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3.26.90 \(\int \frac {(e^{4 x} (32 x-16 x^2+2 x^3) \log (\frac {x}{7})+e^{4 x} (-128 x+64 x^2-8 x^3) \log ^2(\frac {x}{7})+e^{4 x} (192 x-96 x^2+12 x^3) \log ^3(\frac {x}{7})+e^{4 x} (-128 x+64 x^2-8 x^3) \log ^4(\frac {x}{7})+e^{4 x} (32 x-16 x^2+2 x^3) \log ^5(\frac {x}{7})) \log (x)+(e^{4 x} (-64 x+32 x^2-4 x^3)+e^{4 x} (224 x-56 x^2-16 x^3+4 x^4) \log (\frac {x}{7})+e^{4 x} (-320 x-64 x^2+100 x^3-16 x^4) \log ^2(\frac {x}{7})+e^{4 x} (256 x+208 x^2-164 x^3+24 x^4) \log ^3(\frac {x}{7})+e^{4 x} (-128 x-160 x^2+112 x^3-16 x^4) \log ^4(\frac {x}{7})+e^{4 x} (32 x+40 x^2-28 x^3+4 x^4) \log ^5(\frac {x}{7})) \log ^2(x)}{\log ^5(\frac {x}{7})} \, dx\)

Optimal. Leaf size=35 \[ e^{4 x} \left (1-\frac {4}{x}\right )^2 \left (-x+\frac {x}{\log \left (\frac {x}{7}\right )}\right )^4 \log ^2(x) \]

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Rubi [F]  time = 86.96, 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 {\left (e^{4 x} \left (32 x-16 x^2+2 x^3\right ) \log \left (\frac {x}{7}\right )+e^{4 x} \left (-128 x+64 x^2-8 x^3\right ) \log ^2\left (\frac {x}{7}\right )+e^{4 x} \left (192 x-96 x^2+12 x^3\right ) \log ^3\left (\frac {x}{7}\right )+e^{4 x} \left (-128 x+64 x^2-8 x^3\right ) \log ^4\left (\frac {x}{7}\right )+e^{4 x} \left (32 x-16 x^2+2 x^3\right ) \log ^5\left (\frac {x}{7}\right )\right ) \log (x)+\left (e^{4 x} \left (-64 x+32 x^2-4 x^3\right )+e^{4 x} \left (224 x-56 x^2-16 x^3+4 x^4\right ) \log \left (\frac {x}{7}\right )+e^{4 x} \left (-320 x-64 x^2+100 x^3-16 x^4\right ) \log ^2\left (\frac {x}{7}\right )+e^{4 x} \left (256 x+208 x^2-164 x^3+24 x^4\right ) \log ^3\left (\frac {x}{7}\right )+e^{4 x} \left (-128 x-160 x^2+112 x^3-16 x^4\right ) \log ^4\left (\frac {x}{7}\right )+e^{4 x} \left (32 x+40 x^2-28 x^3+4 x^4\right ) \log ^5\left (\frac {x}{7}\right )\right ) \log ^2(x)}{\log ^5\left (\frac {x}{7}\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[((E^(4*x)*(32*x - 16*x^2 + 2*x^3)*Log[x/7] + E^(4*x)*(-128*x + 64*x^2 - 8*x^3)*Log[x/7]^2 + E^(4*x)*(192*x
 - 96*x^2 + 12*x^3)*Log[x/7]^3 + E^(4*x)*(-128*x + 64*x^2 - 8*x^3)*Log[x/7]^4 + E^(4*x)*(32*x - 16*x^2 + 2*x^3
)*Log[x/7]^5)*Log[x] + (E^(4*x)*(-64*x + 32*x^2 - 4*x^3) + E^(4*x)*(224*x - 56*x^2 - 16*x^3 + 4*x^4)*Log[x/7]
+ E^(4*x)*(-320*x - 64*x^2 + 100*x^3 - 16*x^4)*Log[x/7]^2 + E^(4*x)*(256*x + 208*x^2 - 164*x^3 + 24*x^4)*Log[x
/7]^3 + E^(4*x)*(-128*x - 160*x^2 + 112*x^3 - 16*x^4)*Log[x/7]^4 + E^(4*x)*(32*x + 40*x^2 - 28*x^3 + 4*x^4)*Lo
g[x/7]^5)*Log[x]^2)/Log[x/7]^5,x]

[Out]

