right ) \left (-12+4 x-3 \log \left (7-x^2\right )\right )^2\right ) \left (42-131 x+117 x^2+x^3-21 x^4+4 x^5\right )}{9 \left (-7+x^2\right )}-\frac {4 \exp \left (\frac {1}{9} \left (1+x^2\right ) \left (-12+4 x-3 \log \left (7-x^2\right )\right )^2\right ) \left (-14+81 x-40 x^2-15 x^3+6 x^4\right ) \log \left (7-x^2\right )}{3 \left (-7+x^2\right )}+2 \exp \left (\frac {1}{9} \left (1+x^2\right ) \left (-12+4 x-3 \log \left (7-x^2\right )\right )^2\right ) x \log ^2\left (7-x^2\right )\right ) \, dx\\ &=-\left (\frac {4}{3} \int \frac {\exp \left (\frac {1}{9} \left (1+x^2\right ) \left (-12+4 x-3 \log \left (7-x^2\right )\right )^2\right ) \left (-14+81 x-40 x^2-15 x^3+6 x^4\right ) \log \left (7-x^2\right )}{-7+x^2} \, dx\right )+\frac {16}{9} \int \frac {\exp \left (\frac {1}{9} \left (1+x^2\right ) \left (-12+4 x-3 \log \left (7-x^2\right )\right )^2\right ) \left (42-131 x+117 x^2+x^3-21 x^4+4 x^5\right )}{-7+x^2} \, dx+2 \int \exp \left (\frac {1}{9} \left (1+x^2\right ) \left (-12+4 x-3 \log \left (7-x^2\right )\right )^2\right ) x \log ^2\left (7-x^2\right ) \, dx\\ &=-\left (\frac {4}{3} \int \left (2 \exp \left (\frac {1}{9} \left (1+x^2\right ) \left (-12+4 x-3 \log \left (7-x^2\right )\right )^2\right ) \log \left (7-x^2\right )-15 \exp \left (\frac {1}{9} \left (1+x^2\right ) \left (-12+4 x-3 \log \left (7-x^2\right )\right )^2\right ) x \log \left (7-x^2\right )+6 \exp \left (\frac {1}{9} \left (1+x^2\right ) \left (-12+4 x-3 \log \left (7-x^2\right )\right )^2\right ) x^2 \log \left (7-x^2\right )-\frac {24 \exp \left (\frac {1}{9} \left (1+x^2\right ) \left (-12+4 x-3 \log \left (7-x^2\right )\right )^2\right ) x \log \left (7-x^2\right )}{-7+x^2}\right ) \, dx\right )+\frac {16}{9} \int \left (-30 \exp \left (\frac {1}{9} \left (1+x^2\right ) \left (-12+4 x-3 \log \left (7-x^2\right )\right )^2\right )+29 \exp \left (\frac {1}{9} \left (1+x^2\right ) \left (-12+4 x-3 \log \left (7-x^2\right )\right )^2\right ) x-21 \exp \left (\frac {1}{9} \left (1+x^2\right ) \left (-12+4 x-3 \log \left (7-x^2\right )\right )^2\right ) x^2+4 \exp \left (\frac {1}{9} \left (1+x^2\right ) \left (-12+4 x-3 \log \left (7-x^2\right )\right )^2\right ) x^3-\frac {24 \exp \left (\frac {1}{9} \left (1+x^2\right ) \left (-12+4 x-3 \log \left (7-x^2\right )\right )^2\right ) (7-3 x)}{-7+x^2}\right ) \, dx+2 \int \exp \left (\frac {1}{9} \left (1+x^2\right ) \left (-12+4 x-3 \log \left (7-x^2\right )\right )^2\right ) x \log ^2\left (7-x^2\right ) \, dx\\ &=2 \int \exp \left (\frac {1}{9} \left (1+x^2\right ) \left (-12+4 x-3 \log \left (7-x^2\right )\right )^2\right ) x \log ^2\left (7-x^2\right ) \, dx-\frac {8}{3} \int \exp \left (\frac {1}{9} \left (1+x^2\right ) \left (-12+4 x-3 \log \left (7-x^2\right )\right )^2\right ) \log \left (7-x^2\right ) \, dx+\frac {64}{9} \int \exp \left (\frac {1}{9} \left (1+x^2\right ) \left (-12+4 x-3 \log \left (7-x^2\right )\right )^2\right ) x^3 \, dx-8 \int \exp \left (\frac {1}{9} \left (1+x^2\right ) \left (-12+4 x-3 \log \left (7-x^2\right )\right )^2\right ) x^2 \log \left (7-x^2\right ) \, dx+20 \int \exp \left (\frac {1}{9} \left (1+x^2\right ) \left (-12+4 x-3 \log \left (7-x^2\right )\right )^2\right ) x \log \left (7-x^2\right ) \, dx+32 \int \frac {\exp \left (\frac {1}{9} \left (1+x^2\right ) \left (-12+4 x-3 \log \left (7-x^2\right )\right )^2\right ) x \log \left (7-x^2\right )}{-7+x^2} \, dx-\frac {112}{3} \int \exp \left (\frac {1}{9} \left (1+x^2\right ) \left (-12+4 x-3 \log \left (7-x^2\right )\right )^2\right ) x^2 \, dx-\frac {128}{3} \int \frac {\exp \left (\frac {1}{9} \left (1+x^2\right ) \left (-12+4 x-3 \log \left (7-x^2\right )\right )^2\right ) (7-3 x)}{-7+x^2} \, dx+\frac {464}{9} \int \exp \left (\frac {1}{9} \left (1+x^2\right ) \left (-12+4 x-3 \log \left (7-x^2\right )\right )^2\right ) x \, dx-\frac {160}{3} \int \exp \left (\frac {1}{9} \left (1+x^2\right ) \left (-12+4 x-3 \log \left (7-x^2\right )\right )^2\right ) \, dx\\ &=2 \int \exp \left (\frac {1}{9} \left (1+x^2\right ) \left (-12+4 x-3 \log \left (7-x^2\right )\right )^2\right ) x \log ^2\left (7-x^2\right ) \, dx-\frac {8}{3} \int \exp \left (\frac {1}{9} \left (1+x^2\right ) \left (-12+4 x-3 \log \left (7-x^2\right )\right )^2\right ) \log \left (7-x^2\right ) \, dx+\frac {64}{9} \int \exp \left (\frac {1}{9} \left (1+x^2\right ) \left (-12+4 x-3 \log \left (7-x^2\right )\right )^2\right ) x^3 \, dx-8 \int \exp \left (\frac {1}{9} \left (1+x^2\right ) \left (-12+4 x-3 \log \left (7-x^2\right )\right )^2\right ) x^2 \log \left (7-x^2\right ) \, dx+20 \int \exp \left (\frac {1}{9} \left (1+x^2\right ) \left (-12+4 x-3 \log \left (7-x^2\right )\right )^2\right ) x \log \left (7-x^2\right ) \, dx+32 \int \left (-\frac {\exp \left (\frac {1}{9} \left (1+x^2\right ) \left (-12+4 x-3 \log \left (7-x^2\right )\right )^2\right ) \log \left (7-x^2\right )}{2 \left (\sqrt {7}-x\right )}+\frac {\exp \left (\frac {1}{9} \left (1+x^2\right ) \left (-12+4 x-3 \log \left (7-x^2\right )\right )^2\right ) \log \left (7-x^2\right )}{2 \left (\sqrt {7}+x\right )}\right ) \, dx-\frac {112}{3} \int \exp \left (\frac {1}{9} \left (1+x^2\right ) \left (-12+4 x-3 \log \left (7-x^2\right )\right )^2\right ) x^2 \, dx-\frac {128}{3} \int \left (-\frac {\left (-21+7 \sqrt {7}\right ) \exp \left (\frac {1}{9} \left (1+x^2\right ) \left (-12+4 x-3 \log \left (7-x^2\right )\right )^2\right )}{14 \left (\sqrt {7}-x\right )}-\frac {\left (21+7 \sqrt {7}\right ) \exp \left (\frac {1}{9} \left (1+x^2\right ) \left (-12+4 x-3 \log \left (7-x^2\right )\right )^2\right )}{14 \left (\sqrt {7}+x\right )}\right ) \, dx+\frac {464}{9} \int \exp \left (\frac {1}{9} \left (1+x^2\right ) \left (-12+4 x-3 \log \left (7-x^2\right )\right )^2\right ) x \, dx-\frac {160}{3} \int \exp \left (\frac {1}{9} \left (1+x^2\right ) \left (-12+4 x-3 \log \left (7-x^2\right )\right )^2\right ) \, dx\\ &=2 \int \exp \left (\frac {1}{9} \left (1+x^2\right ) \left (-12+4 x-3 \log \left (7-x^2\right )\right )^2\right ) x \log ^2\left (7-x^2\right ) \, dx-\frac {8}{3} \int \exp \left (\frac {1}{9} \left (1+x^2\right ) \left (-12+4 x-3 \log \left (7-x^2\right )\right )^2\right ) \log \left (7-x^2\right ) \, dx+\frac {64}{9} \int \exp \left (\frac {1}{9} \left (1+x^2\right ) \left (-12+4 x-3 \log \left (7-x^2\right )\right )^2\right ) x^3 \, dx-8 \int \exp \left (\frac {1}{9} \left (1+x^2\right ) \left (-12+4 x-3 \log \left (7-x^2\right )\right )^2\right ) x^2 \log \left (7-x^2\right ) \, dx-16 \int \frac {\exp \left (\frac {1}{9} \left (1+x^2\right ) \left (-12+4 x-3 \log \left (7-x^2\right )\right )^2\right ) \log \left (7-x^2\right )}{\sqrt {7}-x} \, dx+16 \int \frac {\exp \left (\frac {1}{9} \left (1+x^2\right ) \left (-12+4 x-3 \log \left (7-x^2\right )\right )^2\right ) \log \left (7-x^2\right )}{\sqrt {7}+x} \, dx+20 \int \exp \left (\frac {1}{9} \left (1+x^2\right ) \left (-12+4 x-3 \log \left (7-x^2\right )\right )^2\right ) x \log \left (7-x^2\right ) \, dx-\frac {112}{3} \int \exp \left (\frac {1}{9} \left (1+x^2\right ) \left (-12+4 x-3 \log \left (7-x^2\right )\right )^2\right ) x^2 \, dx+\frac {464}{9} \int \exp \left (\frac {1}{9} \left (1+x^2\right ) \left (-12+4 x-3 \log \left (7-x^2\right )\right )^2\right ) x \, dx-\frac {160}{3} \int \exp \left (\frac {1}{9} \left (1+x^2\right ) \left (-12+4 x-3 \log \left (7-x^2\right )\right )^2\right ) \, dx-\frac {1}{3} \left (64 \left (3-\sqrt {7}\right )\right ) \int \frac {\exp \left (\frac {1}{9} \left (1+x^2\right ) \left (-12+4 x-3 \log \left (7-x^2\right )\right )^2\right )}{\sqrt {7}-x} \, dx+\frac {1}{3} \left (64 \left (3+\sqrt {7}\right )\right ) \int \frac {\exp \left (\frac {1}{9} \left (1+x^2\right ) \left (-12+4 x-3 \log \left (7-x^2\right )\right )^2\right )}{\sqrt {7}+x} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [B]  time = 0.23, size = 55, normalized size = 2.20 \begin {gather*} e^{\frac {1}{9} \left (1+x^2\right ) \left (16 (-3+x)^2+9 \log ^2\left (7-x^2\right )\right )} \left (7-x^2\right )^{8-\frac {8}{3} x \left (1-3 x+x^2\right )} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^((144 - 96*x + 160*x^2 - 96*x^3 + 16*x^4 + (72 - 24*x + 72*x^2 - 24*x^3)*Log[7 - x^2] + (9 + 9*x^
2)*Log[7 - x^2]^2)/9)*(672 - 2096*x + 1872*x^2 + 16*x^3 - 336*x^4 + 64*x^5 + (168 - 972*x + 480*x^2 + 180*x^3
- 72*x^4)*Log[7 - x^2] + (-126*x + 18*x^3)*Log[7 - x^2]^2))/(-63 + 9*x^2),x]

