Optimal. Leaf size=18 \[ x+x^2 \left (2 x+\log ^2(-81+x)\right )^4 \]
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Rubi [B] time = 2.32, antiderivative size = 170, normalized size of antiderivative = 9.44, number of steps used = 187, number of rules used = 17, integrand size = 131, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.130, Rules used = {6742, 2411, 43, 2334, 2301, 2398, 2346, 2302, 30, 2296, 2295, 2330, 2305, 2304, 2401, 2389, 2390} \begin {gather*} 16 x^6+32 x^5 \log ^2(x-81)+x+(81-x)^2 \log ^8(x-81)-162 (81-x) \log ^8(x-81)+6561 \log ^8(x-81)-8 (81-x)^3 \log ^6(x-81)+1944 (81-x)^2 \log ^6(x-81)-157464 (81-x) \log ^6(x-81)+4251528 \log ^6(x-81)+24 (81-x)^4 \log ^4(x-81)-7776 (81-x)^3 \log ^4(x-81)+944784 (81-x)^2 \log ^4(x-81)-51018336 (81-x) \log ^4(x-81)+1033121304 \log ^4(x-81) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 30
Rule 43
Rule 2295
Rule 2296
Rule 2301
Rule 2302
Rule 2304
Rule 2305
Rule 2330
Rule 2334
Rule 2346
Rule 2389
Rule 2390
Rule 2398
Rule 2401
Rule 2411
Rule 6742
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (1+96 x^5+\frac {64 x^5 \log (-81+x)}{-81+x}+160 x^4 \log ^2(-81+x)+\frac {96 x^4 \log ^3(-81+x)}{-81+x}+96 x^3 \log ^4(-81+x)+\frac {48 x^3 \log ^5(-81+x)}{-81+x}+24 x^2 \log ^6(-81+x)+\frac {8 x^2 \log ^7(-81+x)}{-81+x}+2 x \log ^8(-81+x)\right ) \, dx\\ &=x+16 x^6+2 \int x \log ^8(-81+x) \, dx+8 \int \frac {x^2 \log ^7(-81+x)}{-81+x} \, dx+24 \int x^2 \log ^6(-81+x) \, dx+48 \int \frac {x^3 \log ^5(-81+x)}{-81+x} \, dx+64 \int \frac {x^5 \log (-81+x)}{-81+x} \, dx+96 \int \frac {x^4 \log ^3(-81+x)}{-81+x} \, dx+96 \int x^3 \log ^4(-81+x) \, dx+160 \int x^4 \log ^2(-81+x) \, dx\\ &=x+16 x^6+32 x^5 \log ^2(-81+x)+2 \int \left (81 \log ^8(-81+x)+(-81+x) \log ^8(-81+x)\right ) \, dx+8 \operatorname {Subst}\left (\int \frac {(81+x)^2 \log ^7(x)}{x} \, dx,x,-81+x\right )+24 \int \left (6561 \log ^6(-81+x)+162 (-81+x) \log ^6(-81+x)+(-81+x)^2 \log ^6(-81+x)\right ) \, dx+48 \operatorname {Subst}\left (\int \frac {(81+x)^3 \log ^5(x)}{x} \, dx,x,-81+x\right )-64 \int \frac {x^5 \log (-81+x)}{-81+x} \, dx+64 \operatorname {Subst}\left (\int \frac {(81+x)^5 \log (x)}{x} \, dx,x,-81+x\right )+96 \int \left (531441 \log ^4(-81+x)+19683 (-81+x) \log ^4(-81+x)+243 (-81+x)^2 \log ^4(-81+x)+(-81+x)^3 \log ^4(-81+x)\right ) \, dx+96 \operatorname {Subst}\left (\int \frac {(81+x)^4 \log ^3(x)}{x} \, dx,x,-81+x\right )\\ &=x+16 x^6-\frac {16}{5} \left (4304672100 (81-x)-53144100 (81-x)^2+437400 (81-x)^3-2025 (81-x)^4+4 (81-x)^5-69735688020 \log (-81+x)\right ) \log (-81+x)+32 x^5 \log ^2(-81+x)+2 \int (-81+x) \log ^8(-81+x) \, dx+8 \operatorname {Subst}\left (\int (81+x) \log ^7(x) \, dx,x,-81+x\right )+24 \int (-81+x)^2 \log ^6(-81+x) \, dx+48 \operatorname {Subst}\left (\int (81+x)^2 \log ^5(x) \, dx,x,-81+x\right )-64 \operatorname {Subst}\left (\int \frac {(81+x)^5 \log (x)}{x} \, dx,x,-81+x\right )-64 \operatorname {Subst}\left (\int \left (215233605+2657205 x+21870 x^2+\frac {405 x^3}{4}+\frac {x^4}{5}+\frac {3486784401 \log (x)}{x}\right ) \, dx,x,-81+x\right )+96 \int (-81+x)^3 \log ^4(-81+x) \, dx+96 \operatorname {Subst}\left (\int (81+x)^3 \log ^3(x) \, dx,x,-81+x\right )+162 \int \log ^8(-81+x) \, dx+648 \operatorname {Subst}\left (\int \frac {(81+x) \log ^7(x)}{x} \, dx,x,-81+x\right )+3888 \int (-81+x) \log ^6(-81+x) \, dx+3888 \operatorname {Subst}\left (\int \frac {(81+x)^2 \log ^5(x)}{x} \, dx,x,-81+x\right )+7776 \operatorname {Subst}\left (\int \frac {(81+x)^3 \log ^3(x)}{x} \, dx,x,-81+x\right )+23328 \int (-81+x)^2 \log ^4(-81+x) \, dx+157464 \int \log ^6(-81+x) \, dx+1889568 \int (-81+x) \log ^4(-81+x) \, dx+51018336 \int \log ^4(-81+x) \, dx\\ &=-85030560 (81-x)^2+466560 (81-x)^3-1620 (81-x)^4+\frac {64}{25} (81-x)^5-13774950719 x+16 x^6+32 x^5 \log ^2(-81+x)+2 \operatorname {Subst}\left (\int x \log ^8(x) \, dx,x,-81+x\right )+8 \operatorname {Subst}\left (\int \left (81 \log ^7(x)+x \log ^7(x)\right ) \, dx,x,-81+x\right )+24 \operatorname {Subst}\left (\int x^2 \log ^6(x) \, dx,x,-81+x\right )+48 \operatorname {Subst}\left (\int \left (6561 \log ^5(x)+162 x \log ^5(x)+x^2 \log ^5(x)\right ) \, dx,x,-81+x\right )+64 \operatorname {Subst}\left (\int \left (215233605+2657205 x+21870 x^2+\frac {405 x^3}{4}+\frac {x^4}{5}+\frac {3486784401 \log (x)}{x}\right ) \, dx,x,-81+x\right )+96 \operatorname {Subst}\left (\int x^3 \log ^4(x) \, dx,x,-81+x\right )+96 \operatorname {Subst}\left (\int \left (531441 \log ^3(x)+19683 x \log ^3(x)+243 x^2 \log ^3(x)+x^3 \log ^3(x)\right ) \, dx,x,-81+x\right )+162 \operatorname {Subst}\left (\int \log ^8(x) \, dx,x,-81+x\right )+648 \operatorname {Subst}\left (\int \log ^7(x) \, dx,x,-81+x\right )+3888 \operatorname {Subst}\left (\int (81+x) \log ^5(x) \, dx,x,-81+x\right )+3888 \operatorname {Subst}\left (\int x \log ^6(x) \, dx,x,-81+x\right )+7776 \operatorname {Subst}\left (\int (81+x)^2 \log ^3(x) \, dx,x,-81+x\right )+23328 \operatorname {Subst}\left (\int x^2 \log ^4(x) \, dx,x,-81+x\right )+52488 \operatorname {Subst}\left (\int \frac {\log ^7(x)}{x} \, dx,x,-81+x\right )+157464 \operatorname {Subst}\left (\int \log ^6(x) \, dx,x,-81+x\right )+314928 \operatorname {Subst}\left (\int \frac {(81+x) \log ^5(x)}{x} \, dx,x,-81+x\right )+629856 \operatorname {Subst}\left (\int \frac {(81+x)^2 \log ^3(x)}{x} \, dx,x,-81+x\right )+1889568 \operatorname {Subst}\left (\int x \log ^4(x) \, dx,x,-81+x\right )+51018336 \operatorname {Subst}\left (\int \log ^4(x) \, dx,x,-81+x\right )-223154201664 \operatorname {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,-81+x\right )\\ &=x+16 x^6-111577100832 \log ^2(-81+x)+32 x^5 \log ^2(-81+x)-51018336 (81-x) \log ^4(-81+x)+944784 (81-x)^2 \log ^4(-81+x)-7776 (81-x)^3 \log ^4(-81+x)+24 (81-x)^4 \log ^4(-81+x)-157464 (81-x) \log ^6(-81+x)+1944 (81-x)^2 \log ^6(-81+x)-8 (81-x)^3 \log ^6(-81+x)-648 (81-x) \log ^7(-81+x)-162 (81-x) \log ^8(-81+x)+(81-x)^2 \log ^8(-81+x)+648 \operatorname {Subst}\left (\int \log ^7(x) \, dx,x,-81+x\right )-1296 \operatorname {Subst}\left (\int \log ^7(x) \, dx,x,-81+x\right )+3888 \operatorname {Subst}\left (\int \left (81 \log ^5(x)+x \log ^5(x)\right ) \, dx,x,-81+x\right )-4536 \operatorname {Subst}\left (\int \log ^6(x) \, dx,x,-81+x\right )+7776 \operatorname {Subst}\left (\int x \log ^5(x) \, dx,x,-81+x\right )+7776 \operatorname {Subst}\left (\int \left (6561 \log ^3(x)+162 x \log ^3(x)+x^2 \log ^3(x)\right ) \, dx,x,-81+x\right )-11664 \operatorname {Subst}\left (\int x \log ^5(x) \, dx,x,-81+x\right )+23328 \operatorname {Subst}\left (\int x^2 \log ^3(x) \, dx,x,-81+x\right )-31104 \operatorname {Subst}\left (\int x^2 \log ^3(x) \, dx,x,-81+x\right )+52488 \operatorname {Subst}\left (\int x^7 \, dx,x,\log (-81+x)\right )+2 \left (314928 \operatorname {Subst}\left (\int \log ^5(x) \, dx,x,-81+x\right )\right )+629856 \operatorname {Subst}\left (\int (81+x) \log ^3(x) \, dx,x,-81+x\right )-944784 \operatorname {Subst}\left (\int \log ^5(x) \, dx,x,-81+x\right )+1889568 \operatorname {Subst}\left (\int x \log ^3(x) \, dx,x,-81+x\right )-3779136 \operatorname {Subst}\left (\int x \log ^3(x) \, dx,x,-81+x\right )+25509168 \operatorname {Subst}\left (\int \frac {\log ^5(x)}{x} \, dx,x,-81+x\right )+51018336 \operatorname {Subst}\left (\int \log ^3(x) \, dx,x,-81+x\right )+51018336 \operatorname {Subst}\left (\int \frac {(81+x) \log ^3(x)}{x} \, dx,x,-81+x\right )-204073344 \operatorname {Subst}\left (\int \log ^3(x) \, dx,x,-81+x\right )+223154201664 \operatorname {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,-81+x\right )\\ &=x+16 x^6+32 x^5 \log ^2(-81+x)+153055008 (81-x) \log ^3(-81+x)-944784 (81-x)^2 \log ^3(-81+x)+2592 (81-x)^3 \log ^3(-81+x)-51018336 (81-x) \log ^4(-81+x)+944784 (81-x)^2 \log ^4(-81+x)-7776 (81-x)^3 \log ^4(-81+x)+24 (81-x)^4 \log ^4(-81+x)+944784 (81-x) \log ^5(-81+x)-1944 (81-x)^2 \log ^5(-81+x)-152928 (81-x) \log ^6(-81+x)+1944 (81-x)^2 \log ^6(-81+x)-8 (81-x)^3 \log ^6(-81+x)+6561 \log ^8(-81+x)-162 (81-x) \log ^8(-81+x)+(81-x)^2 \log ^8(-81+x)+3888 \operatorname {Subst}\left (\int x \log ^5(x) \, dx,x,-81+x\right )-4536 \operatorname {Subst}\left (\int \log ^6(x) \, dx,x,-81+x\right )+7776 \operatorname {Subst}\left (\int x^2 \log ^3(x) \, dx,x,-81+x\right )+9072 \operatorname {Subst}\left (\int \log ^6(x) \, dx,x,-81+x\right )-19440 \operatorname {Subst}\left (\int x \log ^4(x) \, dx,x,-81+x\right )-23328 \operatorname {Subst}\left (\int x^2 \log ^2(x) \, dx,x,-81+x\right )+27216 \operatorname {Subst}\left (\int \log ^5(x) \, dx,x,-81+x\right )+29160 \operatorname {Subst}\left (\int x \log ^4(x) \, dx,x,-81+x\right )+31104 \operatorname {Subst}\left (\int x^2 \log ^2(x) \, dx,x,-81+x\right )+314928 \operatorname {Subst}\left (\int \log ^5(x) \, dx,x,-81+x\right )+629856 \operatorname {Subst}\left (\int \left (81 \log ^3(x)+x \log ^3(x)\right ) \, dx,x,-81+x\right )+1259712 \operatorname {Subst}\left (\int x \log ^3(x) \, dx,x,-81+x\right )+2 \left (-314928 (81-x) \log ^5(-81+x)-1574640 \operatorname {Subst}\left (\int \log ^4(x) \, dx,x,-81+x\right )\right )-2834352 \operatorname {Subst}\left (\int x \log ^2(x) \, dx,x,-81+x\right )+4723920 \operatorname {Subst}\left (\int \log ^4(x) \, dx,x,-81+x\right )+5668704 \operatorname {Subst}\left (\int x \log ^2(x) \, dx,x,-81+x\right )+25509168 \operatorname {Subst}\left (\int x^5 \, dx,x,\log (-81+x)\right )+2 \left (51018336 \operatorname {Subst}\left (\int \log ^3(x) \, dx,x,-81+x\right )\right )-153055008 \operatorname {Subst}\left (\int \log ^2(x) \, dx,x,-81+x\right )+612220032 \operatorname {Subst}\left (\int \log ^2(x) \, dx,x,-81+x\right )+4132485216 \operatorname {Subst}\left (\int \frac {\log ^3(x)}{x} \, dx,x,-81+x\right )\\ &=x+16 x^6-459165024 (81-x) \log ^2(-81+x)+1417176 (81-x)^2 \log ^2(-81+x)-2592 (81-x)^3 \log ^2(-81+x)+32 x^5 \log ^2(-81+x)+153055008 (81-x) \log ^3(-81+x)-314928 (81-x)^2 \log ^3(-81+x)-55742256 (81-x) \log ^4(-81+x)+949644 (81-x)^2 \log ^4(-81+x)-7776 (81-x)^3 \log ^4(-81+x)+24 (81-x)^4 \log ^4(-81+x)+602640 (81-x) \log ^5(-81+x)+4251528 \log ^6(-81+x)-157464 (81-x) \log ^6(-81+x)+1944 (81-x)^2 \log ^6(-81+x)-8 (81-x)^3 \log ^6(-81+x)+6561 \log ^8(-81+x)-162 (81-x) \log ^8(-81+x)+(81-x)^2 \log ^8(-81+x)-7776 \operatorname {Subst}\left (\int x^2 \log ^2(x) \, dx,x,-81+x\right )-9720 \operatorname {Subst}\left (\int x \log ^4(x) \, dx,x,-81+x\right )+15552 \operatorname {Subst}\left (\int x^2 \log (x) \, dx,x,-81+x\right )-20736 \operatorname {Subst}\left (\int x^2 \log (x) \, dx,x,-81+x\right )+27216 \operatorname {Subst}\left (\int \log ^5(x) \, dx,x,-81+x\right )+38880 \operatorname {Subst}\left (\int x \log ^3(x) \, dx,x,-81+x\right )-54432 \operatorname {Subst}\left (\int \log ^5(x) \, dx,x,-81+x\right )-58320 \operatorname {Subst}\left (\int x \log ^3(x) \, dx,x,-81+x\right )-136080 \operatorname {Subst}\left (\int \log ^4(x) \, dx,x,-81+x\right )+629856 \operatorname {Subst}\left (\int x \log ^3(x) \, dx,x,-81+x\right )-1574640 \operatorname {Subst}\left (\int \log ^4(x) \, dx,x,-81+x\right )-1889568 \operatorname {Subst}\left (\int x \log ^2(x) \, dx,x,-81+x\right )+2834352 \operatorname {Subst}(\int x \log (x) \, dx,x,-81+x)-5668704 \operatorname {Subst}(\int x \log (x) \, dx,x,-81+x)+2 \left (1574640 (81-x) \log ^4(-81+x)-314928 (81-x) \log ^5(-81+x)+6298560 \operatorname {Subst}\left (\int \log ^3(x) \, dx,x,-81+x\right )\right )-18895680 \operatorname {Subst}\left (\int \log ^3(x) \, dx,x,-81+x\right )+51018336 \operatorname {Subst}\left (\int \log ^3(x) \, dx,x,-81+x\right )+2 \left (-51018336 (81-x) \log ^3(-81+x)-153055008 \operatorname {Subst}\left (\int \log ^2(x) \, dx,x,-81+x\right )\right )+306110016 \operatorname {Subst}(\int \log (x) \, dx,x,-81+x)-1224440064 \operatorname {Subst}(\int \log (x) \, dx,x,-81+x)+4132485216 \operatorname {Subst}\left (\int x^3 \, dx,x,\log (-81+x)\right )\\ &=708588 (81-x)^2-576 (81-x)^3+918330049 x+16 x^6+918330048 (81-x) \log (-81+x)-1417176 (81-x)^2 \log (-81+x)+1728 (81-x)^3 \log (-81+x)-459165024 (81-x) \log ^2(-81+x)+472392 (81-x)^2 \log ^2(-81+x)+32 x^5 \log ^2(-81+x)+120932352 (81-x) \log ^3(-81+x)-9720 (81-x)^2 \log ^3(-81+x)+1033121304 \log ^4(-81+x)-54031536 (81-x) \log ^4(-81+x)+944784 (81-x)^2 \log ^4(-81+x)-7776 (81-x)^3 \log ^4(-81+x)+24 (81-x)^4 \log ^4(-81+x)+629856 (81-x) \log ^5(-81+x)+4251528 \log ^6(-81+x)-157464 (81-x) \log ^6(-81+x)+1944 (81-x)^2 \log ^6(-81+x)-8 (81-x)^3 \log ^6(-81+x)+6561 \log ^8(-81+x)-162 (81-x) \log ^8(-81+x)+(81-x)^2 \log ^8(-81+x)+5184 \operatorname {Subst}\left (\int x^2 \log (x) \, dx,x,-81+x\right )+19440 \operatorname {Subst}\left (\int x \log ^3(x) \, dx,x,-81+x\right )-58320 \operatorname {Subst}\left (\int x \log ^2(x) \, dx,x,-81+x\right )+87480 \operatorname {Subst}\left (\int x \log ^2(x) \, dx,x,-81+x\right )-136080 \operatorname {Subst}\left (\int \log ^4(x) \, dx,x,-81+x\right )+272160 \operatorname {Subst}\left (\int \log ^4(x) \, dx,x,-81+x\right )+544320 \operatorname {Subst}\left (\int \log ^3(x) \, dx,x,-81+x\right )-944784 \operatorname {Subst}\left (\int x \log ^2(x) \, dx,x,-81+x\right )+1889568 \operatorname {Subst}(\int x \log (x) \, dx,x,-81+x)+6298560 \operatorname {Subst}\left (\int \log ^3(x) \, dx,x,-81+x\right )+2 \left (-6298560 (81-x) \log ^3(-81+x)+1574640 (81-x) \log ^4(-81+x)-314928 (81-x) \log ^5(-81+x)-18895680 \operatorname {Subst}\left (\int \log ^2(x) \, dx,x,-81+x\right )\right )+56687040 \operatorname {Subst}\left (\int \log ^2(x) \, dx,x,-81+x\right )-153055008 \operatorname {Subst}\left (\int \log ^2(x) \, dx,x,-81+x\right )+2 \left (153055008 (81-x) \log ^2(-81+x)-51018336 (81-x) \log ^3(-81+x)+306110016 \operatorname {Subst}(\int \log (x) \, dx,x,-81+x)\right )\\ &=236196 (81-x)^2+918330049 x+16 x^6+918330048 (81-x) \log (-81+x)-472392 (81-x)^2 \log (-81+x)-362797056 (81-x) \log ^2(-81+x)+14580 (81-x)^2 \log ^2(-81+x)+32 x^5 \log ^2(-81+x)+114089472 (81-x) \log ^3(-81+x)+1033121304 \log ^4(-81+x)-54167616 (81-x) \log ^4(-81+x)+944784 (81-x)^2 \log ^4(-81+x)-7776 (81-x)^3 \log ^4(-81+x)+24 (81-x)^4 \log ^4(-81+x)+629856 (81-x) \log ^5(-81+x)+4251528 \log ^6(-81+x)-157464 (81-x) \log ^6(-81+x)+1944 (81-x)^2 \log ^6(-81+x)-8 (81-x)^3 \log ^6(-81+x)+6561 \log ^8(-81+x)-162 (81-x) \log ^8(-81+x)+(81-x)^2 \log ^8(-81+x)+2 \left (-306110016 x-306110016 (81-x) \log (-81+x)+153055008 (81-x) \log ^2(-81+x)-51018336 (81-x) \log ^3(-81+x)\right )-29160 \operatorname {Subst}\left (\int x \log ^2(x) \, dx,x,-81+x\right )+58320 \operatorname {Subst}(\int x \log (x) \, dx,x,-81+x)-87480 \operatorname {Subst}(\int x \log (x) \, dx,x,-81+x)+544320 \operatorname {Subst}\left (\int \log ^3(x) \, dx,x,-81+x\right )+944784 \operatorname {Subst}(\int x \log (x) \, dx,x,-81+x)-1088640 \operatorname {Subst}\left (\int \log ^3(x) \, dx,x,-81+x\right )-1632960 \operatorname {Subst}\left (\int \log ^2(x) \, dx,x,-81+x\right )-18895680 \operatorname {Subst}\left (\int \log ^2(x) \, dx,x,-81+x\right )+2 \left (18895680 (81-x) \log ^2(-81+x)-6298560 (81-x) \log ^3(-81+x)+1574640 (81-x) \log ^4(-81+x)-314928 (81-x) \log ^5(-81+x)+37791360 \operatorname {Subst}(\int \log (x) \, dx,x,-81+x)\right )-113374080 \operatorname {Subst}(\int \log (x) \, dx,x,-81+x)+306110016 \operatorname {Subst}(\int \log (x) \, dx,x,-81+x)\\ &=7290 (81-x)^2+725594113 x+16 x^6+725594112 (81-x) \log (-81+x)-14580 (81-x)^2 \log (-81+x)-342268416 (81-x) \log ^2(-81+x)+32 x^5 \log ^2(-81+x)+114633792 (81-x) \log ^3(-81+x)+1033121304 \log ^4(-81+x)-54167616 (81-x) \log ^4(-81+x)+944784 (81-x)^2 \log ^4(-81+x)-7776 (81-x)^3 \log ^4(-81+x)+24 (81-x)^4 \log ^4(-81+x)+629856 (81-x) \log ^5(-81+x)+4251528 \log ^6(-81+x)-157464 (81-x) \log ^6(-81+x)+1944 (81-x)^2 \log ^6(-81+x)-8 (81-x)^3 \log ^6(-81+x)+6561 \log ^8(-81+x)-162 (81-x) \log ^8(-81+x)+(81-x)^2 \log ^8(-81+x)+2 \left (-306110016 x-306110016 (81-x) \log (-81+x)+153055008 (81-x) \log ^2(-81+x)-51018336 (81-x) \log ^3(-81+x)\right )+2 \left (-37791360 x-37791360 (81-x) \log (-81+x)+18895680 (81-x) \log ^2(-81+x)-6298560 (81-x) \log ^3(-81+x)+1574640 (81-x) \log ^4(-81+x)-314928 (81-x) \log ^5(-81+x)\right )+29160 \operatorname {Subst}(\int x \log (x) \, dx,x,-81+x)-1632960 \operatorname {Subst}\left (\int \log ^2(x) \, dx,x,-81+x\right )+3265920 \operatorname {Subst}(\int \log (x) \, dx,x,-81+x)+3265920 \operatorname {Subst}\left (\int \log ^2(x) \, dx,x,-81+x\right )+37791360 \operatorname {Subst}(\int \log (x) \, dx,x,-81+x)\\ &=684536833 x+16 x^6+684536832 (81-x) \log (-81+x)-343901376 (81-x) \log ^2(-81+x)+32 x^5 \log ^2(-81+x)+114633792 (81-x) \log ^3(-81+x)+1033121304 \log ^4(-81+x)-54167616 (81-x) \log ^4(-81+x)+944784 (81-x)^2 \log ^4(-81+x)-7776 (81-x)^3 \log ^4(-81+x)+24 (81-x)^4 \log ^4(-81+x)+629856 (81-x) \log ^5(-81+x)+4251528 \log ^6(-81+x)-157464 (81-x) \log ^6(-81+x)+1944 (81-x)^2 \log ^6(-81+x)-8 (81-x)^3 \log ^6(-81+x)+6561 \log ^8(-81+x)-162 (81-x) \log ^8(-81+x)+(81-x)^2 \log ^8(-81+x)+2 \left (-306110016 x-306110016 (81-x) \log (-81+x)+153055008 (81-x) \log ^2(-81+x)-51018336 (81-x) \log ^3(-81+x)\right )+2 \left (-37791360 x-37791360 (81-x) \log (-81+x)+18895680 (81-x) \log ^2(-81+x)-6298560 (81-x) \log ^3(-81+x)+1574640 (81-x) \log ^4(-81+x)-314928 (81-x) \log ^5(-81+x)\right )+3265920 \operatorname {Subst}(\int \log (x) \, dx,x,-81+x)-6531840 \operatorname {Subst}(\int \log (x) \, dx,x,-81+x)\\ &=687802753 x+16 x^6+687802752 (81-x) \log (-81+x)-343901376 (81-x) \log ^2(-81+x)+32 x^5 \log ^2(-81+x)+114633792 (81-x) \log ^3(-81+x)+1033121304 \log ^4(-81+x)-54167616 (81-x) \log ^4(-81+x)+944784 (81-x)^2 \log ^4(-81+x)-7776 (81-x)^3 \log ^4(-81+x)+24 (81-x)^4 \log ^4(-81+x)+629856 (81-x) \log ^5(-81+x)+4251528 \log ^6(-81+x)-157464 (81-x) \log ^6(-81+x)+1944 (81-x)^2 \log ^6(-81+x)-8 (81-x)^3 \log ^6(-81+x)+6561 \log ^8(-81+x)-162 (81-x) \log ^8(-81+x)+(81-x)^2 \log ^8(-81+x)+2 \left (-306110016 x-306110016 (81-x) \log (-81+x)+153055008 (81-x) \log ^2(-81+x)-51018336 (81-x) \log ^3(-81+x)\right )+2 \left (-37791360 x-37791360 (81-x) \log (-81+x)+18895680 (81-x) \log ^2(-81+x)-6298560 (81-x) \log ^3(-81+x)+1574640 (81-x) \log ^4(-81+x)-314928 (81-x) \log ^5(-81+x)\right )\\ \end {aligned} \end {gather*}
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Mathematica [B] time = 0.13, size = 51, normalized size = 2.83 \begin {gather*} -4518872583777+x+16 x^6+32 x^5 \log ^2(-81+x)+24 x^4 \log ^4(-81+x)+8 x^3 \log ^6(-81+x)+x^2 \log ^8(-81+x) \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.66, size = 50, normalized size = 2.78 \begin {gather*} x^{2} \log \left (x - 81\right )^{8} + 8 \, x^{3} \log \left (x - 81\right )^{6} + 24 \, x^{4} \log \left (x - 81\right )^{4} + 32 \, x^{5} \log \left (x - 81\right )^{2} + 16 \, x^{6} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.29, size = 50, normalized size = 2.78 \begin {gather*} x^{2} \log \left (x - 81\right )^{8} + 8 \, x^{3} \log \left (x - 81\right )^{6} + 24 \, x^{4} \log \left (x - 81\right )^{4} + 32 \, x^{5} \log \left (x - 81\right )^{2} + 16 \, x^{6} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.47, size = 51, normalized size = 2.83
method | result | size |
risch | \(\ln \left (x -81\right )^{8} x^{2}+8 \ln \left (x -81\right )^{6} x^{3}+24 \ln \left (x -81\right )^{4} x^{4}+32 \ln \left (x -81\right )^{2} x^{5}+16 x^{6}+x\) | \(51\) |