(-363*E^(4*x))/128 + (37*E^(4*x)*x)/32 - (E^(4*x)*x^2)/8 + (163*ExpIntegralEi[4*x])/64 - (163*E^(4*x)*Log[x])/
64 + (163*E^(4*x)*x*Log[x])/16 - (35*E^(4*x)*x^2*Log[x])/8 + (E^(4*x)*x^3*Log[x])/2 + 32*Defer[Int][(E^(4*x)*x
*Log[x])/Log[x/7]^4, x] - 16*Defer[Int][(E^(4*x)*x^2*Log[x])/Log[x/7]^4, x] + 2*Defer[Int][(E^(4*x)*x^3*Log[x]
)/Log[x/7]^4, x] - 128*Defer[Int][(E^(4*x)*x*Log[x])/Log[x/7]^3, x] + 64*Defer[Int][(E^(4*x)*x^2*Log[x])/Log[x
/7]^3, x] - 8*Defer[Int][(E^(4*x)*x^3*Log[x])/Log[x/7]^3, x] + 192*Defer[Int][(E^(4*x)*x*Log[x])/Log[x/7]^2, x
] - 96*Defer[Int][(E^(4*x)*x^2*Log[x])/Log[x/7]^2, x] + 12*Defer[Int][(E^(4*x)*x^3*Log[x])/Log[x/7]^2, x] - 12
8*Defer[Int][(E^(4*x)*x*Log[x])/Log[x/7], x] + 64*Defer[Int][(E^(4*x)*x^2*Log[x])/Log[x/7], x] - 8*Defer[Int][
(E^(4*x)*x^3*Log[x])/Log[x/7], x] + 32*Defer[Int][E^(4*x)*x*Log[x]^2, x] + 40*Defer[Int][E^(4*x)*x^2*Log[x]^2,
 x] - 28*Defer[Int][E^(4*x)*x^3*Log[x]^2, x] + 4*Defer[Int][E^(4*x)*x^4*Log[x]^2, x] - 64*Defer[Int][(E^(4*x)*
x*Log[x]^2)/Log[x/7]^5, x] + 32*Defer[Int][(E^(4*x)*x^2*Log[x]^2)/Log[x/7]^5, x] - 4*Defer[Int][(E^(4*x)*x^3*L
og[x]^2)/Log[x/7]^5, x] + 224*Defer[Int][(E^(4*x)*x*Log[x]^2)/Log[x/7]^4, x] - 56*Defer[Int][(E^(4*x)*x^2*Log[
x]^2)/Log[x/7]^4, x] - 16*Defer[Int][(E^(4*x)*x^3*Log[x]^2)/Log[x/7]^4, x] + 4*Defer[Int][(E^(4*x)*x^4*Log[x]^
2)/Log[x/7]^4, x] - 320*Defer[Int][(E^(4*x)*x*Log[x]^2)/Log[x/7]^3, x] - 64*Defer[Int][(E^(4*x)*x^2*Log[x]^2)/
Log[x/7]^3, x] + 100*Defer[Int][(E^(4*x)*x^3*Log[x]^2)/Log[x/7]^3, x] - 16*Defer[Int][(E^(4*x)*x^4*Log[x]^2)/L
og[x/7]^3, x] + 256*Defer[Int][(E^(4*x)*x*Log[x]^2)/Log[x/7]^2, x] + 208*Defer[Int][(E^(4*x)*x^2*Log[x]^2)/Log
[x/7]^2, x] - 164*Defer[Int][(E^(4*x)*x^3*Log[x]^2)/Log[x/7]^2, x] + 24*Defer[Int][(E^(4*x)*x^4*Log[x]^2)/Log[
x/7]^2, x] - 128*Defer[Int][(E^(4*x)*x*Log[x]^2)/Log[x/7], x] - 160*Defer[Int][(E^(4*x)*x^2*Log[x]^2)/Log[x/7]
, x] + 112*Defer[Int][(E^(4*x)*x^3*Log[x]^2)/Log[x/7], x] - 16*Defer[Int][(E^(4*x)*x^4*Log[x]^2)/Log[x/7], x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {2 e^{4 x} (4-x) x \left (1-\log \left (\frac {x}{7}\right )\right )^3 \log (x) \left (2 (-4+x) \log (x)+\log \left (\frac {x}{7}\right ) \left (4-x+\left (4+6 x-2 x^2\right ) \log (x)\right )+\log ^2\left (\frac {x}{7}\right ) \left (-4+x+2 \left (-2-3 x+x^2\right ) \log (x)\right )\right )}{\log ^5\left (\frac {x}{7}\right )} \, dx\\ &=2 \int \frac {e^{4 x} (4-x) x \left (1-\log \left (\frac {x}{7}\right )\right )^3 \log (x) \left (2 (-4+x) \log (x)+\log \left (\frac {x}{7}\right ) \left (4-x+\left (4+6 x-2 x^2\right ) \log (x)\right )+\log ^2\left (\frac {x}{7}\right ) \left (-4+x+2 \left (-2-3 x+x^2\right ) \log (x)\right )\right )}{\log ^5\left (\frac {x}{7}\right )} \, dx\\ &=2 \int \left (\frac {e^{4 x} (-4+x)^2 x \left (-1+\log \left (\frac {x}{7}\right )\right )^4 \log (x)}{\log ^4\left (\frac {x}{7}\right )}+\frac {2 e^{4 x} (-4+x) x \left (-1+\log \left (\frac {x}{7}\right )\right )^3 \left (-4+x+2 \log \left (\frac {x}{7}\right )+3 x \log \left (\frac {x}{7}\right )-x^2 \log \left (\frac {x}{7}\right )-2 \log ^2\left (\frac {x}{7}\right )-3 x \log ^2\left (\frac {x}{7}\right )+x^2 \log ^2\left (\frac {x}{7}\right )\right ) \log ^2(x)}{\log ^5\left (\frac {x}{7}\right )}\right ) \, dx\\ &=2 \int \frac {e^{4 x} (-4+x)^2 x \left (-1+\log \left (\frac {x}{7}\right )\right )^4 \log (x)}{\log ^4\left (\frac {x}{7}\right )} \, dx+4 \int \frac {e^{4 x} (-4+x) x \left (-1+\log \left (\frac {x}{7}\right )\right )^3 \left (-4+x+2 \log \left (\frac {x}{7}\right )+3 x \log \left (\frac {x}{7}\right )-x^2 \log \left (\frac {x}{7}\right )-2 \log ^2\left (\frac {x}{7}\right )-3 x \log ^2\left (\frac {x}{7}\right )+x^2 \log ^2\left (\frac {x}{7}\right )\right ) \log ^2(x)}{\log ^5\left (\frac {x}{7}\right )} \, dx\\ &=2 \int \left (\frac {16 e^{4 x} x \left (-1+\log \left (\frac {x}{7}\right )\right )^4 \log (x)}{\log ^4\left (\frac {x}{7}\right )}-\frac {8 e^{4 x} x^2 \left (-1+\log \left (\frac {x}{7}\right )\right )^4 \log (x)}{\log ^4\left (\frac {x}{7}\right )}+\frac {e^{4 x} x^3 \left (-1+\log \left (\frac {x}{7}\right )\right )^4 \log (x)}{\log ^4\left (\frac {x}{7}\right )}\right ) \, dx+4 \int \frac {e^{4 x} (4-x) x \left (1-\log \left (\frac {x}{7}\right )\right )^3 \left (-4+x+\left (2+3 x-x^2\right ) \log \left (\frac {x}{7}\right )+\left (-2-3 x+x^2\right ) \log ^2\left (\frac {x}{7}\right )\right ) \log ^2(x)}{\log ^5\left (\frac {x}{7}\right )} \, dx\\ &=2 \int \frac {e^{4 x} x^3 \left (-1+\log \left (\frac {x}{7}\right )\right )^4 \log (x)}{\log ^4\left (\frac {x}{7}\right )} \, dx+4 \int \left (-\frac {4 e^{4 x} x \left (-1+\log \left (\frac {x}{7}\right )\right )^3 \left (-4+x+2 \log \left (\frac {x}{7}\right )+3 x \log \left (\frac {x}{7}\right )-x^2 \log \left (\frac {x}{7}\right )-2 \log ^2\left (\frac {x}{7}\right )-3 x \log ^2\left (\frac {x}{7}\right )+x^2 \log ^2\left (\frac {x}{7}\right )\right ) \log ^2(x)}{\log ^5\left (\frac {x}{7}\right )}+\frac {e^{4 x} x^2 \left (-1+\log \left (\frac {x}{7}\right )\right )^3 \left (-4+x+2 \log \left (\frac {x}{7}\right )+3 x \log \left (\frac {x}{7}\right )-x^2 \log \left (\frac {x}{7}\right )-2 \log ^2\left (\frac {x}{7}\right )-3 x \log ^2\left (\frac {x}{7}\right )+x^2 \log ^2\left (\frac {x}{7}\right )\right ) \log ^2(x)}{\log ^5\left (\frac {x}{7}\right )}\right ) \, dx-16 \int \frac {e^{4 x} x^2 \left (-1+\log \left (\frac {x}{7}\right )\right )^4 \log (x)}{\log ^4\left (\frac {x}{7}\right )} \, dx+32 \int \frac {e^{4 x} x \left (-1+\log \left (\frac {x}{7}\right )\right )^4 \log (x)}{\log ^4\left (\frac {x}{7}\right )} \, dx\\ &=2 \int \left (e^{4 x} x^3 \log (x)+\frac {e^{4 x} x^3 \log (x)}{\log ^4\left (\frac {x}{7}\right )}-\frac {4 e^{4 x} x^3 \log (x)}{\log ^3\left (\frac {x}{7}\right )}+\frac {6 e^{4 x} x^3 \log (x)}{\log ^2\left (\frac {x}{7}\right )}-\frac {4 e^{4 x} x^3 \log (x)}{\log \left (\frac {x}{7}\right )}\right ) \, dx+4 \int \frac {e^{4 x} x^2 \left (-1+\log \left (\frac {x}{7}\right )\right )^3 \left (-4+x+2 \log \left (\frac {x}{7}\right )+3 x \log \left (\frac {x}{7}\right )-x^2 \log \left (\frac {x}{7}\right )-2 \log ^2\left (\frac {x}{7}\right )-3 x \log ^2\left (\frac {x}{7}\right )+x^2 \log ^2\left (\frac {x}{7}\right )\right ) \log ^2(x)}{\log ^5\left (\frac {x}{7}\right )} \, dx-16 \int \frac {e^{4 x} x \left (-1+\log \left (\frac {x}{7}\right )\right )^3 \left (-4+x+2 \log \left (\frac {x}{7}\right )+3 x \log \left (\frac {x}{7}\right )-x^2 \log \left (\frac {x}{7}\right )-2 \log ^2\left (\frac {x}{7}\right )-3 x \log ^2\left (\frac {x}{7}\right )+x^2 \log ^2\left (\frac {x}{7}\right )\right ) \log ^2(x)}{\log ^5\left (\frac {x}{7}\right )} \, dx-16 \int \left (e^{4 x} x^2 \log (x)+\frac {e^{4 x} x^2 \log (x)}{\log ^4\left (\frac {x}{7}\right )}-\frac {4 e^{4 x} x^2 \log (x)}{\log ^3\left (\frac {x}{7}\right )}+\frac {6 e^{4 x} x^2 \log (x)}{\log ^2\left (\frac {x}{7}\right )}-\frac {4 e^{4 x} x^2 \log (x)}{\log \left (\frac {x}{7}\right )}\right ) \, dx+32 \int \left (e^{4 x} x \log (x)+\frac {e^{4 x} x \log (x)}{\log ^4\left (\frac {x}{7}\right )}-\frac {4 e^{4 x} x \log (x)}{\log ^3\left (\frac {x}{7}\right )}+\frac {6 e^{4 x} x \log (x)}{\log ^2\left (\frac {x}{7}\right )}-\frac {4 e^{4 x} x \log (x)}{\log \left (\frac {x}{7}\right )}\right ) \, dx\\ &=2 \int e^{4 x} x^3 \log (x) \, dx+2 \int \frac {e^{4 x} x^3 \log (x)}{\log ^4\left (\frac {x}{7}\right )} \, dx+4 \int \frac {e^{4 x} x^2 \left (1-\log \left (\frac {x}{7}\right )\right )^3 \left (4-x-\left (2+3 x-x^2\right ) \log \left (\frac {x}{7}\right )-\left (-2-3 x+x^2\right ) \log ^2\left (\frac {x}{7}\right )\right ) \log ^2(x)}{\log ^5\left (\frac {x}{7}\right )} \, dx-8 \int \frac {e^{4 x} x^3 \log (x)}{\log ^3\left (\frac {x}{7}\right )} \, dx-8 \int \frac {e^{4 x} x^3 \log (x)}{\log \left (\frac {x}{7}\right )} \, dx+12 \int \frac {e^{4 x} x^3 \log (x)}{\log ^2\left (\frac {x}{7}\right )} \, dx-16 \int e^{4 x} x^2 \log (x) \, dx-16 \int \frac {e^{4 x} x^2 \log (x)}{\log ^4\left (\frac {x}{7}\right )} \, dx-16 \int \frac {e^{4 x} x \left (1-\log \left (\frac {x}{7}\right )\right )^3 \left (4-x-\left (2+3 x-x^2\right ) \log \left (\frac {x}{7}\right )-\left (-2-3 x+x^2\right ) \log ^2\left (\frac {x}{7}\right )\right ) \log ^2(x)}{\log ^5\left (\frac {x}{7}\right )} \, dx+32 \int e^{4 x} x \log (x) \, dx+32 \int \frac {e^{4 x} x \log (x)}{\log ^4\left (\frac {x}{7}\right )} \, dx+64 \int \frac {e^{4 x} x^2 \log (x)}{\log ^3\left (\frac {x}{7}\right )} \, dx+64 \int \frac {e^{4 x} x^2 \log (x)}{\log \left (\frac {x}{7}\right )} \, dx-96 \int \frac {e^{4 x} x^2 \log (x)}{\log ^2\left (\frac {x}{7}\right )} \, dx-128 \int \frac {e^{4 x} x \log (x)}{\log ^3\left (\frac {x}{7}\right )} \, dx-128 \int \frac {e^{4 x} x \log (x)}{\log \left (\frac {x}{7}\right )} \, dx+192 \int \frac {e^{4 x} x \log (x)}{\log ^2\left (\frac {x}{7}\right )} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.24, size = 36, normalized size = 1.03 \begin {gather*} \frac {e^{4 x} (-4+x)^2 x^2 \left (-1+\log \left (\frac {x}{7}\right )\right )^4 \log ^2(x)}{\log ^4\left (\frac {x}{7}\right )} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[((E^(4*x)*(32*x - 16*x^2 + 2*x^3)*Log[x/7] + E^(4*x)*(-128*x + 64*x^2 - 8*x^3)*Log[x/7]^2 + E^(4*x)*
(192*x - 96*x^2 + 12*x^3)*Log[x/7]^3 + E^(4*x)*(-128*x + 64*x^2 - 8*x^3)*Log[x/7]^4 + E^(4*x)*(32*x - 16*x^2 +
 2*x^3)*Log[x/7]^5)*Log[x] + (E^(4*x)*(-64*x + 32*x^2 - 4*x^3) + E^(4*x)*(224*x - 56*x^2 - 16*x^3 + 4*x^4)*Log
[x/7] + E^(4*x)*(-320*x - 64*x^2 + 100*x^3 - 16*x^4)*Log[x/7]^2 + E^(4*x)*(256*x + 208*x^2 - 164*x^3 + 24*x^4)
*Log[x/7]^3 + E^(4*x)*(-128*x - 160*x^2 + 112*x^3 - 16*x^4)*Log[x/7]^4 + E^(4*x)*(32*x + 40*x^2 - 28*x^3 + 4*x
^4)*Log[x/7]^5)*Log[x]^2)/Log[x/7]^5,x]

