3.57.64 \(\int \frac {10 x-15 x^2-18 x^3+21 x^4-2 x^5-4 x^6+x^7+e^x (-10 x+5 x^2+8 x^3-6 x^4+x^5)+(5 x^2-4 x^4+x^5) \log (\frac {1+x}{5-5 x+x^2})}{5-30 x+41 x^2+15 x^3-12 x^4+17 x^5-21 x^6+6 x^7-4 x^8+x^9+e^{2 x} (5-4 x^2+x^3)+e^x (-10+30 x+8 x^2-16 x^3+6 x^4-8 x^5+2 x^6)+(10 x-30 x^2-8 x^3+16 x^4-6 x^5+8 x^6-2 x^7+e^x (-10 x+8 x^3-2 x^4)) \log (\frac {1+x}{5-5 x+x^2})+(5 x^2-4 x^4+x^5) \log ^2(\frac {1+x}{5-5 x+x^2})} \, dx\)

Optimal. Leaf size=36 \[ \frac {x}{-3+\frac {1-e^x-x^3}{x}+\log \left (\frac {1+x}{5+(-5+x) x}\right )} \]

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Rubi [F]  time = 78.90, 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 {10 x-15 x^2-18 x^3+21 x^4-2 x^5-4 x^6+x^7+e^x \left (-10 x+5 x^2+8 x^3-6 x^4+x^5\right )+\left (5 x^2-4 x^4+x^5\right ) \log \left (\frac {1+x}{5-5 x+x^2}\right )}{5-30 x+41 x^2+15 x^3-12 x^4+17 x^5-21 x^6+6 x^7-4 x^8+x^9+e^{2 x} \left (5-4 x^2+x^3\right )+e^x \left (-10+30 x+8 x^2-16 x^3+6 x^4-8 x^5+2 x^6\right )+\left (10 x-30 x^2-8 x^3+16 x^4-6 x^5+8 x^6-2 x^7+e^x \left (-10 x+8 x^3-2 x^4\right )\right ) \log \left (\frac {1+x}{5-5 x+x^2}\right )+\left (5 x^2-4 x^4+x^5\right ) \log ^2\left (\frac {1+x}{5-5 x+x^2}\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(10*x - 15*x^2 - 18*x^3 + 21*x^4 - 2*x^5 - 4*x^6 + x^7 + E^x*(-10*x + 5*x^2 + 8*x^3 - 6*x^4 + x^5) + (5*x^
2 - 4*x^4 + x^5)*Log[(1 + x)/(5 - 5*x + x^2)])/(5 - 30*x + 41*x^2 + 15*x^3 - 12*x^4 + 17*x^5 - 21*x^6 + 6*x^7
- 4*x^8 + x^9 + E^(2*x)*(5 - 4*x^2 + x^3) + E^x*(-10 + 30*x + 8*x^2 - 16*x^3 + 6*x^4 - 8*x^5 + 2*x^6) + (10*x
- 30*x^2 - 8*x^3 + 16*x^4 - 6*x^5 + 8*x^6 - 2*x^7 + E^x*(-10*x + 8*x^3 - 2*x^4))*Log[(1 + x)/(5 - 5*x + x^2)]
+ (5*x^2 - 4*x^4 + x^5)*Log[(1 + x)/(5 - 5*x + x^2)]^2),x]

[Out]