[Out]

E^(((1 + x^2)*(16*(-3 + x)^2 + 9*Log[7 - x^2]^2))/9)*(7 - x^2)^(8 - (8*x*(1 - 3*x + x^2))/3)

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fricas [B]  time = 0.65, size = 58, normalized size = 2.32 \begin {gather*} e^{\left (\frac {16}{9} \, x^{4} - \frac {32}{3} \, x^{3} + {\left (x^{2} + 1\right )} \log \left (-x^{2} + 7\right )^{2} + \frac {160}{9} \, x^{2} - \frac {8}{3} \, {\left (x^{3} - 3 \, x^{2} + x - 3\right )} \log \left (-x^{2} + 7\right ) - \frac {32}{3} \, x + 16\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((18*x^3-126*x)*log(-x^2+7)^2+(-72*x^4+180*x^3+480*x^2-972*x+168)*log(-x^2+7)+64*x^5-336*x^4+16*x^3+
1872*x^2-2096*x+672)*exp(1/9*(9*x^2+9)*log(-x^2+7)^2+1/9*(-24*x^3+72*x^2-24*x+72)*log(-x^2+7)+16/9*x^4-32/3*x^
3+160/9*x^2-32/3*x+16)/(9*x^2-63),x, algorithm="fricas")

[Out]

e^(16/9*x^4 - 32/3*x^3 + (x^2 + 1)*log(-x^2 + 7)^2 + 160/9*x^2 - 8/3*(x^3 - 3*x^2 + x - 3)*log(-x^2 + 7) - 32/
3*x + 16)

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giac [B]  time = 37.51, size = 92, normalized size = 3.68 \begin {gather*} e^{\left (\frac {16}{9} \, x^{4} - \frac {8}{3} \, x^{3} \log \left (-x^{2} + 7\right ) + x^{2} \log \left (-x^{2} + 7\right )^{2} - \frac {32}{3} \, x^{3} + 8 \, x^{2} \log \left (-x^{2} + 7\right ) + \frac {160}{9} \, x^{2} - \frac {8}{3} \, x \log \left (-x^{2} + 7\right ) + \log \left (-x^{2} + 7\right )^{2} - \frac {32}{3} \, x + 8 \, \log \left (-x^{2} + 7\right ) + 16\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((18*x^3-126*x)*log(-x^2+7)^2+(-72*x^4+180*x^3+480*x^2-972*x+168)*log(-x^2+7)+64*x^5-336*x^4+16*x^3+
1872*x^2-2096*x+672)*exp(1/9*(9*x^2+9)*log(-x^2+7)^2+1/9*(-24*x^3+72*x^2-24*x+72)*log(-x^2+7)+16/9*x^4-32/3*x^
3+160/9*x^2-32/3*x+16)/(9*x^2-63),x, algorithm="giac")

[Out]

e^(16/9*x^4 - 8/3*x^3*log(-x^2 + 7) + x^2*log(-x^2 + 7)^2 - 32/3*x^3 + 8*x^2*log(-x^2 + 7) + 160/9*x^2 - 8/3*x
*log(-x^2 + 7) + log(-x^2 + 7)^2 - 32/3*x + 8*log(-x^2 + 7) + 16)

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maple [B]  time = 0.06, size = 50, normalized size = 2.00

method	result	size
risch	\(\left (-x^{2}+7\right )^{-\frac {8 \left (x -3\right ) \left (x^{2}+1\right )}{3}} {\mathrm e}^{\frac {\left (x^{2}+1\right ) \left (9 \ln \left (-x^{2}+7\right )^{2}+16 x^{2}-96 x +144\right )}{9}}\)	\(50\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((18*x^3-126*x)*ln(-x^2+7)^2+(-72*x^4+180*x^3+480*x^2-972*x+168)*ln(-x^2+7)+64*x^5-336*x^4+16*x^3+1872*x^2
-2096*x+672)*exp(1/9*(9*x^2+9)*ln(-x^2+7)^2+1/9*(-24*x^3+72*x^2-24*x+72)*ln(-x^2+7)+16/9*x^4-32/3*x^3+160/9*x^
2-32/3*x+16)/(9*x^2-63),x,method=_RETURNVERBOSE)

