∫ −4096−9984x−9600x2−4544x3−864x4+432x5+568x6+300x7+78x8+8x9+(1024+2560x+2560x2+1280x3+256x4−128x5−160x6−80x7−20x8−2x9) log(2)+(−6144x−8832x2−6208x3−1664x4+832x5+776x6+276x7+48x8+(1536x+2304x2+1664x3+448x4−224x5−208x6−72x7−12x8) log(2)) log(5)+(−3072−5440x−7648x2−4128x3−528x4+444x5+402x6+120x7+(768+1408x+1984x2+1120x3+144x4−120x5−108x6−30x7) log(2)) log2(5)+(−3072x−2880x2−1728x3−352x4+344x5+160x6+(768x+768x2+448x3+96x4−96x5−40x6) log(2)) log3(5)+(−768−848x−1256x2−460x3+210x4+120x5+(192+224x+320x2+128x3−60x4−30x5) log(2)) log4(5)+(−384x−168x2+84x3+48x4+(96x+48x2−24x3−12x4) log(2)) log5(5)+(−64−28x+14x2+8x3+(16+8x−4x2−2x3) log(2)) log6(5)______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ 2048+5120x+6656x2+6400x3+4864x4+2944x5+1472x6+608x7+200x8+52x9+10x10+x11+(3072x+7680x2+9216x3+7680x4+4992x5+2496x6+960x7+288x8+60x9+6x10) log(5)+(1536+3840x+6144x2+7680x3+6720x4+4128x5+1920x6+672x7+150x8+15x9) log2(5)+(1536x+3840x2+4480x3+3520x4+2080x5+848x6+200x7+20x8) log3(5)+(384+960x+1440x2+1680x3+1320x4+612x5+150x6+15x7) log4(5)+(192x+480x2+480x3+240x4+60x5+6x6) log5(5)+(32+80x+80x2+40x3+10x4+x5) log6(5) dx

Optimal. Leaf size=29

{(- 4 + \log (2) + \frac{x + \frac{4 x^{2}}{4 + (x + \log (5))^{2}}}{(2 + x)^{2}})}^{2}

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Rubi [B] time = 5.41, antiderivative size = 1749, normalized size of antiderivative = 60.31, number of steps used = 11, number of rules used = 5, integrand size = 767,

\frac{number of rules}{integrand size}

= 0.007, Rules used = {2074, 638, 614, 618, 204}

\begin{matrix} \begin{aligned} integral & = Rest of rules removed due to large latex content \end{aligned} \end{matrix}

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Mathematica [B] time = 10.66, size = 33759, normalized size = 1164.10

\begin{matrix} Result too large to show \end{matrix}

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fricas [B] time = 0.57, size = 426, normalized size = 14.69

\begin{matrix} - \frac{8 x^{7} + 63 x^{6} + 216 x^{5} + (8 x^{3} + 31 x^{2} - 2 (x^{3} + 4 x^{2} + 4 x) \log (2) + 32 x) \log (5)^{4} + 488 x^{4} + 4 (8 x^{4} + 31 x^{3} + 32 x^{2} - 2 (x^{4} + 4 x^{3} + 4 x^{2}) \log (2)) \log (5)^{3} + 864 x^{3} + 2 (24 x^{5} + 109 x^{4} + 188 x^{3} + 188 x^{2} - 2 (3 x^{5} + 14 x^{4} + 24 x^{3} + 24 x^{2} + 16 x) \log (2) + 128 x) \log (5)^{2} + 1008 x^{2} + 4 (8 x^{6} + 47 x^{5} + 124 x^{4} + 188 x^{3} + 128 x^{2} - 2 (x^{6} + 6 x^{5} + 16 x^{4} + 24 x^{3} + 16 x^{2}) \log (2)) \log (5) - 2 (x^{7} + 8 x^{6} + 28 x^{5} + 64 x^{4} + 112 x^{3} + 128 x^{2} + 64 x) \log (2) + 512 x}{x^{8} + 8 x^{7} + 32 x^{6} + 96 x^{5} + (x^{4} + 8 x^{3} + 24 x^{2} + 32 x + 16) \log (5)^{4} + 224 x^{4} + 4 (x^{5} + 8 x^{4} + 24 x^{3} + 32 x^{2} + 16 x) \log (5)^{3} + 384 x^{3} + 2 (3 x^{6} + 24 x^{5} + 76 x^{4} + 128 x^{3} + 144 x^{2} + 128 x + 64) \log (5)^{2} + 512 x^{2} + 4 (x^{7} + 8 x^{6} + 28 x^{5} + 64 x^{4} + 112 x^{3} + 128 x^{2} + 64 x) \log (5) + 512 x + 256} \end{matrix}