[Out]

(E^(4*x)*(-4 + x)^2*x^2*(-1 + Log[x/7])^4*Log[x]^2)/Log[x/7]^4

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fricas [B]  time = 0.68, size = 341, normalized size = 9.74 \begin {gather*} \frac {{\left (x^{4} - 8 \, x^{3} + 16 \, x^{2}\right )} e^{\left (4 \, x\right )} \log \left (\frac {1}{7} \, x\right )^{6} - 2 \, {\left (2 \, x^{4} - 16 \, x^{3} + 32 \, x^{2} - {\left (x^{4} - 8 \, x^{3} + 16 \, x^{2}\right )} \log \relax (7)\right )} e^{\left (4 \, x\right )} \log \left (\frac {1}{7} \, x\right )^{5} + {\left (6 \, x^{4} - 48 \, x^{3} + {\left (x^{4} - 8 \, x^{3} + 16 \, x^{2}\right )} \log \relax (7)^{2} + 96 \, x^{2} - 8 \, {\left (x^{4} - 8 \, x^{3} + 16 \, x^{2}\right )} \log \relax (7)\right )} e^{\left (4 \, x\right )} \log \left (\frac {1}{7} \, x\right )^{4} - 4 \, {\left (x^{4} - 8 \, x^{3} + {\left (x^{4} - 8 \, x^{3} + 16 \, x^{2}\right )} \log \relax (7)^{2} + 16 \, x^{2} - 3 \, {\left (x^{4} - 8 \, x^{3} + 16 \, x^{2}\right )} \log \relax (7)\right )} e^{\left (4 \, x\right )} \log \left (\frac {1}{7} \, x\right )^{3} + {\left (x^{4} - 8 \, x^{3} + 16 \, x^{2}\right )} e^{\left (4 \, x\right )} \log \relax (7)^{2} + {\left (x^{4} - 8 \, x^{3} + 6 \, {\left (x^{4} - 8 \, x^{3} + 16 \, x^{2}\right )} \log \relax (7)^{2} + 16 \, x^{2} - 8 \, {\left (x^{4} - 8 \, x^{3} + 16 \, x^{2}\right )} \log \relax (7)\right )} e^{\left (4 \, x\right )} \log \left (\frac {1}{7} \, x\right )^{2} - 2 \, {\left (2 \, {\left (x^{4} - 8 \, x^{3} + 16 \, x^{2}\right )} \log \relax (7)^{2} - {\left (x^{4} - 8 \, x^{3} + 16 \, x^{2}\right )} \log \relax (7)\right )} e^{\left (4 \, x\right )} \log \left (\frac {1}{7} \, x\right )}{\log \left (\frac {1}{7} \, x\right )^{4}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((4*x^4-28*x^3+40*x^2+32*x)*exp(x)^4*log(1/7*x)^5+(-16*x^4+112*x^3-160*x^2-128*x)*exp(x)^4*log(1/7*
x)^4+(24*x^4-164*x^3+208*x^2+256*x)*exp(x)^4*log(1/7*x)^3+(-16*x^4+100*x^3-64*x^2-320*x)*exp(x)^4*log(1/7*x)^2
+(4*x^4-16*x^3-56*x^2+224*x)*exp(x)^4*log(1/7*x)+(-4*x^3+32*x^2-64*x)*exp(x)^4)*log(x)^2+((2*x^3-16*x^2+32*x)*
exp(x)^4*log(1/7*x)^5+(-8*x^3+64*x^2-128*x)*exp(x)^4*log(1/7*x)^4+(12*x^3-96*x^2+192*x)*exp(x)^4*log(1/7*x)^3+
(-8*x^3+64*x^2-128*x)*exp(x)^4*log(1/7*x)^2+(2*x^3-16*x^2+32*x)*exp(x)^4*log(1/7*x))*log(x))/log(1/7*x)^5,x, a
lgorithm="fricas")

[Out]

((x^4 - 8*x^3 + 16*x^2)*e^(4*x)*log(1/7*x)^6 - 2*(2*x^4 - 16*x^3 + 32*x^2 - (x^4 - 8*x^3 + 16*x^2)*log(7))*e^(
4*x)*log(1/7*x)^5 + (6*x^4 - 48*x^3 + (x^4 - 8*x^3 + 16*x^2)*log(7)^2 + 96*x^2 - 8*(x^4 - 8*x^3 + 16*x^2)*log(
7))*e^(4*x)*log(1/7*x)^4 - 4*(x^4 - 8*x^3 + (x^4 - 8*x^3 + 16*x^2)*log(7)^2 + 16*x^2 - 3*(x^4 - 8*x^3 + 16*x^2
)*log(7))*e^(4*x)*log(1/7*x)^3 + (x^4 - 8*x^3 + 16*x^2)*e^(4*x)*log(7)^2 + (x^4 - 8*x^3 + 6*(x^4 - 8*x^3 + 16*
x^2)*log(7)^2 + 16*x^2 - 8*(x^4 - 8*x^3 + 16*x^2)*log(7))*e^(4*x)*log(1/7*x)^2 - 2*(2*(x^4 - 8*x^3 + 16*x^2)*l
og(7)^2 - (x^4 - 8*x^3 + 16*x^2)*log(7))*e^(4*x)*log(1/7*x))/log(1/7*x)^4

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giac [B]  time = 0.99, size = 717, normalized size = 20.49 result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((4*x^4-28*x^3+40*x^2+32*x)*exp(x)^4*log(1/7*x)^5+(-16*x^4+112*x^3-160*x^2-128*x)*exp(x)^4*log(1/7*
x)^4+(24*x^4-164*x^3+208*x^2+256*x)*exp(x)^4*log(1/7*x)^3+(-16*x^4+100*x^3-64*x^2-320*x)*exp(x)^4*log(1/7*x)^2
+(4*x^4-16*x^3-56*x^2+224*x)*exp(x)^4*log(1/7*x)+(-4*x^3+32*x^2-64*x)*exp(x)^4)*log(x)^2+((2*x^3-16*x^2+32*x)*
exp(x)^4*log(1/7*x)^5+(-8*x^3+64*x^2-128*x)*exp(x)^4*log(1/7*x)^4+(12*x^3-96*x^2+192*x)*exp(x)^4*log(1/7*x)^3+
(-8*x^3+64*x^2-128*x)*exp(x)^4*log(1/7*x)^2+(2*x^3-16*x^2+32*x)*exp(x)^4*log(1/7*x))*log(x))/log(1/7*x)^5,x, a
lgorithm="giac")

[Out]

(x^4*e^(4*x)*log(7)^4*log(x)^2 - 4*x^4*e^(4*x)*log(7)^3*log(x)^3 + 6*x^4*e^(4*x)*log(7)^2*log(x)^4 - 4*x^4*e^(
4*x)*log(7)*log(x)^5 + x^4*e^(4*x)*log(x)^6 + 4*x^4*e^(4*x)*log(7)^3*log(x)^2 - 8*x^3*e^(4*x)*log(7)^4*log(x)^
2 - 12*x^4*e^(4*x)*log(7)^2*log(x)^3 + 32*x^3*e^(4*x)*log(7)^3*log(x)^3 + 12*x^4*e^(4*x)*log(7)*log(x)^4 - 48*
x^3*e^(4*x)*log(7)^2*log(x)^4 - 4*x^4*e^(4*x)*log(x)^5 + 32*x^3*e^(4*x)*log(7)*log(x)^5 - 8*x^3*e^(4*x)*log(x)
^6 + 6*x^4*e^(4*x)*log(7)^2*log(x)^2 - 32*x^3*e^(4*x)*log(7)^3*log(x)^2 + 16*x^2*e^(4*x)*log(7)^4*log(x)^2 - 1
2*x^4*e^(4*x)*log(7)*log(x)^3 + 96*x^3*e^(4*x)*log(7)^2*log(x)^3 - 64*x^2*e^(4*x)*log(7)^3*log(x)^3 + 6*x^4*e^
(4*x)*log(x)^4 - 96*x^3*e^(4*x)*log(7)*log(x)^4 + 96*x^2*e^(4*x)*log(7)^2*log(x)^4 + 32*x^3*e^(4*x)*log(x)^5 -
 64*x^2*e^(4*x)*log(7)*log(x)^5 + 16*x^2*e^(4*x)*log(x)^6 + 4*x^4*e^(4*x)*log(7)*log(x)^2 - 48*x^3*e^(4*x)*log
(7)^2*log(x)^2 + 64*x^2*e^(4*x)*log(7)^3*log(x)^2 - 4*x^4*e^(4*x)*log(x)^3 + 96*x^3*e^(4*x)*log(7)*log(x)^3 -
192*x^2*e^(4*x)*log(7)^2*log(x)^3 - 48*x^3*e^(4*x)*log(x)^4 + 192*x^2*e^(4*x)*log(7)*log(x)^4 - 64*x^2*e^(4*x)
*log(x)^5 + x^4*e^(4*x)*log(x)^2 - 32*x^3*e^(4*x)*log(7)*log(x)^2 + 96*x^2*e^(4*x)*log(7)^2*log(x)^2 + 32*x^3*
e^(4*x)*log(x)^3 - 192*x^2*e^(4*x)*log(7)*log(x)^3 + 96*x^2*e^(4*x)*log(x)^4 - 8*x^3*e^(4*x)*log(x)^2 + 64*x^2
*e^(4*x)*log(7)*log(x)^2 - 64*x^2*e^(4*x)*log(x)^3 + 16*x^2*e^(4*x)*log(x)^2)/(log(7)^4 - 4*log(7)^3*log(x) +
6*log(7)^2*log(x)^2 - 4*log(7)*log(x)^3 + log(x)^4)