[Out]

(-x^2+7)^(-8/3*(x-3)*(x^2+1))*exp(1/9*(x^2+1)*(9*ln(-x^2+7)^2+16*x^2-96*x+144))

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maxima [B]  time = 1.06, size = 142, normalized size = 5.68 \begin {gather*} {\left (x^{16} e^{16} - 56 \, x^{14} e^{16} + 1372 \, x^{12} e^{16} - 19208 \, x^{10} e^{16} + 168070 \, x^{8} e^{16} - 941192 \, x^{6} e^{16} + 3294172 \, x^{4} e^{16} - 6588344 \, x^{2} e^{16} + 5764801 \, e^{16}\right )} e^{\left (\frac {16}{9} \, x^{4} - \frac {8}{3} \, x^{3} \log \left (-x^{2} + 7\right ) + x^{2} \log \left (-x^{2} + 7\right )^{2} - \frac {32}{3} \, x^{3} + 8 \, x^{2} \log \left (-x^{2} + 7\right ) + \frac {160}{9} \, x^{2} - \frac {8}{3} \, x \log \left (-x^{2} + 7\right ) + \log \left (-x^{2} + 7\right )^{2} - \frac {32}{3} \, x\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((18*x^3-126*x)*log(-x^2+7)^2+(-72*x^4+180*x^3+480*x^2-972*x+168)*log(-x^2+7)+64*x^5-336*x^4+16*x^3+
1872*x^2-2096*x+672)*exp(1/9*(9*x^2+9)*log(-x^2+7)^2+1/9*(-24*x^3+72*x^2-24*x+72)*log(-x^2+7)+16/9*x^4-32/3*x^
3+160/9*x^2-32/3*x+16)/(9*x^2-63),x, algorithm="maxima")

[Out]

(x^16*e^16 - 56*x^14*e^16 + 1372*x^12*e^16 - 19208*x^10*e^16 + 168070*x^8*e^16 - 941192*x^6*e^16 + 3294172*x^4
*e^16 - 6588344*x^2*e^16 + 5764801*e^16)*e^(16/9*x^4 - 8/3*x^3*log(-x^2 + 7) + x^2*log(-x^2 + 7)^2 - 32/3*x^3
+ 8*x^2*log(-x^2 + 7) + 160/9*x^2 - 8/3*x*log(-x^2 + 7) + log(-x^2 + 7)^2 - 32/3*x)