14*Defer[Int][(-1 + E^x + 3*x + x^3 - x*Log[(1 + x)/(5 - 5*x + x^2)])^(-2), x] + 30*Sqrt[5]*Defer[Int][1/((5 +
Sqrt[5] - 2*x)*(-1 + E^x + 3*x + x^3 - x*Log[(1 + x)/(5 - 5*x + x^2)])^2), x] + 6*Defer[Int][x/(-1 + E^x + 3*
x + x^3 - x*Log[(1 + x)/(5 - 5*x + x^2)])^2, x] + 5*Defer[Int][x^2/(-1 + E^x + 3*x + x^3 - x*Log[(1 + x)/(5 -
5*x + x^2)])^2, x] - 3*Defer[Int][x^3/(-1 + E^x + 3*x + x^3 - x*Log[(1 + x)/(5 - 5*x + x^2)])^2, x] + 3*Defer[
Int][x^4/(-1 + E^x + 3*x + x^3 - x*Log[(1 + x)/(5 - 5*x + x^2)])^2, x] - Defer[Int][x^5/(-1 + E^x + 3*x + x^3
- x*Log[(1 + x)/(5 - 5*x + x^2)])^2, x] + Defer[Int][1/((1 + x)*(-1 + E^x + 3*x + x^3 - x*Log[(1 + x)/(5 - 5*x
+ x^2)])^2), x] + 50*(1 + Sqrt[5])*Defer[Int][1/((-5 - Sqrt[5] + 2*x)*(-1 + E^x + 3*x + x^3 - x*Log[(1 + x)/(
5 - 5*x + x^2)])^2), x] + 30*Sqrt[5]*Defer[Int][1/((-5 + Sqrt[5] + 2*x)*(-1 + E^x + 3*x + x^3 - x*Log[(1 + x)/
(5 - 5*x + x^2)])^2), x] + 50*(1 - Sqrt[5])*Defer[Int][1/((-5 + Sqrt[5] + 2*x)*(-1 + E^x + 3*x + x^3 - x*Log[(
1 + x)/(5 - 5*x + x^2)])^2), x] - Defer[Int][(x^2*Log[(1 + x)/(5 - 5*x + x^2)])/(-1 + E^x + 3*x + x^3 - x*Log[
(1 + x)/(5 - 5*x + x^2)])^2, x] + Defer[Int][(x^3*Log[(1 + x)/(5 - 5*x + x^2)])/(-1 + E^x + 3*x + x^3 - x*Log[
(1 + x)/(5 - 5*x + x^2)])^2, x] - 2*Defer[Int][x/(-1 + E^x + 3*x + x^3 - x*Log[(1 + x)/(5 - 5*x + x^2)]), x] +
Defer[Int][x^2/(-1 + E^x + 3*x + x^3 - x*Log[(1 + x)/(5 - 5*x + x^2)]), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {x \left (10-15 x-18 x^2+21 x^3-2 x^4-4 x^5+x^6+e^x \left (-10+5 x+8 x^2-6 x^3+x^4\right )+x \left (5-4 x^2+x^3\right ) \log \left (\frac {1+x}{5-5 x+x^2}\right )\right )}{\left (5-4 x^2+x^3\right ) \left (1-e^x-3 x-x^3+x \log \left (\frac {1+x}{5-5 x+x^2}\right )\right )^2} \, dx\\ &=\int \left (\frac {(-2+x) x}{-1+e^x+3 x+x^3-x \log \left (\frac {1+x}{5-5 x+x^2}\right )}-\frac {x^2 \left (-20+25 x-x^2-12 x^3+15 x^4-7 x^5+x^6+5 \log \left (\frac {1+x}{5-5 x+x^2}\right )-5 x \log \left (\frac {1+x}{5-5 x+x^2}\right )-4 x^2 \log \left (\frac {1+x}{5-5 x+x^2}\right )+5 x^3 \log \left (\frac {1+x}{5-5 x+x^2}\right )-x^4 \log \left (\frac {1+x}{5-5 x+x^2}\right )\right )}{\left (5-4 x^2+x^3\right ) \left (-1+e^x+3 x+x^3-x \log \left (\frac {1+x}{5-5 x+x^2}\right )\right )^2}\right ) \, dx\\ &=\int \frac {(-2+x) x}{-1+e^x+3 x+x^3-x \log \left (\frac {1+x}{5-5 x+x^2}\right )} \, dx-\int \frac {x^2 \left (-20+25 x-x^2-12 x^3+15 x^4-7 x^5+x^6+5 \log \left (\frac {1+x}{5-5 x+x^2}\right )-5 x \log \left (\frac {1+x}{5-5 x+x^2}\right )-4 x^2 \log \left (\frac {1+x}{5-5 x+x^2}\right )+5 x^3 \log \left (\frac {1+x}{5-5 x+x^2}\right )-x^4 \log \left (\frac {1+x}{5-5 x+x^2}\right )\right )}{\left (5-4 x^2+x^3\right ) \left (-1+e^x+3 x+x^3-x \log \left (\frac {1+x}{5-5 x+x^2}\right )\right )^2} \, dx\\ &=-\int \frac {x^2 \left (-20+25 x-x^2-12 x^3+15 x^4-7 x^5+x^6-\left (-5+5 x+4 x^2-5 x^3+x^4\right ) \log \left (\frac {1+x}{5-5 x+x^2}\right )\right )}{\left (5-4 x^2+x^3\right ) \left (1-e^x-3 x-x^3+x \log \left (\frac {1+x}{5-5 x+x^2}\right )\right )^2} \, dx+\int \left (-\frac {2 x}{-1+e^x+3 x+x^3-x \log \left (\frac {1+x}{5-5 x+x^2}\right )}+\frac {x^2}{-1+e^x+3 x+x^3-x \log \left (\frac {1+x}{5-5 x+x^2}\right )}\right ) \, dx\\ &=-\left (2 \int \frac {x}{-1+e^x+3 x+x^3-x \log \left (\frac {1+x}{5-5 x+x^2}\right )} \, dx\right )+\int \frac {x^2}{-1+e^x+3 x+x^3-x \log \left (\frac {1+x}{5-5 x+x^2}\right )} \, dx-\int \left (\frac {-20+25 x-x^2-12 x^3+15 x^4-7 x^5+x^6+5 \log \left (\frac {1+x}{5-5 x+x^2}\right )-5 x \log \left (\frac {1+x}{5-5 x+x^2}\right )-4 x^2 \log \left (\frac {1+x}{5-5 x+x^2}\right )+5 x^3 \log \left (\frac {1+x}{5-5 x+x^2}\right )-x^4 \log \left (\frac {1+x}{5-5 x+x^2}\right )}{11 (1+x) \left (-1+e^x+3 x+x^3-x \log \left (\frac {1+x}{5-5 x+x^2}\right )\right )^2}+\frac {5 (-1+2 x) \left (-20+25 x-x^2-12 x^3+15 x^4-7 x^5+x^6+5 \log \left (\frac {1+x}{5-5 x+x^2}\right )-5 x \log \left (\frac {1+x}{5-5 x+x^2}\right )-4 x^2 \log \left (\frac {1+x}{5-5 x+x^2}\right )+5 x^3 \log \left (\frac {1+x}{5-5 x+x^2}\right )-x^4 \log \left (\frac {1+x}{5-5 x+x^2}\right )\right )}{11 \left (5-5 x+x^2\right ) \left (-1+e^x+3 x+x^3-x \log \left (\frac {1+x}{5-5 x+x^2}\right )\right )^2}\right ) \, dx\\ &=-\left (\frac {1}{11} \int \frac {-20+25 x-x^2-12 x^3+15 x^4-7 x^5+x^6+5 \log \left (\frac {1+x}{5-5 x+x^2}\right )-5 x \log \left (\frac {1+x}{5-5 x+x^2}\right )-4 x^2 \log \left (\frac {1+x}{5-5 x+x^2}\right )+5 x^3 \log \left (\frac {1+x}{5-5 x+x^2}\right )-x^4 \log \left (\frac {1+x}{5-5 x+x^2}\right )}{(1+x) \left (-1+e^x+3 x+x^3-x \log \left (\frac {1+x}{5-5 x+x^2}\right )\right )^2} \, dx\right )-\frac {5}{11} \int \frac {(-1+2 x) \left (-20+25 x-x^2-12 x^3+15 x^4-7 x^5+x^6+5 \log \left (\frac {1+x}{5-5 x+x^2}\right )-5 x \log \left (\frac {1+x}{5-5 x+x^2}\right )-4 x^2 \log \left (\frac {1+x}{5-5 x+x^2}\right )+5 x^3 \log \left (\frac {1+x}{5-5 x+x^2}\right )-x^4 \log \left (\frac {1+x}{5-5 x+x^2}\right )\right )}{\left (5-5 x+x^2\right ) \left (-1+e^x+3 x+x^3-x \log \left (\frac {1+x}{5-5 x+x^2}\right )\right )^2} \, dx-2 \int \frac {x}{-1+e^x+3 x+x^3-x \log \left (\frac {1+x}{5-5 x+x^2}\right )} \, dx+\int \frac {x^2}{-1+e^x+3 x+x^3-x \log \left (\frac {1+x}{5-5 x+x^2}\right )} \, dx\\ &=-\left (\frac {1}{11} \int \frac {-20+25 x-x^2-12 x^3+15 x^4-7 x^5+x^6-\left (-5+5 x+4 x^2-5 x^3+x^4\right ) \log \left (\frac {1+x}{5-5 x+x^2}\right )}{(1+x) \left (1-e^x-3 x-x^3+x \log \left (\frac {1+x}{5-5 x+x^2}\right )\right )^2} \, dx\right )-\frac {5}{11} \int \frac {(1-2 x) \left (20-25 x+x^2+12 x^3-15 x^4+7 x^5-x^6+\left (-5+5 x+4 x^2-5 x^3+x^4\right ) \log \left (\frac {1+x}{5-5 x+x^2}\right )\right )}{\left (5-5 x+x^2\right ) \left (1-e^x-3 x-x^3+x \log \left (\frac {1+x}{5-5 x+x^2}\right )\right )^2} \, dx-2 \int \frac {x}{-1+e^x+3 x+x^3-x \log \left (\frac {1+x}{5-5 x+x^2}\right )} \, dx+\int \frac {x^2}{-1+e^x+3 x+x^3-x \log \left (\frac {1+x}{5-5 x+x^2}\right )} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.11, size = 38, normalized size = 1.06 \begin {gather*} \frac {x^2}{1-e^x-3 x-x^3+x \log \left (\frac {1+x}{5-5 x+x^2}\right )} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(10*x - 15*x^2 - 18*x^3 + 21*x^4 - 2*x^5 - 4*x^6 + x^7 + E^x*(-10*x + 5*x^2 + 8*x^3 - 6*x^4 + x^5) +
(5*x^2 - 4*x^4 + x^5)*Log[(1 + x)/(5 - 5*x + x^2)])/(5 - 30*x + 41*x^2 + 15*x^3 - 12*x^4 + 17*x^5 - 21*x^6 +
6*x^7 - 4*x^8 + x^9 + E^(2*x)*(5 - 4*x^2 + x^3) + E^x*(-10 + 30*x + 8*x^2 - 16*x^3 + 6*x^4 - 8*x^5 + 2*x^6) +
(10*x - 30*x^2 - 8*x^3 + 16*x^4 - 6*x^5 + 8*x^6 - 2*x^7 + E^x*(-10*x + 8*x^3 - 2*x^4))*Log[(1 + x)/(5 - 5*x +
x^2)] + (5*x^2 - 4*x^4 + x^5)*Log[(1 + x)/(5 - 5*x + x^2)]^2),x]