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maple [B]  time = 4.19, size = 407, normalized size = 11.63

method result size
risch \(x^{2} \left (x^{2}-8 x +16\right ) {\mathrm e}^{4 x} \ln \relax (x )^{2}-4 x^{2} \left (x^{2}-8 x +16\right ) {\mathrm e}^{4 x} \ln \relax (x )-2 \left (32 x^{2} \ln \relax (7)-48 x^{2}-16 \ln \relax (7) x^{3}+24 x^{3}+2 \ln \relax (7) x^{4}-3 x^{4}\right ) {\mathrm e}^{4 x}+\frac {2 x^{2} {\mathrm e}^{4 x} \left (384 x \ln \relax (7)^{4}+256 x \ln \relax (x )^{3}+8 x^{2} \ln \relax (x )^{2}-512 \ln \relax (x )^{3}+128 \ln \relax (x )^{2}-64 x \ln \relax (x )^{2}-768 \ln \relax (7)^{4}-32 x^{2} \ln \relax (x )^{3}+32 \ln \relax (7)^{5} x^{2}-256 \ln \relax (7)^{5} x -48 \ln \relax (7)^{4} x^{2}-3840 \ln \relax (7)^{2} \ln \relax (x )^{2}+512 \ln \relax (7) \ln \relax (x )^{2}-1536 \ln \relax (7)^{4} \ln \relax (x )+1536 \ln \relax (7)^{3} \ln \relax (x )^{2}-512 \ln \relax (7)^{2} \ln \relax (x )^{3}+3072 \ln \relax (7)^{3} \ln \relax (x )+1536 \ln \relax (7) \ln \relax (x )^{3}+512 \ln \relax (7)^{5}-96 \ln \relax (7)^{4} x^{2} \ln \relax (x )+96 \ln \relax (7)^{3} x^{2} \ln \relax (x )^{2}-32 \ln \relax (7)^{2} x^{2} \ln \relax (x )^{3}+768 \ln \relax (7)^{4} x \ln \relax (x )-768 \ln \relax (7)^{3} x \ln \relax (x )^{2}+256 \ln \relax (7)^{2} x \ln \relax (x )^{3}-240 \ln \relax (7)^{2} x^{2} \ln \relax (x )^{2}+1920 \ln \relax (7)^{2} x \ln \relax (x )^{2}+192 \ln \relax (7)^{3} x^{2} \ln \relax (x )-1536 \ln \relax (7)^{3} x \ln \relax (x )+96 \ln \relax (7) x^{2} \ln \relax (x )^{3}-768 \ln \relax (7) x \ln \relax (x )^{3}+32 \ln \relax (7) x^{2} \ln \relax (x )^{2}-256 \ln \relax (7) x \ln \relax (x )^{2}\right )}{\left (2 \ln \relax (7)-2 \ln \relax (x )\right )^{4}}\) \(407\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((4*x^4-28*x^3+40*x^2+32*x)*exp(x)^4*ln(1/7*x)^5+(-16*x^4+112*x^3-160*x^2-128*x)*exp(x)^4*ln(1/7*x)^4+(24
*x^4-164*x^3+208*x^2+256*x)*exp(x)^4*ln(1/7*x)^3+(-16*x^4+100*x^3-64*x^2-320*x)*exp(x)^4*ln(1/7*x)^2+(4*x^4-16
*x^3-56*x^2+224*x)*exp(x)^4*ln(1/7*x)+(-4*x^3+32*x^2-64*x)*exp(x)^4)*ln(x)^2+((2*x^3-16*x^2+32*x)*exp(x)^4*ln(
1/7*x)^5+(-8*x^3+64*x^2-128*x)*exp(x)^4*ln(1/7*x)^4+(12*x^3-96*x^2+192*x)*exp(x)^4*ln(1/7*x)^3+(-8*x^3+64*x^2-
128*x)*exp(x)^4*ln(1/7*x)^2+(2*x^3-16*x^2+32*x)*exp(x)^4*ln(1/7*x))*ln(x))/ln(1/7*x)^5,x,method=_RETURNVERBOSE
)

[Out]

x^2*(x^2-8*x+16)*exp(4*x)*ln(x)^2-4*x^2*(x^2-8*x+16)*exp(4*x)*ln(x)-2*(32*x^2*ln(7)-48*x^2-16*ln(7)*x^3+24*x^3
+2*ln(7)*x^4-3*x^4)*exp(4*x)+2*x^2*exp(4*x)*(384*x*ln(7)^4+256*x*ln(x)^3+8*x^2*ln(x)^2-512*ln(x)^3+128*ln(x)^2
-64*x*ln(x)^2-768*ln(7)^4-32*x^2*ln(x)^3+32*ln(7)^5*x^2-256*ln(7)^5*x-48*ln(7)^4*x^2-3840*ln(7)^2*ln(x)^2+512*
ln(7)*ln(x)^2-1536*ln(7)^4*ln(x)+1536*ln(7)^3*ln(x)^2-512*ln(7)^2*ln(x)^3+3072*ln(7)^3*ln(x)+1536*ln(7)*ln(x)^
3+512*ln(7)^5-96*ln(7)^4*x^2*ln(x)+96*ln(7)^3*x^2*ln(x)^2-32*ln(7)^2*x^2*ln(x)^3+768*ln(7)^4*x*ln(x)-768*ln(7)
^3*x*ln(x)^2+256*ln(7)^2*x*ln(x)^3-240*ln(7)^2*x^2*ln(x)^2+1920*ln(7)^2*x*ln(x)^2+192*ln(7)^3*x^2*ln(x)-1536*l
n(7)^3*x*ln(x)+96*ln(7)*x^2*ln(x)^3-768*ln(7)*x*ln(x)^3+32*ln(7)*x^2*ln(x)^2-256*ln(7)*x*ln(x)^2)/(2*ln(7)-2*l
n(x))^4

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maxima [B]  time = 0.96, size = 301, normalized size = 8.60 \begin {gather*} \frac {{\left ({\left (x^{4} - 8 \, x^{3} + 16 \, x^{2}\right )} \log \relax (x)^{6} - 4 \, {\left (x^{4} {\left (\log \relax (7) + 1\right )} - 8 \, x^{3} {\left (\log \relax (7) + 1\right )} + 16 \, x^{2} {\left (\log \relax (7) + 1\right )}\right )} \log \relax (x)^{5} + 6 \, {\left ({\left (\log \relax (7)^{2} + 2 \, \log \relax (7) + 1\right )} x^{4} - 8 \, {\left (\log \relax (7)^{2} + 2 \, \log \relax (7) + 1\right )} x^{3} + 16 \, {\left (\log \relax (7)^{2} + 2 \, \log \relax (7) + 1\right )} x^{2}\right )} \log \relax (x)^{4} - 4 \, {\left ({\left (\log \relax (7)^{3} + 3 \, \log \relax (7)^{2} + 3 \, \log \relax (7) + 1\right )} x^{4} - 8 \, {\left (\log \relax (7)^{3} + 3 \, \log \relax (7)^{2} + 3 \, \log \relax (7) + 1\right )} x^{3} + 16 \, {\left (\log \relax (7)^{3} + 3 \, \log \relax (7)^{2} + 3 \, \log \relax (7) + 1\right )} x^{2}\right )} \log \relax (x)^{3} + {\left ({\left (\log \relax (7)^{4} + 4 \, \log \relax (7)^{3} + 6 \, \log \relax (7)^{2} + 4 \, \log \relax (7) + 1\right )} x^{4} - 8 \, {\left (\log \relax (7)^{4} + 4 \, \log \relax (7)^{3} + 6 \, \log \relax (7)^{2} + 4 \, \log \relax (7) + 1\right )} x^{3} + 16 \, {\left (\log \relax (7)^{4} + 4 \, \log \relax (7)^{3} + 6 \, \log \relax (7)^{2} + 4 \, \log \relax (7) + 1\right )} x^{2}\right )} \log \relax (x)^{2}\right )} e^{\left (4 \, x\right )}}{\log \relax (7)^{4} - 4 \, \log \relax (7)^{3} \log \relax (x) + 6 \, \log \relax (7)^{2} \log \relax (x)^{2} - 4 \, \log \relax (7) \log \relax (x)^{3} + \log \relax (x)^{4}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((4*x^4-28*x^3+40*x^2+32*x)*exp(x)^4*log(1/7*x)^5+(-16*x^4+112*x^3-160*x^2-128*x)*exp(x)^4*log(1/7*
x)^4+(24*x^4-164*x^3+208*x^2+256*x)*exp(x)^4*log(1/7*x)^3+(-16*x^4+100*x^3-64*x^2-320*x)*exp(x)^4*log(1/7*x)^2
+(4*x^4-16*x^3-56*x^2+224*x)*exp(x)^4*log(1/7*x)+(-4*x^3+32*x^2-64*x)*exp(x)^4)*log(x)^2+((2*x^3-16*x^2+32*x)*
exp(x)^4*log(1/7*x)^5+(-8*x^3+64*x^2-128*x)*exp(x)^4*log(1/7*x)^4+(12*x^3-96*x^2+192*x)*exp(x)^4*log(1/7*x)^3+
(-8*x^3+64*x^2-128*x)*exp(x)^4*log(1/7*x)^2+(2*x^3-16*x^2+32*x)*exp(x)^4*log(1/7*x))*log(x))/log(1/7*x)^5,x, a
lgorithm="maxima")

[Out]