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mupad [B]  time = 0.34, size = 780, normalized size = 31.20 \begin {gather*} 5764801\,{\mathrm {e}}^{\frac {16\,x^4}{9}-\frac {8\,x^3\,\ln \left (7-x^2\right )}{3}-\frac {32\,x^3}{3}+x^2\,{\ln \left (7-x^2\right )}^2+\frac {160\,x^2}{9}-\frac {8\,x\,\ln \left (7-x^2\right )}{3}-\frac {32\,x}{3}+{\ln \left (7-x^2\right )}^2+16}\,{\left (7-x^2\right )}^{8\,x^2}-6588344\,x^2\,{\mathrm {e}}^{\frac {16\,x^4}{9}-\frac {8\,x^3\,\ln \left (7-x^2\right )}{3}-\frac {32\,x^3}{3}+x^2\,{\ln \left (7-x^2\right )}^2+\frac {160\,x^2}{9}-\frac {8\,x\,\ln \left (7-x^2\right )}{3}-\frac {32\,x}{3}+{\ln \left (7-x^2\right )}^2+16}\,{\left (7-x^2\right )}^{8\,x^2}+3294172\,x^4\,{\mathrm {e}}^{\frac {16\,x^4}{9}-\frac {8\,x^3\,\ln \left (7-x^2\right )}{3}-\frac {32\,x^3}{3}+x^2\,{\ln \left (7-x^2\right )}^2+\frac {160\,x^2}{9}-\frac {8\,x\,\ln \left (7-x^2\right )}{3}-\frac {32\,x}{3}+{\ln \left (7-x^2\right )}^2+16}\,{\left (7-x^2\right )}^{8\,x^2}-941192\,x^6\,{\mathrm {e}}^{\frac {16\,x^4}{9}-\frac {8\,x^3\,\ln \left (7-x^2\right )}{3}-\frac {32\,x^3}{3}+x^2\,{\ln \left (7-x^2\right )}^2+\frac {160\,x^2}{9}-\frac {8\,x\,\ln \left (7-x^2\right )}{3}-\frac {32\,x}{3}+{\ln \left (7-x^2\right )}^2+16}\,{\left (7-x^2\right )}^{8\,x^2}+168070\,x^8\,{\mathrm {e}}^{\frac {16\,x^4}{9}-\frac {8\,x^3\,\ln \left (7-x^2\right )}{3}-\frac {32\,x^3}{3}+x^2\,{\ln \left (7-x^2\right )}^2+\frac {160\,x^2}{9}-\frac {8\,x\,\ln \left (7-x^2\right )}{3}-\frac {32\,x}{3}+{\ln \left (7-x^2\right )}^2+16}\,{\left (7-x^2\right )}^{8\,x^2}-19208\,x^{10}\,{\mathrm {e}}^{\frac {16\,x^4}{9}-\frac {8\,x^3\,\ln \left (7-x^2\right )}{3}-\frac {32\,x^3}{3}+x^2\,{\ln \left (7-x^2\right )}^2+\frac {160\,x^2}{9}-\frac {8\,x\,\ln \left (7-x^2\right )}{3}-\frac {32\,x}{3}+{\ln \left (7-x^2\right )}^2+16}\,{\left (7-x^2\right )}^{8\,x^2}+1372\,x^{12}\,{\mathrm {e}}^{\frac {16\,x^4}{9}-\frac {8\,x^3\,\ln \left (7-x^2\right )}{3}-\frac {32\,x^3}{3}+x^2\,{\ln \left (7-x^2\right )}^2+\frac {160\,x^2}{9}-\frac {8\,x\,\ln \left (7-x^2\right )}{3}-\frac {32\,x}{3}+{\ln \left (7-x^2\right )}^2+16}\,{\left (7-x^2\right )}^{8\,x^2}-56\,x^{14}\,{\mathrm {e}}^{\frac {16\,x^4}{9}-\frac {8\,x^3\,\ln \left (7-x^2\right )}{3}-\frac {32\,x^3}{3}+x^2\,{\ln \left (7-x^2\right )}^2+\frac {160\,x^2}{9}-\frac {8\,x\,\ln \left (7-x^2\right )}{3}-\frac {32\,x}{3}+{\ln \left (7-x^2\right )}^2+16}\,{\left (7-x^2\right )}^{8\,x^2}+x^{16}\,{\mathrm {e}}^{\frac {16\,x^4}{9}-\frac {8\,x^3\,\ln \left (7-x^2\right )}{3}-\frac {32\,x^3}{3}+x^2\,{\ln \left (7-x^2\right )}^2+\frac {160\,x^2}{9}-\frac {8\,x\,\ln \left (7-x^2\right )}{3}-\frac {32\,x}{3}+{\ln \left (7-x^2\right )}^2+16}\,{\left (7-x^2\right )}^{8\,x^2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp((log(7 - x^2)^2*(9*x^2 + 9))/9 - (log(7 - x^2)*(24*x - 72*x^2 + 24*x^3 - 72))/9 - (32*x)/3 + (160*x^2
)/9 - (32*x^3)/3 + (16*x^4)/9 + 16)*(log(7 - x^2)*(480*x^2 - 972*x + 180*x^3 - 72*x^4 + 168) - log(7 - x^2)^2*
(126*x - 18*x^3) - 2096*x + 1872*x^2 + 16*x^3 - 336*x^4 + 64*x^5 + 672))/(9*x^2 - 63),x)

[Out]