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giac [B] time = 1.22, size = 1494, normalized size = 51.52 result too large to display

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method	result	size

norman	$\frac{(2 \ln (2) - 8) x^{7} + (8 \ln (2) \ln (5) + 16 \ln (2) - 32 \ln (5) - 63) x^{6} + (12 \ln (2) \ln (5)^{2} + 48 \ln (2) \ln (5) - 48 \ln (5)^{2} + 56 \ln (2) - 188 \ln (5) - 216) x^{5} + (8 \ln (2) \ln (5)^{4} - 32 \ln (5)^{4} + 64 \ln (2) \ln (5)^{2} - 256 \ln (5)^{2} + 128 \ln (2) - 512) x + (8 \ln (2) \ln (5)^{3} + 56 \ln (2) \ln (5)^{2} - 32 \ln (5)^{3} + 128 \ln (2) \ln (5) - 218 \ln (5)^{2} + 128 \ln (2) - 496 \ln (5) - 488) x^{4} + (2 \ln (2) \ln (5)^{4} + 32 \ln (2) \ln (5)^{3} - 8 \ln (5)^{4} + 96 \ln (2) \ln (5)^{2} - 124 \ln (5)^{3} + 192 \ln (2) \ln (5) - 376 \ln (5)^{2} + 224 \ln (2) - 752 \ln (5) - 864) x^{3} + (8 \ln (2) \ln (5)^{4} + 32 \ln (2) \ln (5)^{3} - 31 \ln (5)^{4} + 96 \ln (2) \ln (5)^{2} - 128 \ln (5)^{3} + 128 \ln (2) \ln (5) - 376 \ln (5)^{2} + 256 \ln (2) - 512 \ln (5) - 1008) x^{2}}{{(2 + x)}^{4} {(\ln (5)^{2} + 2 x \ln (5) + x^{2} + 4)}^{2}}$	$296$
risch	$\frac{(2 \ln (2) - 8) x^{7} + (8 \ln (2) \ln (5) + 16 \ln (2) - 32 \ln (5) - 63) x^{6} + (12 \ln (2) \ln (5)^{2} + 48 \ln (2) \ln (5) - 48 \ln (5)^{2} + 56 \ln (2) - 188 \ln (5) - 216) x^{5} + (8 \ln (2) \ln (5)^{4} - 32 \ln (5)^{4} + 64 \ln (2) \ln (5)^{2} - 256 \ln (5)^{2} + 128 \ln (2) - 512) x + (8 \ln (2) \ln (5)^{3} + 56 \ln (2) \ln (5)^{2} - 32 \ln (5)^{3} + 128 \ln (2) \ln (5) - 218 \ln (5)^{2} + 128 \ln (2) - 496 \ln (5) - 488) x^{4} + (2 \ln (2) \ln (5)^{4} + 32 \ln (2) \ln (5)^{3} - 8 \ln (5)^{4} + 96 \ln (2) \ln (5)^{2} - 124 \ln (5)^{3} + 192 \ln (2) \ln (5) - 376 \ln (5)^{2} + 224 \ln (2) - 752 \ln (5) - 864) x^{3} + (8 \ln (2) \ln (5)^{4} + 32 \ln (2) \ln (5)^{3} - 31 \ln (5)^{4} + 96 \ln (2) \ln (5)^{2} - 128 \ln (5)^{3} + 128 \ln (2) \ln (5) - 376 \ln (5)^{2} + 256 \ln (2) - 512 \ln (5) - 1008) x^{2}}{256 + 512 x + 256 x^{3} \ln (5)^{2} + 48 x^{5} \ln (5)^{2} + x^{4} \ln (5)^{4} + 6 x^{6} \ln (5)^{2} + 512 x^{2} \ln (5) + 16 \ln (5)^{4} + 32 x^{4} \ln (5)^{3} + 4 x^{5} \ln (5)^{3} + 128 \ln (5)^{2} + 8 x^{7} + x^{8} + 224 x^{4} + 384 x^{3} + 512 x^{2} + 32 x^{6} + 96 x^{5} + 96 x^{3} \ln (5)^{3} + 112 x^{5} \ln (5) + 32 x^{6} \ln (5) + 32 x \ln (5)^{4} + 256 x \ln (5) + 288 x^{2} \ln (5)^{2} + 448 x^{3} \ln (5) + 8 x^{3} \ln (5)^{4} + 4 x^{7} \ln (5) + 64 \ln (5)^{3} x + 24 \ln (5)^{4} x^{2} + 152 x^{4} \ln (5)^{2} + 256 x \ln (5)^{2} + 256 x^{4} \ln (5) + 128 x^{2} \ln (5)^{3}}$	$502$
