3.74.76 \(\int \frac {e^{2 x} (-150+400 x^2+310 x^3-574 x^4-740 x^5-16 x^6+310 x^7+100 x^8)+e^{2 x} (-300+50 x+400 x^2+110 x^3-360 x^4-200 x^5) \log (3+2 x)+e^{2 x} (-150+50 x+100 x^2) \log ^2(3+2 x)}{3 x^3+2 x^4} \, dx\)

Optimal. Leaf size=31 \[ e^{2 x} \left (x+\frac {5 \left (1-x \left (-1+x^2\right )+\log (3+2 x)\right )}{x}\right )^2 \]

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Rubi [F]  time = 180.00, 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*} \text {\$Aborted} \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^(2*x)*(-150 + 400*x^2 + 310*x^3 - 574*x^4 - 740*x^5 - 16*x^6 + 310*x^7 + 100*x^8) + E^(2*x)*(-300 + 50*
x + 400*x^2 + 110*x^3 - 360*x^4 - 200*x^5)*Log[3 + 2*x] + E^(2*x)*(-150 + 50*x + 100*x^2)*Log[3 + 2*x]^2)/(3*x
^3 + 2*x^4),x]

[Out]

$Aborted

Rubi steps

Aborted

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Mathematica [A]  time = 0.07, size = 32, normalized size = 1.03 \begin {gather*} \frac {e^{2 x} \left (5+5 x+x^2-5 x^3+5 \log (3+2 x)\right )^2}{x^2} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^(2*x)*(-150 + 400*x^2 + 310*x^3 - 574*x^4 - 740*x^5 - 16*x^6 + 310*x^7 + 100*x^8) + E^(2*x)*(-300
+ 50*x + 400*x^2 + 110*x^3 - 360*x^4 - 200*x^5)*Log[3 + 2*x] + E^(2*x)*(-150 + 50*x + 100*x^2)*Log[3 + 2*x]^2
)/(3*x^3 + 2*x^4),x]

[Out]

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

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fricas [B]  time = 0.65, size = 83, normalized size = 2.68 \begin {gather*} -\frac {10 \, {\left (5 \, x^{3} - x^{2} - 5 \, x - 5\right )} e^{\left (2 \, x\right )} \log \left (2 \, x + 3\right ) - 25 \, e^{\left (2 \, x\right )} \log \left (2 \, x + 3\right )^{2} - {\left (25 \, x^{6} - 10 \, x^{5} - 49 \, x^{4} - 40 \, x^{3} + 35 \, x^{2} + 50 \, x + 25\right )} e^{\left (2 \, x\right )}}{x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((100*x^2+50*x-150)*exp(x)^2*log(2*x+3)^2+(-200*x^5-360*x^4+110*x^3+400*x^2+50*x-300)*exp(x)^2*log(2
*x+3)+(100*x^8+310*x^7-16*x^6-740*x^5-574*x^4+310*x^3+400*x^2-150)*exp(x)^2)/(2*x^4+3*x^3),x, algorithm="frica
s")

[Out]

-(10*(5*x^3 - x^2 - 5*x - 5)*e^(2*x)*log(2*x + 3) - 25*e^(2*x)*log(2*x + 3)^2 - (25*x^6 - 10*x^5 - 49*x^4 - 40
*x^3 + 35*x^2 + 50*x + 25)*e^(2*x))/x^2

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giac [B]  time = 0.19, size = 132, normalized size = 4.26 \begin {gather*} \frac {25 \, x^{6} e^{\left (2 \, x\right )} - 10 \, x^{5} e^{\left (2 \, x\right )} - 49 \, x^{4} e^{\left (2 \, x\right )} - 50 \, x^{3} e^{\left (2 \, x\right )} \log \left (2 \, x + 3\right ) - 40 \, x^{3} e^{\left (2 \, x\right )} + 10 \, x^{2} e^{\left (2 \, x\right )} \log \left (2 \, x + 3\right ) + 35 \, x^{2} e^{\left (2 \, x\right )} + 50 \, x e^{\left (2 \, x\right )} \log \left (2 \, x + 3\right ) + 25 \, e^{\left (2 \, x\right )} \log \left (2 \, x + 3\right )^{2} + 50 \, x e^{\left (2 \, x\right )} + 50 \, e^{\left (2 \, x\right )} \log \left (2 \, x + 3\right ) + 25 \, e^{\left (2 \, x\right )}}{x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((100*x^2+50*x-150)*exp(x)^2*log(2*x+3)^2+(-200*x^5-360*x^4+110*x^3+400*x^2+50*x-300)*exp(x)^2*log(2
*x+3)+(100*x^8+310*x^7-16*x^6-740*x^5-574*x^4+310*x^3+400*x^2-150)*exp(x)^2)/(2*x^4+3*x^3),x, algorithm="giac"
)

[Out]

(25*x^6*e^(2*x) - 10*x^5*e^(2*x) - 49*x^4*e^(2*x) - 50*x^3*e^(2*x)*log(2*x + 3) - 40*x^3*e^(2*x) + 10*x^2*e^(2
*x)*log(2*x + 3) + 35*x^2*e^(2*x) + 50*x*e^(2*x)*log(2*x + 3) + 25*e^(2*x)*log(2*x + 3)^2 + 50*x*e^(2*x) + 50*
e^(2*x)*log(2*x + 3) + 25*e^(2*x))/x^2