5764801*exp(log(7 - x^2)^2 - (8*x^3*log(7 - x^2))/3 - (32*x)/3 + x^2*log(7 - x^2)^2 + (160*x^2)/9 - (32*x^3)/3
+ (16*x^4)/9 - (8*x*log(7 - x^2))/3 + 16)*(7 - x^2)^(8*x^2) - 6588344*x^2*exp(log(7 - x^2)^2 - (8*x^3*log(7 -
x^2))/3 - (32*x)/3 + x^2*log(7 - x^2)^2 + (160*x^2)/9 - (32*x^3)/3 + (16*x^4)/9 - (8*x*log(7 - x^2))/3 + 16)*
(7 - x^2)^(8*x^2) + 3294172*x^4*exp(log(7 - x^2)^2 - (8*x^3*log(7 - x^2))/3 - (32*x)/3 + x^2*log(7 - x^2)^2 +
(160*x^2)/9 - (32*x^3)/3 + (16*x^4)/9 - (8*x*log(7 - x^2))/3 + 16)*(7 - x^2)^(8*x^2) - 941192*x^6*exp(log(7 -
x^2)^2 - (8*x^3*log(7 - x^2))/3 - (32*x)/3 + x^2*log(7 - x^2)^2 + (160*x^2)/9 - (32*x^3)/3 + (16*x^4)/9 - (8*x
*log(7 - x^2))/3 + 16)*(7 - x^2)^(8*x^2) + 168070*x^8*exp(log(7 - x^2)^2 - (8*x^3*log(7 - x^2))/3 - (32*x)/3 +
x^2*log(7 - x^2)^2 + (160*x^2)/9 - (32*x^3)/3 + (16*x^4)/9 - (8*x*log(7 - x^2))/3 + 16)*(7 - x^2)^(8*x^2) - 1
9208*x^10*exp(log(7 - x^2)^2 - (8*x^3*log(7 - x^2))/3 - (32*x)/3 + x^2*log(7 - x^2)^2 + (160*x^2)/9 - (32*x^3)
/3 + (16*x^4)/9 - (8*x*log(7 - x^2))/3 + 16)*(7 - x^2)^(8*x^2) + 1372*x^12*exp(log(7 - x^2)^2 - (8*x^3*log(7 -
x^2))/3 - (32*x)/3 + x^2*log(7 - x^2)^2 + (160*x^2)/9 - (32*x^3)/3 + (16*x^4)/9 - (8*x*log(7 - x^2))/3 + 16)*
(7 - x^2)^(8*x^2) - 56*x^14*exp(log(7 - x^2)^2 - (8*x^3*log(7 - x^2))/3 - (32*x)/3 + x^2*log(7 - x^2)^2 + (160
*x^2)/9 - (32*x^3)/3 + (16*x^4)/9 - (8*x*log(7 - x^2))/3 + 16)*(7 - x^2)^(8*x^2) + x^16*exp(log(7 - x^2)^2 - (
8*x^3*log(7 - x^2))/3 - (32*x)/3 + x^2*log(7 - x^2)^2 + (160*x^2)/9 - (32*x^3)/3 + (16*x^4)/9 - (8*x*log(7 - x
^2))/3 + 16)*(7 - x^2)^(8*x^2)

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sympy [B]  time = 1.07, size = 66, normalized size = 2.64 \begin {gather*} e^{\frac {16 x^{4}}{9} - \frac {32 x^{3}}{3} + \frac {160 x^{2}}{9} - \frac {32 x}{3} + \left (x^{2} + 1\right ) \log {\left (7 - x^{2} \right )}^{2} + \left (- \frac {8 x^{3}}{3} + 8 x^{2} - \frac {8 x}{3} + 8\right ) \log {\left (7 - x^{2} \right )} + 16} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((18*x**3-126*x)*ln(-x**2+7)**2+(-72*x**4+180*x**3+480*x**2-972*x+168)*ln(-x**2+7)+64*x**5-336*x**4+
16*x**3+1872*x**2-2096*x+672)*exp(1/9*(9*x**2+9)*ln(-x**2+7)**2+1/9*(-24*x**3+72*x**2-24*x+72)*ln(-x**2+7)+16/
9*x**4-32/3*x**3+160/9*x**2-32/3*x+16)/(9*x**2-63),x)

[Out]

exp(16*x**4/9 - 32*x**3/3 + 160*x**2/9 - 32*x/3 + (x**2 + 1)*log(7 - x**2)**2 + (-8*x**3/3 + 8*x**2 - 8*x/3 +
8)*log(7 - x**2) + 16)

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