3.76.28 \(\int \frac {125+2100 x+11835 x^2+22792 x^3+2367 x^4+84 x^5+x^6+e^{\frac {12544+896 x+16 x^2}{25+280 x+794 x^2+56 x^3+x^4}} (697984 x+75104 x^2+2688 x^3+32 x^4)}{125 x+2100 x^2+11835 x^3+22792 x^4+2367 x^5+84 x^6+x^7} \, dx\)

Optimal. Leaf size=23 \[ \log \left (8 e^{-e^{\frac {16}{\left (x+\frac {5}{28+x}\right )^2}}} x\right ) \]

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Rubi [F]  time = 3.95, 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 {125+2100 x+11835 x^2+22792 x^3+2367 x^4+84 x^5+x^6+e^{\frac {12544+896 x+16 x^2}{25+280 x+794 x^2+56 x^3+x^4}} \left (697984 x+75104 x^2+2688 x^3+32 x^4\right )}{125 x+2100 x^2+11835 x^3+22792 x^4+2367 x^5+84 x^6+x^7} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(125 + 2100*x + 11835*x^2 + 22792*x^3 + 2367*x^4 + 84*x^5 + x^6 + E^((12544 + 896*x + 16*x^2)/(25 + 280*x
+ 794*x^2 + 56*x^3 + x^4))*(697984*x + 75104*x^2 + 2688*x^3 + 32*x^4))/(125*x + 2100*x^2 + 11835*x^3 + 22792*x
^4 + 2367*x^5 + 84*x^6 + x^7),x]

[Out]

(-5243*x)/145924 - (525*(14 + x))/(191*(5 + 28*x + x^2)^2) - (2367*x^3*(14 + x))/(764*(5 + 28*x + x^2)^2) + (1
1835*(5 + 14*x))/(764*(5 + 28*x + x^2)^2) + (5698*x*(5 + 14*x))/(191*(5 + 28*x + x^2)^2) + (21*x^3*(5 + 14*x))
/(191*(5 + 28*x + x^2)^2) + (x^4*(5 + 14*x))/(764*(5 + 28*x + x^2)^2) + (25*(387 + 14*x))/(764*(5 + 28*x + x^2
)^2) - (245385*(14 + x))/(145924*(5 + 28*x + x^2)) + (49077*x*(5 + 14*x))/(145924*(5 + 28*x + x^2)) + (2849*(2
10 + 397*x))/(36481*(5 + 28*x + x^2)) + (x^2*(440 + 2569*x))/(145924*(5 + 28*x + x^2)) + (5*(146364 + 5243*x))
/(145924*(5 + 28*x + x^2)) - (2016721*ArcTanh[(14 + x)/Sqrt[191]])/(72962*Sqrt[191]) + Log[x] + ((27871484 - 2
016721*Sqrt[191])*Log[14 - Sqrt[191] + x])/55742968 - ((27871484 + 2016721*Sqrt[191])*Log[14 - Sqrt[191] + x])
/55742968 - ((27871484 - 2016721*Sqrt[191])*Log[14 + Sqrt[191] + x])/55742968 + ((27871484 + 2016721*Sqrt[191]
)*Log[14 + Sqrt[191] + x])/55742968 - (689024*Defer[Int][E^((16*(28 + x)^2)/(5 + 28*x + x^2)^2)/(-28 + 2*Sqrt[
191] - 2*x)^3, x])/(191*Sqrt[191]) - (24768*(191 - 14*Sqrt[191])*Defer[Int][E^((16*(28 + x)^2)/(5 + 28*x + x^2
)^2)/(-28 + 2*Sqrt[191] - 2*x)^3, x])/36481 - (174496*Defer[Int][E^((16*(28 + x)^2)/(5 + 28*x + x^2)^2)/(-28 +
2*Sqrt[191] - 2*x)^2, x])/36481 - (32*(14 - Sqrt[191])*Defer[Int][E^((16*(28 + x)^2)/(5 + 28*x + x^2)^2)/(-28
+ 2*Sqrt[191] - 2*x)^2, x])/191 + (6192*(42 - Sqrt[191])*Defer[Int][E^((16*(28 + x)^2)/(5 + 28*x + x^2)^2)/(-
28 + 2*Sqrt[191] - 2*x)^2, x])/36481 - (689024*Defer[Int][E^((16*(28 + x)^2)/(5 + 28*x + x^2)^2)/(28 + 2*Sqrt[
191] + 2*x)^3, x])/(191*Sqrt[191]) + (24768*(191 + 14*Sqrt[191])*Defer[Int][E^((16*(28 + x)^2)/(5 + 28*x + x^2
)^2)/(28 + 2*Sqrt[191] + 2*x)^3, x])/36481 - (174496*Defer[Int][E^((16*(28 + x)^2)/(5 + 28*x + x^2)^2)/(28 + 2
*Sqrt[191] + 2*x)^2, x])/36481 - (32*(14 + Sqrt[191])*Defer[Int][E^((16*(28 + x)^2)/(5 + 28*x + x^2)^2)/(28 +
2*Sqrt[191] + 2*x)^2, x])/191 + (6192*(42 + Sqrt[191])*Defer[Int][E^((16*(28 + x)^2)/(5 + 28*x + x^2)^2)/(28 +
2*Sqrt[191] + 2*x)^2, x])/36481