[Out]

x^2/(1 - E^x - 3*x - x^3 + x*Log[(1 + x)/(5 - 5*x + x^2)])

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fricas [A]  time = 0.64, size = 35, normalized size = 0.97 \begin {gather*} -\frac {x^{2}}{x^{3} - x \log \left (\frac {x + 1}{x^{2} - 5 \, x + 5}\right ) + 3 \, x + e^{x} - 1} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((x^5-4*x^4+5*x^2)*log((x+1)/(x^2-5*x+5))+(x^5-6*x^4+8*x^3+5*x^2-10*x)*exp(x)+x^7-4*x^6-2*x^5+21*x^4
-18*x^3-15*x^2+10*x)/((x^5-4*x^4+5*x^2)*log((x+1)/(x^2-5*x+5))^2+((-2*x^4+8*x^3-10*x)*exp(x)-2*x^7+8*x^6-6*x^5
+16*x^4-8*x^3-30*x^2+10*x)*log((x+1)/(x^2-5*x+5))+(x^3-4*x^2+5)*exp(x)^2+(2*x^6-8*x^5+6*x^4-16*x^3+8*x^2+30*x-
10)*exp(x)+x^9-4*x^8+6*x^7-21*x^6+17*x^5-12*x^4+15*x^3+41*x^2-30*x+5),x, algorithm="fricas")

[Out]

-x^2/(x^3 - x*log((x + 1)/(x^2 - 5*x + 5)) + 3*x + e^x - 1)

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giac [A]  time = 0.65, size = 35, normalized size = 0.97 \begin {gather*} -\frac {x^{2}}{x^{3} - x \log \left (\frac {x + 1}{x^{2} - 5 \, x + 5}\right ) + 3 \, x + e^{x} - 1} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((x^5-4*x^4+5*x^2)*log((x+1)/(x^2-5*x+5))+(x^5-6*x^4+8*x^3+5*x^2-10*x)*exp(x)+x^7-4*x^6-2*x^5+21*x^4
-18*x^3-15*x^2+10*x)/((x^5-4*x^4+5*x^2)*log((x+1)/(x^2-5*x+5))^2+((-2*x^4+8*x^3-10*x)*exp(x)-2*x^7+8*x^6-6*x^5
+16*x^4-8*x^3-30*x^2+10*x)*log((x+1)/(x^2-5*x+5))+(x^3-4*x^2+5)*exp(x)^2+(2*x^6-8*x^5+6*x^4-16*x^3+8*x^2+30*x-
10)*exp(x)+x^9-4*x^8+6*x^7-21*x^6+17*x^5-12*x^4+15*x^3+41*x^2-30*x+5),x, algorithm="giac")

[Out]

-x^2/(x^3 - x*log((x + 1)/(x^2 - 5*x + 5)) + 3*x + e^x - 1)

