Integrand size = 60, antiderivative size = 26 \[ \int \frac {4 x^3-5996 x^4-6959 x^5-1812 x^6+84 x^7+\left (-300 x^2-388 x^3-109 x^4+5 x^5\right ) \log (25-x)}{-25+x} \, dx=2+\left (2 x+x^2\right )^2 \left (12 x^3+x \log (25-x)\right ) \] Output:
(x*ln(-x+25)+12*x^3)*(x^2+2*x)^2+2
Time = 0.05 (sec) , antiderivative size = 48, normalized size of antiderivative = 1.85 \[ \int \frac {4 x^3-5996 x^4-6959 x^5-1812 x^6+84 x^7+\left (-300 x^2-388 x^3-109 x^4+5 x^5\right ) \log (25-x)}{-25+x} \, dx=48 x^5+48 x^6+12 x^7+4 x^3 \log (25-x)+4 x^4 \log (25-x)+x^5 \log (25-x) \] Input:
Integrate[(4*x^3 - 5996*x^4 - 6959*x^5 - 1812*x^6 + 84*x^7 + (-300*x^2 - 3 88*x^3 - 109*x^4 + 5*x^5)*Log[25 - x])/(-25 + x),x]
Output:
48*x^5 + 48*x^6 + 12*x^7 + 4*x^3*Log[25 - x] + 4*x^4*Log[25 - x] + x^5*Log [25 - x]
Time = 0.72 (sec) , antiderivative size = 48, normalized size of antiderivative = 1.85, number of steps used = 3, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {7292, 7293, 2009}
Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.
\(\displaystyle \int \frac {84 x^7-1812 x^6-6959 x^5-5996 x^4+4 x^3+\left (5 x^5-109 x^4-388 x^3-300 x^2\right ) \log (25-x)}{x-25} \, dx\) |
\(\Big \downarrow \) 7292 |
\(\displaystyle \int \frac {x^2 (x+2) \left (-84 x^4+1980 x^3+2999 x^2-5 x^2 \log (25-x)-2 x+119 x \log (25-x)+150 \log (25-x)\right )}{25-x}dx\) |
\(\Big \downarrow \) 7293 |
\(\displaystyle \int \left (\left (5 x^2+16 x+12\right ) x^2 \log (25-x)+\frac {\left (84 x^4-1812 x^3-6959 x^2-5996 x+4\right ) x^3}{x-25}\right )dx\) |
\(\Big \downarrow \) 2009 |
\(\displaystyle 12 x^7+48 x^6+48 x^5+x^5 \log (25-x)+4 x^4 \log (25-x)+4 x^3 \log (25-x)\) |
Input:
Int[(4*x^3 - 5996*x^4 - 6959*x^5 - 1812*x^6 + 84*x^7 + (-300*x^2 - 388*x^3 - 109*x^4 + 5*x^5)*Log[25 - x])/(-25 + x),x]
Output:
48*x^5 + 48*x^6 + 12*x^7 + 4*x^3*Log[25 - x] + 4*x^4*Log[25 - x] + x^5*Log [25 - x]
Time = 1.23 (sec) , antiderivative size = 38, normalized size of antiderivative = 1.46
method | result | size |
risch | \(\left (x^{5}+4 x^{4}+4 x^{3}\right ) \ln \left (-x +25\right )+12 x^{7}+48 x^{6}+48 x^{5}\) | \(38\) |
norman | \(x^{5} \ln \left (-x +25\right )+48 x^{5}+48 x^{6}+12 x^{7}+4 \ln \left (-x +25\right ) x^{3}+4 \ln \left (-x +25\right ) x^{4}\) | \(49\) |
parallelrisch | \(x^{5} \ln \left (-x +25\right )+48 x^{5}+48 x^{6}+12 x^{7}+4 \ln \left (-x +25\right ) x^{3}+4 \ln \left (-x +25\right ) x^{4}\) | \(49\) |