((x^4 - 8*x^3 + 16*x^2)*log(x)^6 - 4*(x^4*(log(7) + 1) - 8*x^3*(log(7) + 1) + 16*x^2*(log(7) + 1))*log(x)^5 +
6*((log(7)^2 + 2*log(7) + 1)*x^4 - 8*(log(7)^2 + 2*log(7) + 1)*x^3 + 16*(log(7)^2 + 2*log(7) + 1)*x^2)*log(x)^
4 - 4*((log(7)^3 + 3*log(7)^2 + 3*log(7) + 1)*x^4 - 8*(log(7)^3 + 3*log(7)^2 + 3*log(7) + 1)*x^3 + 16*(log(7)^
3 + 3*log(7)^2 + 3*log(7) + 1)*x^2)*log(x)^3 + ((log(7)^4 + 4*log(7)^3 + 6*log(7)^2 + 4*log(7) + 1)*x^4 - 8*(l
og(7)^4 + 4*log(7)^3 + 6*log(7)^2 + 4*log(7) + 1)*x^3 + 16*(log(7)^4 + 4*log(7)^3 + 6*log(7)^2 + 4*log(7) + 1)
*x^2)*log(x)^2)*e^(4*x)/(log(7)^4 - 4*log(7)^3*log(x) + 6*log(7)^2*log(x)^2 - 4*log(7)*log(x)^3 + log(x)^4)

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mupad [B]  time = 3.66, size = 6440, normalized size = 184.00 result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(log(x)^2*(exp(4*x)*(64*x - 32*x^2 + 4*x^3) - log(x/7)^5*exp(4*x)*(32*x + 40*x^2 - 28*x^3 + 4*x^4) + log(
x/7)^4*exp(4*x)*(128*x + 160*x^2 - 112*x^3 + 16*x^4) + log(x/7)^2*exp(4*x)*(320*x + 64*x^2 - 100*x^3 + 16*x^4)
 - log(x/7)^3*exp(4*x)*(256*x + 208*x^2 - 164*x^3 + 24*x^4) - log(x/7)*exp(4*x)*(224*x - 56*x^2 - 16*x^3 + 4*x
^4)) - log(x)*(log(x/7)*exp(4*x)*(32*x - 16*x^2 + 2*x^3) + log(x/7)^5*exp(4*x)*(32*x - 16*x^2 + 2*x^3) - log(x
/7)^2*exp(4*x)*(128*x - 64*x^2 + 8*x^3) - log(x/7)^4*exp(4*x)*(128*x - 64*x^2 + 8*x^3) + log(x/7)^3*exp(4*x)*(
192*x - 96*x^2 + 12*x^3)))/log(x/7)^5,x)

[Out]