gosper	$\frac{x (- 512 + 192 x^{2} \ln (2) \ln (5) - 1008 x - 218 x^{3} \ln (5)^{2} + 48 x^{4} \ln (5) \ln (2) + 96 x \ln (2) \ln (5)^{2} + 128 x \ln (2) \ln (5) - 752 x^{2} \ln (5) - 32 \ln (5)^{4} - 256 \ln (5)^{2} + 128 \ln (2) - 216 x^{4} - 488 x^{3} - 864 x^{2} - 8 x^{6} - 63 x^{5} - 32 x^{3} \ln (5)^{3} - 32 x^{5} \ln (5) - 31 x \ln (5)^{4} + 56 x^{4} \ln (2) + 16 x^{5} \ln (2) + 2 x^{6} \ln (2) - 512 x \ln (5) - 376 x^{2} \ln (5)^{2} - 496 x^{3} \ln (5) + 256 x \ln (2) + 224 x^{2} \ln (2) + 128 x^{3} \ln (2) + 8 \ln (2) \ln (5)^{4} - 128 \ln (5)^{3} x + 64 \ln (2) \ln (5)^{2} - 8 \ln (5)^{4} x^{2} - 48 x^{4} \ln (5)^{2} - 376 x \ln (5)^{2} - 188 x^{4} \ln (5) - 124 x^{2} \ln (5)^{3} + 2 \ln (2) \ln (5)^{4} x^{2} + 8 \ln (2) \ln (5)^{3} x^{3} + 12 \ln (2) \ln (5)^{2} x^{4} + 8 \ln (2) \ln (5) x^{5} + 8 \ln (2) \ln (5)^{4} x + 32 \ln (2) \ln (5)^{3} x^{2} + 56 \ln (2) \ln (5)^{2} x^{3} + 32 \ln (2) \ln (5)^{3} x + 96 \ln (2) \ln (5)^{2} x^{2} + 128 \ln (2) \ln (5) x^{3})}{256 + 512 x + 256 x^{3} \ln (5)^{2} + 48 x^{5} \ln (5)^{2} + x^{4} \ln (5)^{4} + 6 x^{6} \ln (5)^{2} + 512 x^{2} \ln (5) + 16 \ln (5)^{4} + 32 x^{4} \ln (5)^{3} + 4 x^{5} \ln (5)^{3} + 128 \ln (5)^{2} + 8 x^{7} + x^{8} + 224 x^{4} + 384 x^{3} + 512 x^{2} + 32 x^{6} + 96 x^{5} + 96 x^{3} \ln (5)^{3} + 112 x^{5} \ln (5) + 32 x^{6} \ln (5) + 32 x \ln (5)^{4} + 256 x \ln (5) + 288 x^{2} \ln (5)^{2} + 448 x^{3} \ln (5) + 8 x^{3} \ln (5)^{4} + 4 x^{7} \ln (5) + 64 \ln (5)^{3} x + 24 \ln (5)^{4} x^{2} + 152 x^{4} \ln (5)^{2} + 256 x \ln (5)^{2} + 256 x^{4} \ln (5) + 128 x^{2} \ln (5)^{3}}$	$576$
default	$- \frac{8 (4464 \ln (5)^{8} - 11616 \ln (5)^{7} + 24416 \ln (5)^{6} - 39808 \ln (5)^{5} - 48128 \ln (5)^{3} + 53248 \ln (5)^{4} + 34816 \ln (5)^{2} + (- 4 \ln (2) \ln (5)^{8} + 56 \ln (2) \ln (5)^{7} + 17 \ln (5)^{8} - 400 \ln (2) \ln (5)^{6} - 228 \ln (5)^{7} + 1792 \ln (2) \ln (5)^{5} + 1580 \ln (5)^{6} - 5504 \ln (2) \ln (5)^{4} - 7056 \ln (5)^{5} + 11776 \ln (2) \ln (5)^{3} + 21600 \ln (5)^{4} - 17408 \ln (2) \ln (5)^{2} - 46208 \ln (5)^{3} + 16384 \ln (2) \ln (5) + 68608 \ln (5)^{2} - 8192 \ln (2) - 64512 \ln (5) + 32768) x^{3} + (- \ln (2) \ln (5)^{10} + 4 \ln (2) \ln (5)^{9} + 4 \ln (5)^{10} + 36 \ln (2) \ln (5)^{8} - 12 \ln (5)^{9} - 496 \ln (2) \ln (5)^{7} - 168 \ln (5)^{8} + 2720 \ln (2) \ln (5)^{6} + 1984 \ln (5)^{7} - 9216 \ln (2) \ln (5)^{5} - 10800 \ln (5)^{6} + 20736 \ln (2) \ln (5)^{4} + 36480 \ln (5)^{5} - 31744 \ln (2) \ln (5)^{3} - 82368 \ln (5)^{4} + 30720 \ln (2) \ln (5)^{2} + 128256 \ln (5)^{3} - 16384 \ln (2) \ln (5) - 125952 \ln (5)^{2} + 71680 \ln (5) - 4096) x^{2} + (- 2 \ln (2) \ln (5)^{11} + 20 \ln (2) \ln (5)^{10} + 8 \ln (5)^{11} - 96 \ln (2) \ln (5)^{9} - 75 \ln (5)^{10} + 192 \ln (2) \ln (5)^{8} + 348 \ln (5)^{9} + 288 \ln (2) \ln (5)^{7} - 720 \ln (5)^{8} - 3520 \ln (2) \ln (5)^{6} - 1184 \ln (5)^{7} + 13312 \ln (2) \ln (5)^{5} + 13584 \ln (5)^{6} - 33280 \ln (2) \ln (5)^{4} - 51136 \ln (5)^{5} + 59392 \ln (2) \ln (5)^{3} + 129152 \ln (5)^{4} - 77824 \ln (2) \ln (5)^{2} - 229888 \ln (5)^{3} + 65536 \ln (2) \ln (5) + 305152 \ln (5)^{2} - 32768 \ln (2) - 258048 \ln (5) + 131072) x - 80 \ln (2) \ln (5)^{10} - \ln (2) \ln (5)^{12} + 12 \ln (2) \ln (5)^{11} + 352 \ln (2) \ln (5)^{9} + 12288 \ln (2) \ln (5)^{3} + 3008 \ln (2) \ln (5)^{7} + 10240 \ln (2) \ln (5)^{5} - 13312 \ln (2) \ln (5)^{4} - 8192 \ln (2) \ln (5)^{2} - 6272 \ln (2) \ln (5)^{6} - 1168 \ln (2) \ln (5)^{8} + 302 \ln (5)^{10} - 1352 \ln (5)^{9} + 4 \ln (5)^{12} - 46 \ln (5)^{11})}{{(\ln (5)^{2} - 4 \ln (5) + 8)}^{5} {(\ln (5)^{2} + 2 x \ln (5) + x^{2} + 4)}^{2}} - \frac{\ln (5) (4 \ln (2) \ln (5)^{7} - 64 \ln (2) \ln (5)^{6} - 17 \ln (5)^{7} + 480 \ln (2) \ln (5)^{5} + 272 \ln (5)^{6} - 2176 \ln (2) \ln (5)^{4} - 2000 \ln (5)^{5} + 6400 \ln (2) \ln (5)^{3} + 8960 \ln (5)^{4} - 12288 \ln (2) \ln (5)^{2} - 26432 \ln (5)^{3} + 14336 \ln (2) \ln (5) + 50688 \ln (5)^{2} - 8192 \ln (2) - 59904 \ln (5) + 34816)}{{(\ln (5)^{2} - 4 \ln (5) + 8)}^{4} {(2 + x)}^{2}} + \frac{2 \ln (5) (\ln (2) \ln (5)^{9} - 20 \ln (2) \ln (5)^{8} - 4 \ln (5)^{9} + 184 \ln (2) \ln (5)^{7} + 80 \ln (5)^{8} - 1056 \ln (2) \ln (5)^{6} - 732 \ln (5)^{7} + 4160 \ln (2) \ln (5)^{5} + 4208 \ln (5)^{6} - 11776 \ln (2) \ln (5)^{4} - 16720 \ln (5)^{5} + 24064 \ln (2) \ln (5)^{3} + 47552 \ln (5)^{4} - 34816 \ln (2) \ln (5)^{2} - 97920 \ln (5)^{3} + 32768 \ln (2) \ln (5) + 142848 \ln (5)^{2} - 16384 \ln (2) - 135168 \ln (5) + 69632)}{{(\ln (5)^{2} - 4 \ln (5) + 8)}^{5} (2 + x)} + \frac{4 \ln (5)^{2} (\ln (5)^{2} - 8 \ln (5) + 16)}{{(\ln (5)^{2} - 4 \ln (5) + 8)}^{2} {(2 + x)}^{4}} - \frac{4 \ln (5)^{2} (\ln (5)^{4} - 12 \ln (5)^{3} + 48 \ln (5)^{2} - 96 \ln (5) + 128)}{{(\ln (5)^{2} - 4 \ln (5) + 8)}^{3} {(2 + x)}^{3}}$	$952$