parts | \(12 x^{7}+48 x^{6}+48 x^{5}+11390625 \ln \left (x -25\right )-\ln \left (-x +25\right ) \left (-x +25\right )^{5}+\frac {102671875}{4}+129 \ln \left (-x +25\right ) \left (-x +25\right )^{4}-6654 \ln \left (-x +25\right ) \left (-x +25\right )^{3}+171550 \ln \left (-x +25\right ) \left (-x +25\right )^{2}-2210625 \ln \left (-x +25\right ) \left (-x +25\right )\) | \(97\) |
derivativedivides | \(-12 \left (-x +25\right )^{7}-\ln \left (-x +25\right ) \left (-x +25\right )^{5}-164748 \left (-x +25\right )^{5}+2148 \left (-x +25\right )^{6}+129 \ln \left (-x +25\right ) \left (-x +25\right )^{4}+7018500 \left (-x +25\right )^{4}-6654 \ln \left (-x +25\right ) \left (-x +25\right )^{3}-179362500 \left (-x +25\right )^{3}+171550 \ln \left (-x +25\right ) \left (-x +25\right )^{2}+2749687500 \left (-x +25\right )^{2}-2210625 \ln \left (-x +25\right ) \left (-x +25\right )+23414062500 x -585351562500+11390625 \ln \left (-x +25\right )\) | \(141\) |
default | \(-12 \left (-x +25\right )^{7}-\ln \left (-x +25\right ) \left (-x +25\right )^{5}-164748 \left (-x +25\right )^{5}+2148 \left (-x +25\right )^{6}+129 \ln \left (-x +25\right ) \left (-x +25\right )^{4}+7018500 \left (-x +25\right )^{4}-6654 \ln \left (-x +25\right ) \left (-x +25\right )^{3}-179362500 \left (-x +25\right )^{3}+171550 \ln \left (-x +25\right ) \left (-x +25\right )^{2}+2749687500 \left (-x +25\right )^{2}-2210625 \ln \left (-x +25\right ) \left (-x +25\right )+23414062500 x -585351562500+11390625 \ln \left (-x +25\right )\) | \(141\) |
orering | \(\frac {3 x \left (88 x^{5}-4112 x^{4}+40827 x^{3}+168726 x^{2}+139740 x -200\right ) \left (\left (5 x^{5}-109 x^{4}-388 x^{3}-300 x^{2}\right ) \ln \left (-x +25\right )+84 x^{7}-1812 x^{6}-6959 x^{5}-5996 x^{4}+4 x^{3}\right )}{\left (840 x^{5}-39888 x^{4}+420865 x^{3}+1247306 x^{2}+898236 x -1200\right ) \left (x -25\right )}-\frac {\left (x -25\right ) \left (24 x^{4}-504 x^{3}-2303 x^{2}-2396 x +4\right ) x^{2} \left (\frac {\left (25 x^{4}-436 x^{3}-1164 x^{2}-600 x \right ) \ln \left (-x +25\right )-\frac {5 x^{5}-109 x^{4}-388 x^{3}-300 x^{2}}{-x +25}+588 x^{6}-10872 x^{5}-34795 x^{4}-23984 x^{3}+12 x^{2}}{x -25}-\frac {\left (5 x^{5}-109 x^{4}-388 x^{3}-300 x^{2}\right ) \ln \left (-x +25\right )+84 x^{7}-1812 x^{6}-6959 x^{5}-5996 x^{4}+4 x^{3}}{\left (x -25\right )^{2}}\right )}{840 x^{5}-39888 x^{4}+420865 x^{3}+1247306 x^{2}+898236 x -1200}\) | \(321\) |
Input:
int(((5*x^5-109*x^4-388*x^3-300*x^2)*ln(-x+25)+84*x^7-1812*x^6-6959*x^5-59 96*x^4+4*x^3)/(x-25),x,method=_RETURNVERBOSE)
Output:
(x^5+4*x^4+4*x^3)*ln(-x+25)+12*x^7+48*x^6+48*x^5