exp(4*x)*(x^6*(32*log(7) - 240*log(7)^2 - 992*log(7)^3 + 1220*log(7)^4 - (1352*log(7)^5)/3 + 8) - x^5*(136*log
(7) - 1364*log(7)^2 + 1624*log(7)^3 + 313*log(7)^4 - 566*log(7)^5 + 62) - x^4*(244*log(7) + 608*log(7)^2 - 502
4*log(7)^3 + 4552*log(7)^4 - 1456*log(7)^5 - 142) + x^3*(1008*log(7) - 3880*log(7)^2 + 5488*log(7)^3 - 2878*lo
g(7)^4 + (1756*log(7)^5)/3 - 84) + (64*x^8*log(7)^4*(2*log(7) - 3))/3 + (64*x^2*log(7)*(42*log(7)^2 - 51*log(7
) - 15*log(7)^3 + 2*log(7)^4 + 21))/3 + (32*x^7*log(7)^3*(3*log(7) - 10*log(7)^2 + 24))/3) - ((2*x*log(x)^4*(6
4*x*exp(4*x) + 878*x^2*exp(4*x) + 2184*x^3*exp(4*x) + 849*x^4*exp(4*x) - 676*x^5*exp(4*x) - 160*x^6*exp(4*x) +
 64*x^7*exp(4*x) + 878*x^2*exp(4*x)*log(7)^2 + 2184*x^3*exp(4*x)*log(7)^2 + 849*x^4*exp(4*x)*log(7)^2 - 676*x^
5*exp(4*x)*log(7)^2 - 160*x^6*exp(4*x)*log(7)^2 + 64*x^7*exp(4*x)*log(7)^2 - 192*x*exp(4*x)*log(7) + 64*x*exp(
4*x)*log(7)^2 - 2634*x^2*exp(4*x)*log(7) - 6552*x^3*exp(4*x)*log(7) - 2547*x^4*exp(4*x)*log(7) + 2028*x^5*exp(
4*x)*log(7) + 480*x^6*exp(4*x)*log(7) - 192*x^7*exp(4*x)*log(7)))/3 - (x*(24*x*exp(4*x) - 54*x^2*exp(4*x) + 24
*x^3*exp(4*x) - 3*x^4*exp(4*x) - 2052*x^2*exp(4*x)*log(7)^2 + 9048*x^2*exp(4*x)*log(7)^3 + 93*x^3*exp(4*x)*log
(7)^2 - 14598*x^2*exp(4*x)*log(7)^4 + 1644*x^3*exp(4*x)*log(7)^3 + 498*x^4*exp(4*x)*log(7)^2 + 8134*x^2*exp(4*
x)*log(7)^5 - 13968*x^3*exp(4*x)*log(7)^4 - 3300*x^4*exp(4*x)*log(7)^3 - 96*x^5*exp(4*x)*log(7)^2 - 1756*x^2*e
xp(4*x)*log(7)^6 + 13064*x^3*exp(4*x)*log(7)^5 + 4257*x^4*exp(4*x)*log(7)^4 + 576*x^5*exp(4*x)*log(7)^3 - 4368
*x^3*exp(4*x)*log(7)^6 + 1073*x^4*exp(4*x)*log(7)^5 + 2844*x^5*exp(4*x)*log(7)^4 - 1698*x^4*exp(4*x)*log(7)^6
- 3524*x^5*exp(4*x)*log(7)^5 - 720*x^6*exp(4*x)*log(7)^4 + 1352*x^5*exp(4*x)*log(7)^6 - 128*x^6*exp(4*x)*log(7
)^5 + 320*x^6*exp(4*x)*log(7)^6 + 192*x^7*exp(4*x)*log(7)^5 - 128*x^7*exp(4*x)*log(7)^6 + 48*x*exp(4*x)*log(7)
 - 768*x*exp(4*x)*log(7)^2 + 60*x^2*exp(4*x)*log(7) + 2400*x*exp(4*x)*log(7)^3 - 333*x^3*exp(4*x)*log(7) - 230
4*x*exp(4*x)*log(7)^4 + 174*x^4*exp(4*x)*log(7) + 896*x*exp(4*x)*log(7)^5 - 24*x^5*exp(4*x)*log(7) - 128*x*exp
(4*x)*log(7)^6))/3 + (x*log(x)^2*(1504*x*exp(4*x) + 4946*x^2*exp(4*x) - 776*x^3*exp(4*x) - 2015*x^4*exp(4*x) +
 908*x^5*exp(4*x) - 112*x^6*exp(4*x) + 98708*x^2*exp(4*x)*log(7)^2 - 80412*x^2*exp(4*x)*log(7)^3 + 114816*x^3*
exp(4*x)*log(7)^2 + 21072*x^2*exp(4*x)*log(7)^4 - 157008*x^3*exp(4*x)*log(7)^3 - 22806*x^4*exp(4*x)*log(7)^2 +
 52416*x^3*exp(4*x)*log(7)^4 - 37002*x^4*exp(4*x)*log(7)^3 - 26344*x^5*exp(4*x)*log(7)^2 + 20376*x^4*exp(4*x)*
log(7)^4 + 45480*x^5*exp(4*x)*log(7)^3 + 5024*x^6*exp(4*x)*log(7)^2 - 16224*x^5*exp(4*x)*log(7)^4 + 6528*x^6*e
xp(4*x)*log(7)^3 + 256*x^7*exp(4*x)*log(7)^2 - 3840*x^6*exp(4*x)*log(7)^4 - 3456*x^7*exp(4*x)*log(7)^3 + 1536*
x^7*exp(4*x)*log(7)^4 - 7552*x*exp(4*x)*log(7) + 13312*x*exp(4*x)*log(7)^2 - 38210*x^2*exp(4*x)*log(7) - 7680*
x*exp(4*x)*log(7)^3 - 24200*x^3*exp(4*x)*log(7) + 1536*x*exp(4*x)*log(7)^4 + 13393*x^4*exp(4*x)*log(7) + 3196*
x^5*exp(4*x)*log(7) - 1376*x^6*exp(4*x)*log(7) + 64*x^7*exp(4*x)*log(7)))/6 - (x*log(x)^3*(3797*x^4*exp(4*x) -
 10122*x^2*exp(4*x) - 10840*x^3*exp(4*x) - 1344*x*exp(4*x) + 2316*x^5*exp(4*x) - 864*x^6*exp(4*x) + 64*x^7*exp
(4*x) - 47876*x^2*exp(4*x)*log(7)^2 + 14048*x^2*exp(4*x)*log(7)^3 - 104752*x^3*exp(4*x)*log(7)^2 + 34944*x^3*e
xp(4*x)*log(7)^3 - 32710*x^4*exp(4*x)*log(7)^2 + 13584*x^4*exp(4*x)*log(7)^3 + 31384*x^5*exp(4*x)*log(7)^2 - 1
0816*x^5*exp(4*x)*log(7)^3 + 6016*x^6*exp(4*x)*log(7)^2 - 2560*x^6*exp(4*x)*log(7)^3 - 2688*x^7*exp(4*x)*log(7
)^2 + 1024*x^7*exp(4*x)*log(7)^3 + 4736*x*exp(4*x)*log(7) - 4096*x*exp(4*x)*log(7)^2 + 40024*x^2*exp(4*x)*log(
7) + 1024*x*exp(4*x)*log(7)^3 + 56544*x^3*exp(4*x)*log(7) - 2052*x^4*exp(4*x)*log(7) - 14384*x^5*exp(4*x)*log(
7) + 832*x^6*exp(4*x)*log(7) + 512*x^7*exp(4*x)*log(7)))/6 + (x*log(x)*(48*x*exp(4*x) - 66*x^2*exp(4*x) - 120*
x^3*exp(4*x) + 81*x^4*exp(4*x) - 12*x^5*exp(4*x) + 23092*x^2*exp(4*x)*log(7)^2 - 45696*x^2*exp(4*x)*log(7)^3 +
 8324*x^3*exp(4*x)*log(7)^2 + 29670*x^2*exp(4*x)*log(7)^4 - 47472*x^3*exp(4*x)*log(7)^3 - 8098*x^4*exp(4*x)*lo
g(7)^2 - 7024*x^2*exp(4*x)*log(7)^5 + 52296*x^3*exp(4*x)*log(7)^4 + 12936*x^4*exp(4*x)*log(7)^3 + 136*x^5*exp(
4*x)*log(7)^2 - 17472*x^3*exp(4*x)*log(7)^5 + 8313*x^4*exp(4*x)*log(7)^4 + 10176*x^5*exp(4*x)*log(7)^3 + 256*x
^6*exp(4*x)*log(7)^2 - 6792*x^4*exp(4*x)*log(7)^5 - 14628*x^5*exp(4*x)*log(7)^4 - 2496*x^6*exp(4*x)*log(7)^3 +
 5408*x^5*exp(4*x)*log(7)^5 - 1344*x^6*exp(4*x)*log(7)^4 + 1280*x^6*exp(4*x)*log(7)^5 + 960*x^7*exp(4*x)*log(7
)^4 - 512*x^7*exp(4*x)*log(7)^5 - 1504*x*exp(4*x)*log(7) + 5504*x*exp(4*x)*log(7)^2 - 4568*x^2*exp(4*x)*log(7)
 - 6720*x*exp(4*x)*log(7)^3 + 428*x^3*exp(4*x)*log(7) + 3072*x*exp(4*x)*log(7)^4 + 1628*x^4*exp(4*x)*log(7) -
512*x*exp(4*x)*log(7)^5 - 608*x^5*exp(4*x)*log(7) + 64*x^6*exp(4*x)*log(7)))/3)/(log(7) - log(x)) - ((x*(4*x^3
*exp(4*x)*log(7)^2 - 48*x^2*exp(4*x)*log(7)^3 - 32*x^2*exp(4*x)*log(7)^2 + 648*x^2*exp(4*x)*log(7)^4 + 6*x^3*e
xp(4*x)*log(7)^3 - 984*x^2*exp(4*x)*log(7)^5 - 426*x^3*exp(4*x)*log(7)^4 + 496*x^2*exp(4*x)*log(7)^6 + 24*x^3*
exp(4*x)*log(7)^5 + 60*x^4*exp(4*x)*log(7)^4 + 96*x^3*exp(4*x)*log(7)^6 + 252*x^4*exp(4*x)*log(7)^5 - 184*x^4*
exp(4*x)*log(7)^6 - 48*x^5*exp(4*x)*log(7)^5 + 32*x^5*exp(4*x)*log(7)^6 + 16*x*exp(4*x)*log(7) + 64*x*exp(4*x)
*log(7)^2 - 8*x^2*exp(4*x)*log(7) + 96*x*exp(4*x)*log(7)^3 + x^3*exp(4*x)*log(7) + 384*x*exp(4*x)*log(7)^4 - 3
84*x*exp(4*x)*log(7)^5 + 128*x*exp(4*x)*log(7)^6))/6 + (x*log(x)^3*(80*x*exp(4*x) + 58*x^2*exp(4*x) - 96*x^3*e
xp(4*x) + 35*x^4*exp(4*x) - 4*x^5*exp(4*x) + 2724*x^2*exp(4*x)*log(7)^2 - 992*x^2*exp(4*x)*log(7)^3 + 420*x^3*
exp(4*x)*log(7)^2 - 192*x^3*exp(4*x)*log(7)^3 - 954*x^4*exp(4*x)*log(7)^2 + 368*x^4*exp(4*x)*log(7)^3 + 168*x^
5*exp(4*x)*log(7)^2 - 64*x^5*exp(4*x)*log(7)^3 - 416*x*exp(4*x)*log(7) + 768*x*exp(4*x)*log(7)^2 - 856*x^2*exp
(4*x)*log(7) - 256*x*exp(4*x)*log(7)^3 + 156*x^3*exp(4*x)*log(7) + 148*x^4*exp(4*x)*log(7) - 32*x^5*exp(4*x)*l
og(7)))/3 + (4*x*log(x)^4*(16*x*exp(4*x) + 62*x^2*exp(4*x) + 12*x^3*exp(4*x) - 23*x^4*exp(4*x) + 4*x^5*exp(4*x
) + 62*x^2*exp(4*x)*log(7)^2 + 12*x^3*exp(4*x)*log(7)^2 - 23*x^4*exp(4*x)*log(7)^2 + 4*x^5*exp(4*x)*log(7)^2 -
 48*x*exp(4*x)*log(7) + 16*x*exp(4*x)*log(7)^2 - 186*x^2*exp(4*x)*log(7) - 36*x^3*exp(4*x)*log(7) + 69*x^4*exp
(4*x)*log(7) - 12*x^5*exp(4*x)*log(7)))/3 + (x*log(x)^2*(14*x^2*exp(4*x) - 56*x*exp(4*x) + 4*x^3*exp(4*x) - x^
4*exp(4*x) + 1292*x^2*exp(4*x)*log(7)^2 - 3708*x^2*exp(4*x)*log(7)^3 - 669*x^3*exp(4*x)*log(7)^2 + 1488*x^2*ex
p(4*x)*log(7)^4 - 396*x^3*exp(4*x)*log(7)^3 + 10*x^4*exp(4*x)*log(7)^2 + 288*x^3*exp(4*x)*log(7)^4 + 1206*x^4*
exp(4*x)*log(7)^3 + 16*x^5*exp(4*x)*log(7)^2 - 552*x^4*exp(4*x)*log(7)^4 - 216*x^5*exp(4*x)*log(7)^3 + 96*x^5*
exp(4*x)*log(7)^4 - 64*x*exp(4*x)*log(7) + 832*x*exp(4*x)*log(7)^2 - 290*x^2*exp(4*x)*log(7) - 1152*x*exp(4*x)
*log(7)^3 + 217*x^3*exp(4*x)*log(7) + 384*x*exp(4*x)*log(7)^4 - 51*x^4*exp(4*x)*log(7) + 4*x^5*exp(4*x)*log(7)
))/3 + (x*log(x)*(16*x*exp(4*x) - 8*x^2*exp(4*x) + x^3*exp(4*x) + 256*x^2*exp(4*x)*log(7)^2 - 1008*x^2*exp(4*x
)*log(7)^3 - 124*x^3*exp(4*x)*log(7)^2 + 2220*x^2*exp(4*x)*log(7)^4 + 678*x^3*exp(4*x)*log(7)^3 + 16*x^4*exp(4
*x)*log(7)^2 - 992*x^2*exp(4*x)*log(7)^5 + 108*x^3*exp(4*x)*log(7)^4 - 96*x^4*exp(4*x)*log(7)^3 - 192*x^3*exp(
4*x)*log(7)^5 - 654*x^4*exp(4*x)*log(7)^4 + 368*x^4*exp(4*x)*log(7)^5 + 120*x^5*exp(4*x)*log(7)^4 - 64*x^5*exp
(4*x)*log(7)^5 - 64*x*exp(4*x)*log(7)^2 + 56*x^2*exp(4*x)*log(7) - 672*x*exp(4*x)*log(7)^3 - 30*x^3*exp(4*x)*l
og(7) + 768*x*exp(4*x)*log(7)^4 + 4*x^4*exp(4*x)*log(7) - 256*x*exp(4*x)*log(7)^5))/3)/(3*log(7)*log(x)^2 - 3*
log(7)^2*log(x) - log(x)^3 + log(7)^3) + ((x*log(x)*(4*x^3*exp(4*x)*log(7)^2 - 48*x^2*exp(4*x)*log(7)^3 - 32*x
^2*exp(4*x)*log(7)^2 + 648*x^2*exp(4*x)*log(7)^4 + 6*x^3*exp(4*x)*log(7)^3 - 320*x^2*exp(4*x)*log(7)^5 - 426*x
^3*exp(4*x)*log(7)^4 + 224*x^3*exp(4*x)*log(7)^5 + 60*x^4*exp(4*x)*log(7)^4 - 32*x^4*exp(4*x)*log(7)^5 + 16*x*
exp(4*x)*log(7) + 64*x*exp(4*x)*log(7)^2 - 8*x^2*exp(4*x)*log(7) + 96*x*exp(4*x)*log(7)^3 + x^3*exp(4*x)*log(7
) + 384*x*exp(4*x)*log(7)^4 - 256*x*exp(4*x)*log(7)^5))/2 - x*log(x)^3*(24*x*exp(4*x) + 2*x^2*exp(4*x) - 6*x^3
*exp(4*x) + x^4*exp(4*x) - 428*x^2*exp(4*x)*log(7)^2 + 160*x^2*exp(4*x)*log(7)^3 + 295*x^3*exp(4*x)*log(7)^2 -
 112*x^3*exp(4*x)*log(7)^3 - 42*x^4*exp(4*x)*log(7)^2 + 16*x^4*exp(4*x)*log(7)^3 + 16*x*exp(4*x)*log(7) - 320*
x*exp(4*x)*log(7)^2 + 104*x^2*exp(4*x)*log(7) + 128*x*exp(4*x)*log(7)^3 - 59*x^3*exp(4*x)*log(7) + 8*x^4*exp(4
*x)*log(7)) + (x*log(x)^2*(16*x*exp(4*x) - 8*x^2*exp(4*x) + x^3*exp(4*x) + 176*x^2*exp(4*x)*log(7)^2 - 1128*x^
2*exp(4*x)*log(7)^3 - 68*x^3*exp(4*x)*log(7)^2 + 480*x^2*exp(4*x)*log(7)^4 + 762*x^3*exp(4*x)*log(7)^3 + 8*x^4
*exp(4*x)*log(7)^2 - 336*x^3*exp(4*x)*log(7)^4 - 108*x^4*exp(4*x)*log(7)^3 + 48*x^4*exp(4*x)*log(7)^4 - 16*x*e
xp(4*x)*log(7) - 128*x*exp(4*x)*log(7)^2 + 36*x^2*exp(4*x)*log(7) - 768*x*exp(4*x)*log(7)^3 - 16*x^3*exp(4*x)*
log(7) + 384*x*exp(4*x)*log(7)^4 + 2*x^4*exp(4*x)*log(7)))/2 - x*log(7)^5*(32*x*exp(4*x) + 68*x^2*exp(4*x) - 4
3*x^3*exp(4*x) + 6*x^4*exp(4*x) - 32*x*exp(4*x)*log(7) - 40*x^2*exp(4*x)*log(7) + 28*x^3*exp(4*x)*log(7) - 4*x
^4*exp(4*x)*log(7)) + 4*x*log(x)^4*(8*x*exp(4*x) + 10*x^2*exp(4*x) - 7*x^3*exp(4*x) + x^4*exp(4*x) + 10*x^2*ex
p(4*x)*log(7)^2 - 7*x^3*exp(4*x)*log(7)^2 + x^4*exp(4*x)*log(7)^2 - 24*x*exp(4*x)*log(7) + 8*x*exp(4*x)*log(7)
^2 - 30*x^2*exp(4*x)*log(7) + 21*x^3*exp(4*x)*log(7) - 3*x^4*exp(4*x)*log(7)))/(log(x)^4 - 4*log(7)^3*log(x) -
 4*log(7)*log(x)^3 + 6*log(7)^2*log(x)^2 + log(7)^4) + ((x*(16*x*exp(4*x) - 8*x^2*exp(4*x) + x^3*exp(4*x) + 33
6*x^2*exp(4*x)*log(7)^2 - 888*x^2*exp(4*x)*log(7)^3 - 180*x^3*exp(4*x)*log(7)^2 + 3960*x^2*exp(4*x)*log(7)^4 +
 594*x^3*exp(4*x)*log(7)^3 + 24*x^4*exp(4*x)*log(7)^2 - 3236*x^2*exp(4*x)*log(7)^5 + 552*x^3*exp(4*x)*log(7)^4
 - 84*x^4*exp(4*x)*log(7)^3 + 1000*x^2*exp(4*x)*log(7)^6 - 2112*x^3*exp(4*x)*log(7)^5 - 1356*x^4*exp(4*x)*log(
7)^4 + 1184*x^3*exp(4*x)*log(7)^6 + 1046*x^4*exp(4*x)*log(7)^5 + 240*x^5*exp(4*x)*log(7)^4 - 268*x^4*exp(4*x)*
log(7)^6 + 296*x^5*exp(4*x)*log(7)^5 - 272*x^5*exp(4*x)*log(7)^6 - 96*x^6*exp(4*x)*log(7)^5 + 64*x^6*exp(4*x)*
log(7)^6 + 16*x*exp(4*x)*log(7) + 76*x^2*exp(4*x)*log(7) - 576*x*exp(4*x)*log(7)^3 - 44*x^3*exp(4*x)*log(7) +
1152*x*exp(4*x)*log(7)^4 + 6*x^4*exp(4*x)*log(7) - 640*x*exp(4*x)*log(7)^5 + 128*x*exp(4*x)*log(7)^6))/6 - (x*
log(x)*(40*x*exp(4*x) - 34*x^2*exp(4*x) + 10*x^3*exp(4*x) - x^4*exp(4*x) - 1548*x^2*exp(4*x)*log(7)^2 + 6564*x
^2*exp(4*x)*log(7)^3 + 405*x^3*exp(4*x)*log(7)^2 - 6354*x^2*exp(4*x)*log(7)^4 + 1056*x^3*exp(4*x)*log(7)^3 + 1
98*x^4*exp(4*x)*log(7)^2 + 2000*x^2*exp(4*x)*log(7)^5 - 4944*x^3*exp(4*x)*log(7)^4 - 2322*x^4*exp(4*x)*log(7)^
3 - 48*x^5*exp(4*x)*log(7)^2 + 2368*x^3*exp(4*x)*log(7)^5 + 1971*x^4*exp(4*x)*log(7)^4 + 408*x^5*exp(4*x)*log(
7)^3 - 536*x^4*exp(4*x)*log(7)^5 + 852*x^5*exp(4*x)*log(7)^4 - 544*x^5*exp(4*x)*log(7)^5 - 240*x^6*exp(4*x)*lo
g(7)^4 + 128*x^6*exp(4*x)*log(7)^5 + 64*x*exp(4*x)*log(7) - 768*x*exp(4*x)*log(7)^2 + 206*x^2*exp(4*x)*log(7)
+ 1824*x*exp(4*x)*log(7)^3 - 269*x^3*exp(4*x)*log(7) - 1152*x*exp(4*x)*log(7)^4 + 101*x^4*exp(4*x)*log(7) + 25
6*x*exp(4*x)*log(7)^5 - 12*x^5*exp(4*x)*log(7)))/3 + (x*log(x)^2*(128*x*exp(4*x) - 8*x^2*exp(4*x) - 216*x^3*ex
p(4*x) + 116*x^4*exp(4*x) - 16*x^5*exp(4*x) + 15376*x^2*exp(4*x)*log(7)^2 - 18708*x^2*exp(4*x)*log(7)^3 + 3752
*x^3*exp(4*x)*log(7)^2 + 6000*x^2*exp(4*x)*log(7)^4 - 16992*x^3*exp(4*x)*log(7)^3 - 5488*x^4*exp(4*x)*log(7)^2
 + 7104*x^3*exp(4*x)*log(7)^4 + 5550*x^4*exp(4*x)*log(7)^3 + 640*x^5*exp(4*x)*log(7)^2 - 1608*x^4*exp(4*x)*log
(7)^4 + 3336*x^5*exp(4*x)*log(7)^3 + 64*x^6*exp(4*x)*log(7)^2 - 1632*x^5*exp(4*x)*log(7)^4 - 864*x^6*exp(4*x)*
log(7)^3 + 384*x^6*exp(4*x)*log(7)^4 - 1376*x*exp(4*x)*log(7) + 3968*x*exp(4*x)*log(7)^2 - 3694*x^2*exp(4*x)*l
og(7) - 3072*x*exp(4*x)*log(7)^3 + 176*x^3*exp(4*x)*log(7) + 768*x*exp(4*x)*log(7)^4 + 1057*x^4*exp(4*x)*log(7
) - 276*x^5*exp(4*x)*log(7) + 16*x^6*exp(4*x)*log(7)))/6 + (2*x*log(x)^4*(32*x*exp(4*x) + 250*x^2*exp(4*x) + 2
96*x^3*exp(4*x) - 67*x^4*exp(4*x) - 68*x^5*exp(4*x) + 16*x^6*exp(4*x) + 250*x^2*exp(4*x)*log(7)^2 + 296*x^3*ex
p(4*x)*log(7)^2 - 67*x^4*exp(4*x)*log(7)^2 - 68*x^5*exp(4*x)*log(7)^2 + 16*x^6*exp(4*x)*log(7)^2 - 96*x*exp(4*
x)*log(7) + 32*x*exp(4*x)*log(7)^2 - 750*x^2*exp(4*x)*log(7) - 888*x^3*exp(4*x)*log(7) + 201*x^4*exp(4*x)*log(
7) + 204*x^5*exp(4*x)*log(7) - 48*x^6*exp(4*x)*log(7)))/3 + (x*log(x)^3*(416*x*exp(4*x) + 1486*x^2*exp(4*x) +
40*x^3*exp(4*x) - 577*x^4*exp(4*x) + 180*x^5*exp(4*x) - 16*x^6*exp(4*x) + 12236*x^2*exp(4*x)*log(7)^2 - 4000*x
^2*exp(4*x)*log(7)^3 + 12768*x^3*exp(4*x)*log(7)^2 - 4736*x^3*exp(4*x)*log(7)^3 - 3458*x^4*exp(4*x)*log(7)^2 +
 1072*x^4*exp(4*x)*log(7)^3 - 2744*x^5*exp(4*x)*log(7)^2 + 1088*x^5*exp(4*x)*log(7)^3 + 672*x^6*exp(4*x)*log(7
)^2 - 256*x^6*exp(4*x)*log(7)^3 - 1600*x*exp(4*x)*log(7) + 1792*x*exp(4*x)*log(7)^2 - 7208*x^2*exp(4*x)*log(7)
 - 512*x*exp(4*x)*log(7)^3 - 3376*x^3*exp(4*x)*log(7) + 2468*x^4*exp(4*x)*log(7) + 208*x^5*exp(4*x)*log(7) - 1
28*x^6*exp(4*x)*log(7)))/6)/(log(x)^2 - 2*log(7)*log(x) + log(7)^2) - exp(4*x)*log(x)^3*((x^2*(128*log(7)^2 -
384*log(7) + 128))/3 + (x^8*(128*log(7)^2 - 384*log(7) + 128))/3 - (x^7*(320*log(7)^2 - 960*log(7) + 320))/3 -
 (x^6*(1352*log(7)^2 - 4056*log(7) + 1352))/3 + (x^5*(1698*log(7)^2 - 5094*log(7) + 1698))/3 + (x^3*(1756*log(
7)^2 - 5268*log(7) + 1756))/3 + (x^4*(4368*log(7)^2 - 13104*log(7) + 4368))/3) + exp(4*x)*log(x)^2*((x^8*(256*
log(7) - 1920*log(7)^2 + 768*log(7)^3 + 64))/6 + (x^7*(1664*log(7) + 4032*log(7)^2 - 1920*log(7)^3 - 928))/6 +
 (x^2*(4864*log(7) - 3456*log(7)^2 + 768*log(7)^3 - 1376))/6 - (x^5*(6252*log(7) + 22254*log(7)^2 - 10188*log(
7)^3 - 4065))/6 - (x^6*(12496*log(7) - 23544*log(7)^2 + 8112*log(7)^3 - 2588))/6 + (x^3*(39512*log(7) - 38340*
log(7)^2 + 10536*log(7)^3 - 11170))/6 + (x^4*(51360*log(7) - 79728*log(7)^2 + 26208*log(7)^3 - 12018))/6) + ex
p(4*x)*log(x)*((x*(1890*log(7)^3 - 945*log(7)^4 + 945*log(7)^3*(log(7) - 2)))/3 - (315*log(7)^3)/2 + (315*log(
7)^4)/4 + (x^7*(256*log(7) - 1920*log(7)^2 + 384*log(7)^3 + 192*log(7)^4 + 768*log(7)^3*(log(7) - 2) + 64))/3
- (x^2*(4992*log(7)^2 - 3968*log(7) + 1476*log(7)^3 - 1506*log(7)^4 + 1890*log(7)^3*(log(7) - 2) + 1216))/3 -
(x^6*(224*log(7) - 7872*log(7)^2 + 14064*log(7)^3 - 5400*log(7)^4 + 1344*log(7)^3*(log(7) - 2) + 560))/3 + (x^
5*(9696*log(7)^2 - 6040*log(7) + 11004*log(7)^3 - 7110*log(7)^4 + 2016*log(7)^3*(log(7) - 2) + 1388))/3 + (x^4
*(7328*log(7) - 36384*log(7)^2 + 35376*log(7)^3 - 10584*log(7)^4 - 2520*log(7)^3*(log(7) - 2) + 308))/3 + (x^3
*(17392*log(7) - 34464*log(7)^2 + 27576*log(7)^3 - 7788*log(7)^4 + 2520*log(7)^3*(log(7) - 2) - 3368))/3 - (31
5*log(7)^3*(log(7) - 2))/4 - 128*x^8*log(7)^3*(log(7) - 2))