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maple [C]  time = 0.14, size = 177, normalized size = 4.92

method	result	size
risch	\(-\frac {2 x^{2}}{i \pi x \,\mathrm {csgn}\left (i \left (x +1\right )\right ) \mathrm {csgn}\left (\frac {i}{x^{2}-5 x +5}\right ) \mathrm {csgn}\left (\frac {i \left (x +1\right )}{x^{2}-5 x +5}\right )-i \pi x \,\mathrm {csgn}\left (i \left (x +1\right )\right ) \mathrm {csgn}\left (\frac {i \left (x +1\right )}{x^{2}-5 x +5}\right )^{2}-i \pi x \,\mathrm {csgn}\left (\frac {i}{x^{2}-5 x +5}\right ) \mathrm {csgn}\left (\frac {i \left (x +1\right )}{x^{2}-5 x +5}\right )^{2}+i \pi x \mathrm {csgn}\left (\frac {i \left (x +1\right )}{x^{2}-5 x +5}\right )^{3}+2 x^{3}-2 \ln \left (x +1\right ) x +2 x \ln \left (x^{2}-5 x +5\right )+6 x +2 \,{\mathrm e}^{x}-2}\)	\(177\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((x^5-4*x^4+5*x^2)*ln((x+1)/(x^2-5*x+5))+(x^5-6*x^4+8*x^3+5*x^2-10*x)*exp(x)+x^7-4*x^6-2*x^5+21*x^4-18*x^3
-15*x^2+10*x)/((x^5-4*x^4+5*x^2)*ln((x+1)/(x^2-5*x+5))^2+((-2*x^4+8*x^3-10*x)*exp(x)-2*x^7+8*x^6-6*x^5+16*x^4-
8*x^3-30*x^2+10*x)*ln((x+1)/(x^2-5*x+5))+(x^3-4*x^2+5)*exp(x)^2+(2*x^6-8*x^5+6*x^4-16*x^3+8*x^2+30*x-10)*exp(x
)+x^9-4*x^8+6*x^7-21*x^6+17*x^5-12*x^4+15*x^3+41*x^2-30*x+5),x,method=_RETURNVERBOSE)

[Out]

-2*x^2/(I*Pi*x*csgn(I*(x+1))*csgn(I/(x^2-5*x+5))*csgn(I*(x+1)/(x^2-5*x+5))-I*Pi*x*csgn(I*(x+1))*csgn(I*(x+1)/(
x^2-5*x+5))^2-I*Pi*x*csgn(I/(x^2-5*x+5))*csgn(I*(x+1)/(x^2-5*x+5))^2+I*Pi*x*csgn(I*(x+1)/(x^2-5*x+5))^3+2*x^3-
2*ln(x+1)*x+2*x*ln(x^2-5*x+5)+6*x+2*exp(x)-2)

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maxima [A]  time = 0.54, size = 35, normalized size = 0.97 \begin {gather*} -\frac {x^{2}}{x^{3} + x \log \left (x^{2} - 5 \, x + 5\right ) - x \log \left (x + 1\right ) + 3 \, x + e^{x} - 1} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((x^5-4*x^4+5*x^2)*log((x+1)/(x^2-5*x+5))+(x^5-6*x^4+8*x^3+5*x^2-10*x)*exp(x)+x^7-4*x^6-2*x^5+21*x^4
-18*x^3-15*x^2+10*x)/((x^5-4*x^4+5*x^2)*log((x+1)/(x^2-5*x+5))^2+((-2*x^4+8*x^3-10*x)*exp(x)-2*x^7+8*x^6-6*x^5
+16*x^4-8*x^3-30*x^2+10*x)*log((x+1)/(x^2-5*x+5))+(x^3-4*x^2+5)*exp(x)^2+(2*x^6-8*x^5+6*x^4-16*x^3+8*x^2+30*x-
10)*exp(x)+x^9-4*x^8+6*x^7-21*x^6+17*x^5-12*x^4+15*x^3+41*x^2-30*x+5),x, algorithm="maxima")

[Out]

-x^2/(x^3 + x*log(x^2 - 5*x + 5) - x*log(x + 1) + 3*x + e^x - 1)