Time = 0.21 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.42 \[ \int \frac {4 x^3-5996 x^4-6959 x^5-1812 x^6+84 x^7+\left (-300 x^2-388 x^3-109 x^4+5 x^5\right ) \log (25-x)}{-25+x} \, dx=12 \, x^{7} + 48 \, x^{6} + 48 \, x^{5} + {\left (x^{5} + 4 \, x^{4} + 4 \, x^{3}\right )} \log \left (-x + 25\right ) \] Input:
integrate(((5*x^5-109*x^4-388*x^3-300*x^2)*log(-x+25)+84*x^7-1812*x^6-6959 *x^5-5996*x^4+4*x^3)/(x-25),x, algorithm="fricas")
Output:
12*x^7 + 48*x^6 + 48*x^5 + (x^5 + 4*x^4 + 4*x^3)*log(-x + 25)
Time = 0.07 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.23 \[ \int \frac {4 x^3-5996 x^4-6959 x^5-1812 x^6+84 x^7+\left (-300 x^2-388 x^3-109 x^4+5 x^5\right ) \log (25-x)}{-25+x} \, dx=12 x^{7} + 48 x^{6} + 48 x^{5} + \left (x^{5} + 4 x^{4} + 4 x^{3}\right ) \log {\left (25 - x \right )} \] Input:
integrate(((5*x**5-109*x**4-388*x**3-300*x**2)*ln(-x+25)+84*x**7-1812*x**6 -6959*x**5-5996*x**4+4*x**3)/(x-25),x)
Output:
12*x**7 + 48*x**6 + 48*x**5 + (x**5 + 4*x**4 + 4*x**3)*log(25 - x)
Leaf count of result is larger than twice the leaf count of optimal. 136 vs. \(2 (26) = 52\).
Time = 0.03 (sec) , antiderivative size = 136, normalized size of antiderivative = 5.23 \[ \int \frac {4 x^3-5996 x^4-6959 x^5-1812 x^6+84 x^7+\left (-300 x^2-388 x^3-109 x^4+5 x^5\right ) \log (25-x)}{-25+x} \, dx=12 \, x^{7} + 48 \, x^{6} + 48 \, x^{5} + \frac {1}{12} \, {\left (12 \, x^{5} + 375 \, x^{4} + 12500 \, x^{3} + 468750 \, x^{2} + 23437500 \, x + 585937500 \, \log \left (x - 25\right )\right )} \log \left (-x + 25\right ) - \frac {109}{12} \, {\left (3 \, x^{4} + 100 \, x^{3} + 3750 \, x^{2} + 187500 \, x + 4687500 \, \log \left (x - 25\right )\right )} \log \left (-x + 25\right ) - \frac {194}{3} \, {\left (2 \, x^{3} + 75 \, x^{2} + 3750 \, x + 93750 \, \log \left (x - 25\right )\right )} \log \left (-x + 25\right ) - 150 \, {\left (x^{2} + 50 \, x + 1250 \, \log \left (x - 25\right )\right )} \log \left (-x + 25\right ) \] Input:
integrate(((5*x^5-109*x^4-388*x^3-300*x^2)*log(-x+25)+84*x^7-1812*x^6-6959 *x^5-5996*x^4+4*x^3)/(x-25),x, algorithm="maxima")
Output:
12*x^7 + 48*x^6 + 48*x^5 + 1/12*(12*x^5 + 375*x^4 + 12500*x^3 + 468750*x^2 + 23437500*x + 585937500*log(x - 25))*log(-x + 25) - 109/12*(3*x^4 + 100* x^3 + 3750*x^2 + 187500*x + 4687500*log(x - 25))*log(-x + 25) - 194/3*(2*x ^3 + 75*x^2 + 3750*x + 93750*log(x - 25))*log(-x + 25) - 150*(x^2 + 50*x + 1250*log(x - 25))*log(-x + 25)
Leaf count of result is larger than twice the leaf count of optimal. 93 vs. \(2 (26) = 52\).