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sympy [B]  time = 1.46, size = 632, normalized size = 18.06 \begin {gather*} \frac {\left (x^{4} \log {\relax (x )}^{6} - 4 x^{4} \log {\relax (7 )} \log {\relax (x )}^{5} - 4 x^{4} \log {\relax (x )}^{5} + 6 x^{4} \log {\relax (x )}^{4} + 6 x^{4} \log {\relax (7 )}^{2} \log {\relax (x )}^{4} + 12 x^{4} \log {\relax (7 )} \log {\relax (x )}^{4} - 12 x^{4} \log {\relax (7 )}^{2} \log {\relax (x )}^{3} - 4 x^{4} \log {\relax (7 )}^{3} \log {\relax (x )}^{3} - 12 x^{4} \log {\relax (7 )} \log {\relax (x )}^{3} - 4 x^{4} \log {\relax (x )}^{3} + x^{4} \log {\relax (x )}^{2} + 4 x^{4} \log {\relax (7 )} \log {\relax (x )}^{2} + x^{4} \log {\relax (7 )}^{4} \log {\relax (x )}^{2} + 6 x^{4} \log {\relax (7 )}^{2} \log {\relax (x )}^{2} + 4 x^{4} \log {\relax (7 )}^{3} \log {\relax (x )}^{2} - 8 x^{3} \log {\relax (x )}^{6} + 32 x^{3} \log {\relax (x )}^{5} + 32 x^{3} \log {\relax (7 )} \log {\relax (x )}^{5} - 96 x^{3} \log {\relax (7 )} \log {\relax (x )}^{4} - 48 x^{3} \log {\relax (7 )}^{2} \log {\relax (x )}^{4} - 48 x^{3} \log {\relax (x )}^{4} + 32 x^{3} \log {\relax (x )}^{3} + 96 x^{3} \log {\relax (7 )} \log {\relax (x )}^{3} + 32 x^{3} \log {\relax (7 )}^{3} \log {\relax (x )}^{3} + 96 x^{3} \log {\relax (7 )}^{2} \log {\relax (x )}^{3} - 32 x^{3} \log {\relax (7 )}^{3} \log {\relax (x )}^{2} - 48 x^{3} \log {\relax (7 )}^{2} \log {\relax (x )}^{2} - 8 x^{3} \log {\relax (7 )}^{4} \log {\relax (x )}^{2} - 32 x^{3} \log {\relax (7 )} \log {\relax (x )}^{2} - 8 x^{3} \log {\relax (x )}^{2} + 16 x^{2} \log {\relax (x )}^{6} - 64 x^{2} \log {\relax (7 )} \log {\relax (x )}^{5} - 64 x^{2} \log {\relax (x )}^{5} + 96 x^{2} \log {\relax (x )}^{4} + 96 x^{2} \log {\relax (7 )}^{2} \log {\relax (x )}^{4} + 192 x^{2} \log {\relax (7 )} \log {\relax (x )}^{4} - 192 x^{2} \log {\relax (7 )}^{2} \log {\relax (x )}^{3} - 64 x^{2} \log {\relax (7 )}^{3} \log {\relax (x )}^{3} - 192 x^{2} \log {\relax (7 )} \log {\relax (x )}^{3} - 64 x^{2} \log {\relax (x )}^{3} + 16 x^{2} \log {\relax (x )}^{2} + 64 x^{2} \log {\relax (7 )} \log {\relax (x )}^{2} + 16 x^{2} \log {\relax (7 )}^{4} \log {\relax (x )}^{2} + 96 x^{2} \log {\relax (7 )}^{2} \log {\relax (x )}^{2} + 64 x^{2} \log {\relax (7 )}^{3} \log {\relax (x )}^{2}\right ) e^{4 x}}{\log {\relax (x )}^{4} - 4 \log {\relax (7 )} \log {\relax (x )}^{3} + 6 \log {\relax (7 )}^{2} \log {\relax (x )}^{2} - 4 \log {\relax (7 )}^{3} \log {\relax (x )} + \log {\relax (7 )}^{4}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((4*x**4-28*x**3+40*x**2+32*x)*exp(x)**4*ln(1/7*x)**5+(-16*x**4+112*x**3-160*x**2-128*x)*exp(x)**4*
ln(1/7*x)**4+(24*x**4-164*x**3+208*x**2+256*x)*exp(x)**4*ln(1/7*x)**3+(-16*x**4+100*x**3-64*x**2-320*x)*exp(x)
**4*ln(1/7*x)**2+(4*x**4-16*x**3-56*x**2+224*x)*exp(x)**4*ln(1/7*x)+(-4*x**3+32*x**2-64*x)*exp(x)**4)*ln(x)**2
+((2*x**3-16*x**2+32*x)*exp(x)**4*ln(1/7*x)**5+(-8*x**3+64*x**2-128*x)*exp(x)**4*ln(1/7*x)**4+(12*x**3-96*x**2
+192*x)*exp(x)**4*ln(1/7*x)**3+(-8*x**3+64*x**2-128*x)*exp(x)**4*ln(1/7*x)**2+(2*x**3-16*x**2+32*x)*exp(x)**4*
ln(1/7*x))*ln(x))/ln(1/7*x)**5,x)