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maxima [B] time = 0.44, size = 407, normalized size = 14.03

\begin{matrix} \frac{2 x^{7} (\log (2) - 4) + (8 (\log (2) - 4) \log (5) + 16 \log (2) - 63) x^{6} + 4 (3 (\log (2) - 4) \log (5)^{2} + (12 \log (2) - 47) \log (5) + 14 \log (2) - 54) x^{5} + 2 (4 (\log (2) - 4) \log (5)^{3} + (28 \log (2) - 109) \log (5)^{2} + 8 (8 \log (2) - 31) \log (5) + 64 \log (2) - 244) x^{4} + 2 ((\log (2) - 4) \log (5)^{4} + 2 (8 \log (2) - 31) \log (5)^{3} + 4 (12 \log (2) - 47) \log (5)^{2} + 8 (12 \log (2) - 47) \log (5) + 112 \log (2) - 432) x^{3} + ((8 \log (2) - 31) \log (5)^{4} + 32 (\log (2) - 4) \log (5)^{3} + 8 (12 \log (2) - 47) \log (5)^{2} + 128 (\log (2) - 4) \log (5) + 256 \log (2) - 1008) x^{2} + 8 ((\log (2) - 4) \log (5)^{4} + 8 (\log (2) - 4) \log (5)^{2} + 16 \log (2) - 64) x}{x^{8} + 4 x^{7} (\log (5) + 2) + 2 (3 \log (5)^{2} + 16 \log (5) + 16) x^{6} + 4 (\log (5)^{3} + 12 \log (5)^{2} + 28 \log (5) + 24) x^{5} + (\log (5)^{4} + 32 \log (5)^{3} + 152 \log (5)^{2} + 256 \log (5) + 224) x^{4} + 8 (\log (5)^{4} + 12 \log (5)^{3} + 32 \log (5)^{2} + 56 \log (5) + 48) x^{3} + 16 \log (5)^{4} + 8 (3 \log (5)^{4} + 16 \log (5)^{3} + 36 \log (5)^{2} + 64 \log (5) + 64) x^{2} + 32 (\log (5)^{4} + 2 \log (5)^{3} + 8 \log (5)^{2} + 8 \log (5) + 16) x + 128 \log (5)^{2} + 256} \end{matrix}

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mupad [F(-1)] time = 0.00, size = -1, normalized size = -0.03

\begin{matrix} Hanged \end{matrix}

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sympy [F(-1)] time = 0.00, size = 0, normalized size = 0.00

\begin{matrix} Timed out \end{matrix}

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