Time = 0.11 (sec) , antiderivative size = 93, normalized size of antiderivative = 3.58 \[ \int \frac {4 x^3-5996 x^4-6959 x^5-1812 x^6+84 x^7+\left (-300 x^2-388 x^3-109 x^4+5 x^5\right ) \log (25-x)}{-25+x} \, dx=12 \, {\left (x - 25\right )}^{7} + 2148 \, {\left (x - 25\right )}^{6} + 164748 \, {\left (x - 25\right )}^{5} + 7018500 \, {\left (x - 25\right )}^{4} + 179362500 \, {\left (x - 25\right )}^{3} + 2749687500 \, {\left (x - 25\right )}^{2} + {\left ({\left (x - 25\right )}^{5} + 129 \, {\left (x - 25\right )}^{4} + 6654 \, {\left (x - 25\right )}^{3} + 171550 \, {\left (x - 25\right )}^{2} + 2210625 \, x - 55265625\right )} \log \left (-x + 25\right ) + 23414062500 \, x + 11390625 \, \log \left (-x + 25\right ) - 585351562500 \] Input:
integrate(((5*x^5-109*x^4-388*x^3-300*x^2)*log(-x+25)+84*x^7-1812*x^6-6959 *x^5-5996*x^4+4*x^3)/(x-25),x, algorithm="giac")
Output:
12*(x - 25)^7 + 2148*(x - 25)^6 + 164748*(x - 25)^5 + 7018500*(x - 25)^4 + 179362500*(x - 25)^3 + 2749687500*(x - 25)^2 + ((x - 25)^5 + 129*(x - 25) ^4 + 6654*(x - 25)^3 + 171550*(x - 25)^2 + 2210625*x - 55265625)*log(-x + 25) + 23414062500*x + 11390625*log(-x + 25) - 585351562500
Time = 0.09 (sec) , antiderivative size = 21, normalized size of antiderivative = 0.81 \[ \int \frac {4 x^3-5996 x^4-6959 x^5-1812 x^6+84 x^7+\left (-300 x^2-388 x^3-109 x^4+5 x^5\right ) \log (25-x)}{-25+x} \, dx=x^3\,\left (\ln \left (25-x\right )+12\,x^2\right )\,{\left (x+2\right )}^2 \] Input:
int(-(log(25 - x)*(300*x^2 + 388*x^3 + 109*x^4 - 5*x^5) - 4*x^3 + 5996*x^4 + 6959*x^5 + 1812*x^6 - 84*x^7)/(x - 25),x)
Output:
x^3*(log(25 - x) + 12*x^2)*(x + 2)^2
Time = 0.18 (sec) , antiderivative size = 62, normalized size of antiderivative = 2.38 \[ \int \frac {4 x^3-5996 x^4-6959 x^5-1812 x^6+84 x^7+\left (-300 x^2-388 x^3-109 x^4+5 x^5\right ) \log (25-x)}{-25+x} \, dx=\mathrm {log}\left (-x +25\right ) x^{5}+4 \,\mathrm {log}\left (-x +25\right ) x^{4}+4 \,\mathrm {log}\left (-x +25\right ) x^{3}-11390625 \,\mathrm {log}\left (-x +25\right )+11390625 \,\mathrm {log}\left (x -25\right )+12 x^{7}+48 x^{6}+48 x^{5} \] Input:
int(((5*x^5-109*x^4-388*x^3-300*x^2)*log(-x+25)+84*x^7-1812*x^6-6959*x^5-5 996*x^4+4*x^3)/(x-25),x)
Output:
log( - x + 25)*x**5 + 4*log( - x + 25)*x**4 + 4*log( - x + 25)*x**3 - 1139 0625*log( - x + 25) + 11390625*log(x - 25) + 12*x**7 + 48*x**6 + 48*x**5