derivativedivides | \(-27113235502257+334731302497 x +111577100832 \ln \left (x -81\right )^{2}+10331213040 \left (x -81\right )^{2}+\ln \left (x -81\right )^{8} \left (x -81\right )^{2}+162 \ln \left (x -81\right )^{8} \left (x -81\right )+8 \ln \left (x -81\right )^{6} \left (x -81\right )^{3}+1944 \ln \left (x -81\right )^{6} \left (x -81\right )^{2}+24 \ln \left (x -81\right )^{4} \left (x -81\right )^{4}+157464 \ln \left (x -81\right )^{6} \left (x -81\right )+7776 \ln \left (x -81\right )^{4} \left (x -81\right )^{3}+32 \ln \left (x -81\right )^{2} \left (x -81\right )^{5}+944784 \ln \left (x -81\right )^{4} \left (x -81\right )^{2}+12960 \ln \left (x -81\right )^{2} \left (x -81\right )^{4}+51018336 \ln \left (x -81\right )^{4} \left (x -81\right )+2099520 \ln \left (x -81\right )^{2} \left (x -81\right )^{3}+170061120 \ln \left (x -81\right )^{2} \left (x -81\right )^{2}+6887475360 \ln \left (x -81\right )^{2} \left (x -81\right )+6561 \ln \left (x -81\right )^{8}+4251528 \ln \left (x -81\right )^{6}+1033121304 \ln \left (x -81\right )^{4}+16 \left (x -81\right )^{6}+7776 \left (x -81\right )^{5}+1574640 \left (x -81\right )^{4}+170061120 \left (x -81\right )^{3}\) | \(246\) |
default | \(-27113235502257+334731302497 x +111577100832 \ln \left (x -81\right )^{2}+10331213040 \left (x -81\right )^{2}+\ln \left (x -81\right )^{8} \left (x -81\right )^{2}+162 \ln \left (x -81\right )^{8} \left (x -81\right )+8 \ln \left (x -81\right )^{6} \left (x -81\right )^{3}+1944 \ln \left (x -81\right )^{6} \left (x -81\right )^{2}+24 \ln \left (x -81\right )^{4} \left (x -81\right )^{4}+157464 \ln \left (x -81\right )^{6} \left (x -81\right )+7776 \ln \left (x -81\right )^{4} \left (x -81\right )^{3}+32 \ln \left (x -81\right )^{2} \left (x -81\right )^{5}+944784 \ln \left (x -81\right )^{4} \left (x -81\right )^{2}+12960 \ln \left (x -81\right )^{2} \left (x -81\right )^{4}+51018336 \ln \left (x -81\right )^{4} \left (x -81\right )+2099520 \ln \left (x -81\right )^{2} \left (x -81\right )^{3}+170061120 \ln \left (x -81\right )^{2} \left (x -81\right )^{2}+6887475360 \ln \left (x -81\right )^{2} \left (x -81\right )+6561 \ln \left (x -81\right )^{8}+4251528 \ln \left (x -81\right )^{6}+1033121304 \ln \left (x -81\right )^{4}+16 \left (x -81\right )^{6}+7776 \left (x -81\right )^{5}+1574640 \left (x -81\right )^{4}+170061120 \left (x -81\right )^{3}\) | \(246\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.40, size = 1044, normalized size = 58.00 result too large to display
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.86, size = 50, normalized size = 2.78 \begin {gather*} 16\,x^6+32\,x^5\,{\ln \left (x-81\right )}^2+24\,x^4\,{\ln \left (x-81\right )}^4+8\,x^3\,{\ln \left (x-81\right )}^6+x^2\,{\ln \left (x-81\right )}^8+x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.20, size = 51, normalized size = 2.83 \begin {gather*} 16 x^{6} + 32 x^{5} \log {\left (x - 81 \right )}^{2} + 24 x^{4} \log {\left (x - 81 \right )}^{4} + 8 x^{3} \log {\left (x - 81 \right )}^{6} + x^{2} \log {\left (x - 81 \right )}^{8} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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