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maple [B]  time = 0.16, size = 87, normalized size = 2.81

method	result	size
risch	\(\frac {25 \,{\mathrm e}^{2 x} \ln \left (2 x +3\right )^{2}}{x^{2}}-\frac {10 \left (5 x^{3}-x^{2}-5 x -5\right ) {\mathrm e}^{2 x} \ln \left (2 x +3\right )}{x^{2}}+\frac {\left (25 x^{6}-10 x^{5}-49 x^{4}-40 x^{3}+35 x^{2}+50 x +25\right ) {\mathrm e}^{2 x}}{x^{2}}\)	\(87\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((100*x^2+50*x-150)*exp(x)^2*ln(2*x+3)^2+(-200*x^5-360*x^4+110*x^3+400*x^2+50*x-300)*exp(x)^2*ln(2*x+3)+(1
00*x^8+310*x^7-16*x^6-740*x^5-574*x^4+310*x^3+400*x^2-150)*exp(x)^2)/(2*x^4+3*x^3),x,method=_RETURNVERBOSE)

[Out]

25/x^2*exp(2*x)*ln(2*x+3)^2-10*(5*x^3-x^2-5*x-5)/x^2*exp(2*x)*ln(2*x+3)+(25*x^6-10*x^5-49*x^4-40*x^3+35*x^2+50
*x+25)/x^2*exp(2*x)

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maxima [B]  time = 0.42, size = 83, normalized size = 2.68 \begin {gather*} -\frac {10 \, {\left (5 \, x^{3} - x^{2} - 5 \, x - 5\right )} e^{\left (2 \, x\right )} \log \left (2 \, x + 3\right ) - 25 \, e^{\left (2 \, x\right )} \log \left (2 \, x + 3\right )^{2} - {\left (25 \, x^{6} - 10 \, x^{5} - 49 \, x^{4} - 40 \, x^{3} + 35 \, x^{2} + 50 \, x + 25\right )} e^{\left (2 \, x\right )}}{x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((100*x^2+50*x-150)*exp(x)^2*log(2*x+3)^2+(-200*x^5-360*x^4+110*x^3+400*x^2+50*x-300)*exp(x)^2*log(2
*x+3)+(100*x^8+310*x^7-16*x^6-740*x^5-574*x^4+310*x^3+400*x^2-150)*exp(x)^2)/(2*x^4+3*x^3),x, algorithm="maxim
a")

[Out]

-(10*(5*x^3 - x^2 - 5*x - 5)*e^(2*x)*log(2*x + 3) - 25*e^(2*x)*log(2*x + 3)^2 - (25*x^6 - 10*x^5 - 49*x^4 - 40
*x^3 + 35*x^2 + 50*x + 25)*e^(2*x))/x^2

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mupad [F]  time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int \frac {{\mathrm {e}}^{2\,x}\,\left (100\,x^2+50\,x-150\right )\,{\ln \left (2\,x+3\right )}^2+{\mathrm {e}}^{2\,x}\,\left (-200\,x^5-360\,x^4+110\,x^3+400\,x^2+50\,x-300\right )\,\ln \left (2\,x+3\right )+{\mathrm {e}}^{2\,x}\,\left (100\,x^8+310\,x^7-16\,x^6-740\,x^5-574\,x^4+310\,x^3+400\,x^2-150\right )}{2\,x^4+3\,x^3} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(2*x)*(400*x^2 + 310*x^3 - 574*x^4 - 740*x^5 - 16*x^6 + 310*x^7 + 100*x^8 - 150) + exp(2*x)*log(2*x +
3)^2*(50*x + 100*x^2 - 150) + exp(2*x)*log(2*x + 3)*(50*x + 400*x^2 + 110*x^3 - 360*x^4 - 200*x^5 - 300))/(3*x
^3 + 2*x^4),x)

[Out]

int((exp(2*x)*(400*x^2 + 310*x^3 - 574*x^4 - 740*x^5 - 16*x^6 + 310*x^7 + 100*x^8 - 150) + exp(2*x)*log(2*x +
3)^2*(50*x + 100*x^2 - 150) + exp(2*x)*log(2*x + 3)*(50*x + 400*x^2 + 110*x^3 - 360*x^4 - 200*x^5 - 300))/(3*x
^3 + 2*x^4), x)

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sympy [B]  time = 0.44, size = 90, normalized size = 2.90 \begin {gather*} \frac {\left (25 x^{6} - 10 x^{5} - 49 x^{4} - 50 x^{3} \log {\left (2 x + 3 \right )} - 40 x^{3} + 10 x^{2} \log {\left (2 x + 3 \right )} + 35 x^{2} + 50 x \log {\left (2 x + 3 \right )} + 50 x + 25 \log {\left (2 x + 3 \right )}^{2} + 50 \log {\left (2 x + 3 \right )} + 25\right ) e^{2 x}}{x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((100*x**2+50*x-150)*exp(x)**2*ln(2*x+3)**2+(-200*x**5-360*x**4+110*x**3+400*x**2+50*x-300)*exp(x)**
2*ln(2*x+3)+(100*x**8+310*x**7-16*x**6-740*x**5-574*x**4+310*x**3+400*x**2-150)*exp(x)**2)/(2*x**4+3*x**3),x)

[Out]

(25*x**6 - 10*x**5 - 49*x**4 - 50*x**3*log(2*x + 3) - 40*x**3 + 10*x**2*log(2*x + 3) + 35*x**2 + 50*x*log(2*x
+ 3) + 50*x + 25*log(2*x + 3)**2 + 50*log(2*x + 3) + 25)*exp(2*x)/x**2

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