[Out]

(x**4*log(x)**6 - 4*x**4*log(7)*log(x)**5 - 4*x**4*log(x)**5 + 6*x**4*log(x)**4 + 6*x**4*log(7)**2*log(x)**4 +
 12*x**4*log(7)*log(x)**4 - 12*x**4*log(7)**2*log(x)**3 - 4*x**4*log(7)**3*log(x)**3 - 12*x**4*log(7)*log(x)**
3 - 4*x**4*log(x)**3 + x**4*log(x)**2 + 4*x**4*log(7)*log(x)**2 + x**4*log(7)**4*log(x)**2 + 6*x**4*log(7)**2*
log(x)**2 + 4*x**4*log(7)**3*log(x)**2 - 8*x**3*log(x)**6 + 32*x**3*log(x)**5 + 32*x**3*log(7)*log(x)**5 - 96*
x**3*log(7)*log(x)**4 - 48*x**3*log(7)**2*log(x)**4 - 48*x**3*log(x)**4 + 32*x**3*log(x)**3 + 96*x**3*log(7)*l
og(x)**3 + 32*x**3*log(7)**3*log(x)**3 + 96*x**3*log(7)**2*log(x)**3 - 32*x**3*log(7)**3*log(x)**2 - 48*x**3*l
og(7)**2*log(x)**2 - 8*x**3*log(7)**4*log(x)**2 - 32*x**3*log(7)*log(x)**2 - 8*x**3*log(x)**2 + 16*x**2*log(x)
**6 - 64*x**2*log(7)*log(x)**5 - 64*x**2*log(x)**5 + 96*x**2*log(x)**4 + 96*x**2*log(7)**2*log(x)**4 + 192*x**
2*log(7)*log(x)**4 - 192*x**2*log(7)**2*log(x)**3 - 64*x**2*log(7)**3*log(x)**3 - 192*x**2*log(7)*log(x)**3 -
64*x**2*log(x)**3 + 16*x**2*log(x)**2 + 64*x**2*log(7)*log(x)**2 + 16*x**2*log(7)**4*log(x)**2 + 96*x**2*log(7
)**2*log(x)**2 + 64*x**2*log(7)**3*log(x)**2)*exp(4*x)/(log(x)**4 - 4*log(7)*log(x)**3 + 6*log(7)**2*log(x)**2
 - 4*log(7)**3*log(x) + log(7)**4)

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