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mupad [B]  time = 3.93, size = 216, normalized size = 6.00 \begin {gather*} -\frac {25\,x^3\,{\mathrm {e}}^x+x^9\,\left ({\mathrm {e}}^x+33\right )-x^8\,\left (9\,{\mathrm {e}}^x-19\right )-x^2\,\left (25\,{\mathrm {e}}^x-25\right )-x^6\,\left (6\,{\mathrm {e}}^x-61\right )-x^5\,\left (50\,{\mathrm {e}}^x-70\right )+x^4\,\left (40\,{\mathrm {e}}^x-90\right )+x^7\,\left (24\,{\mathrm {e}}^x-106\right )-16\,x^{10}+2\,x^{11}}{\left (3\,x+{\mathrm {e}}^x+x^3-x\,\ln \left (\frac {x+1}{x^2-5\,x+5}\right )-1\right )\,\left (40\,x^2\,{\mathrm {e}}^x-25\,{\mathrm {e}}^x-50\,x^3\,{\mathrm {e}}^x-6\,x^4\,{\mathrm {e}}^x+24\,x^5\,{\mathrm {e}}^x-9\,x^6\,{\mathrm {e}}^x+x^7\,{\mathrm {e}}^x+25\,x\,{\mathrm {e}}^x-90\,x^2+70\,x^3+61\,x^4-106\,x^5+19\,x^6+33\,x^7-16\,x^8+2\,x^9+25\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((10*x + log((x + 1)/(x^2 - 5*x + 5))*(5*x^2 - 4*x^4 + x^5) - 15*x^2 - 18*x^3 + 21*x^4 - 2*x^5 - 4*x^6 + x^
7 + exp(x)*(5*x^2 - 10*x + 8*x^3 - 6*x^4 + x^5))/(exp(2*x)*(x^3 - 4*x^2 + 5) - 30*x + log((x + 1)/(x^2 - 5*x +
5))^2*(5*x^2 - 4*x^4 + x^5) + exp(x)*(30*x + 8*x^2 - 16*x^3 + 6*x^4 - 8*x^5 + 2*x^6 - 10) - log((x + 1)/(x^2
- 5*x + 5))*(30*x^2 - 10*x + 8*x^3 - 16*x^4 + 6*x^5 - 8*x^6 + 2*x^7 + exp(x)*(10*x - 8*x^3 + 2*x^4)) + 41*x^2
+ 15*x^3 - 12*x^4 + 17*x^5 - 21*x^6 + 6*x^7 - 4*x^8 + x^9 + 5),x)

[Out]

-(25*x^3*exp(x) + x^9*(exp(x) + 33) - x^8*(9*exp(x) - 19) - x^2*(25*exp(x) - 25) - x^6*(6*exp(x) - 61) - x^5*(
50*exp(x) - 70) + x^4*(40*exp(x) - 90) + x^7*(24*exp(x) - 106) - 16*x^10 + 2*x^11)/((3*x + exp(x) + x^3 - x*lo
g((x + 1)/(x^2 - 5*x + 5)) - 1)*(40*x^2*exp(x) - 25*exp(x) - 50*x^3*exp(x) - 6*x^4*exp(x) + 24*x^5*exp(x) - 9*
x^6*exp(x) + x^7*exp(x) + 25*x*exp(x) - 90*x^2 + 70*x^3 + 61*x^4 - 106*x^5 + 19*x^6 + 33*x^7 - 16*x^8 + 2*x^9
+ 25))

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sympy [A]  time = 0.57, size = 31, normalized size = 0.86 \begin {gather*} - \frac {x^{2}}{x^{3} - x \log {\left (\frac {x + 1}{x^{2} - 5 x + 5} \right )} + 3 x + e^{x} - 1} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((x**5-4*x**4+5*x**2)*ln((x+1)/(x**2-5*x+5))+(x**5-6*x**4+8*x**3+5*x**2-10*x)*exp(x)+x**7-4*x**6-2*x
**5+21*x**4-18*x**3-15*x**2+10*x)/((x**5-4*x**4+5*x**2)*ln((x+1)/(x**2-5*x+5))**2+((-2*x**4+8*x**3-10*x)*exp(x
)-2*x**7+8*x**6-6*x**5+16*x**4-8*x**3-30*x**2+10*x)*ln((x+1)/(x**2-5*x+5))+(x**3-4*x**2+5)*exp(x)**2+(2*x**6-8
*x**5+6*x**4-16*x**3+8*x**2+30*x-10)*exp(x)+x**9-4*x**8+6*x**7-21*x**6+17*x**5-12*x**4+15*x**3+41*x**2-30*x+5)
,x)

[Out]

-x**2/(x**3 - x*log((x + 1)/(x**2 - 5*x + 5)) + 3*x + exp(x) - 1)

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