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {125+2100 x+11835 x^2+22792 x^3+2367 x^4+84 x^5+x^6+32 e^{\frac {16 (28+x)^2}{\left (5+28 x+x^2\right )^2}} x \left (21812+2347 x+84 x^2+x^3\right )}{x \left (5+28 x+x^2\right )^3} \, dx\\ &=\int \left (\frac {2100}{\left (5+28 x+x^2\right )^3}+\frac {125}{x \left (5+28 x+x^2\right )^3}+\frac {11835 x}{\left (5+28 x+x^2\right )^3}+\frac {22792 x^2}{\left (5+28 x+x^2\right )^3}+\frac {2367 x^3}{\left (5+28 x+x^2\right )^3}+\frac {84 x^4}{\left (5+28 x+x^2\right )^3}+\frac {x^5}{\left (5+28 x+x^2\right )^3}+\frac {32 e^{\frac {16 (28+x)^2}{\left (5+28 x+x^2\right )^2}} (28+x) \left (779+56 x+x^2\right )}{\left (5+28 x+x^2\right )^3}\right ) \, dx\\ &=32 \int \frac {e^{\frac {16 (28+x)^2}{\left (5+28 x+x^2\right )^2}} (28+x) \left (779+56 x+x^2\right )}{\left (5+28 x+x^2\right )^3} \, dx+84 \int \frac {x^4}{\left (5+28 x+x^2\right )^3} \, dx+125 \int \frac {1}{x \left (5+28 x+x^2\right )^3} \, dx+2100 \int \frac {1}{\left (5+28 x+x^2\right )^3} \, dx+2367 \int \frac {x^3}{\left (5+28 x+x^2\right )^3} \, dx+11835 \int \frac {x}{\left (5+28 x+x^2\right )^3} \, dx+22792 \int \frac {x^2}{\left (5+28 x+x^2\right )^3} \, dx+\int \frac {x^5}{\left (5+28 x+x^2\right )^3} \, dx\\ &=-\frac {525 (14+x)}{191 \left (5+28 x+x^2\right )^2}-\frac {2367 x^3 (14+x)}{764 \left (5+28 x+x^2\right )^2}+\frac {11835 (5+14 x)}{764 \left (5+28 x+x^2\right )^2}+\frac {5698 x (5+14 x)}{191 \left (5+28 x+x^2\right )^2}+\frac {21 x^3 (5+14 x)}{191 \left (5+28 x+x^2\right )^2}+\frac {x^4 (5+14 x)}{764 \left (5+28 x+x^2\right )^2}+\frac {25 (387+14 x)}{764 \left (5+28 x+x^2\right )^2}-\frac {\int \frac {x^3 (40+28 x)}{\left (5+28 x+x^2\right )^2} \, dx}{1528}-\frac {25 \int \frac {-1528-84 x}{x \left (5+28 x+x^2\right )^2} \, dx}{1528}-\frac {315}{191} \int \frac {x^2}{\left (5+28 x+x^2\right )^2} \, dx-\frac {1575}{191} \int \frac {1}{\left (5+28 x+x^2\right )^2} \, dx-\frac {2849}{191} \int \frac {10-56 x}{\left (5+28 x+x^2\right )^2} \, dx+32 \int \left (\frac {2 e^{\frac {16 (28+x)^2}{\left (5+28 x+x^2\right )^2}} (10766+387 x)}{\left (5+28 x+x^2\right )^3}+\frac {e^{\frac {16 (28+x)^2}{\left (5+28 x+x^2\right )^2}} (56+x)}{\left (5+28 x+x^2\right )^2}\right ) \, dx+\frac {49707}{382} \int \frac {x^2}{\left (5+28 x+x^2\right )^2} \, dx+\frac {248535}{382} \int \frac {1}{\left (5+28 x+x^2\right )^2} \, dx\\ &=-\frac {525 (14+x)}{191 \left (5+28 x+x^2\right )^2}-\frac {2367 x^3 (14+x)}{764 \left (5+28 x+x^2\right )^2}+\frac {11835 (5+14 x)}{764 \left (5+28 x+x^2\right )^2}+\frac {5698 x (5+14 x)}{191 \left (5+28 x+x^2\right )^2}+\frac {21 x^3 (5+14 x)}{191 \left (5+28 x+x^2\right )^2}+\frac {x^4 (5+14 x)}{764 \left (5+28 x+x^2\right )^2}+\frac {25 (387+14 x)}{764 \left (5+28 x+x^2\right )^2}-\frac {245385 (14+x)}{145924 \left (5+28 x+x^2\right )}+\frac {49077 x (5+14 x)}{145924 \left (5+28 x+x^2\right )}+\frac {2849 (210+397 x)}{36481 \left (5+28 x+x^2\right )}+\frac {x^2 (440+2569 x)}{145924 \left (5+28 x+x^2\right )}+\frac {5 (146364+5243 x)}{145924 \left (5+28 x+x^2\right )}-\frac {\int \frac {x (7040+41944 x)}{5+28 x+x^2} \, dx}{1167392}+\frac {5 \int \frac {1167392+41944 x}{x \left (5+28 x+x^2\right )} \, dx}{1167392}+2 \frac {1575 \int \frac {1}{5+28 x+x^2} \, dx}{72962}-2 \frac {248535 \int \frac {1}{5+28 x+x^2} \, dx}{145924}+\frac {1131053 \int \frac {1}{5+28 x+x^2} \, dx}{36481}+32 \int \frac {e^{\frac {16 (28+x)^2}{\left (5+28 x+x^2\right )^2}} (56+x)}{\left (5+28 x+x^2\right )^2} \, dx+64 \int \frac {e^{\frac {16 (28+x)^2}{\left (5+28 x+x^2\right )^2}} (10766+387 x)}{\left (5+28 x+x^2\right )^3} \, dx\\ &=-\frac {5243 x}{145924}-\frac {525 (14+x)}{191 \left (5+28 x+x^2\right )^2}-\frac {2367 x^3 (14+x)}{764 \left (5+28 x+x^2\right )^2}+\frac {11835 (5+14 x)}{764 \left (5+28 x+x^2\right )^2}+\frac {5698 x (5+14 x)}{191 \left (5+28 x+x^2\right )^2}+\frac {21 x^3 (5+14 x)}{191 \left (5+28 x+x^2\right )^2}+\frac {x^4 (5+14 x)}{764 \left (5+28 x+x^2\right )^2}+\frac {25 (387+14 x)}{764 \left (5+28 x+x^2\right )^2}-\frac {245385 (14+x)}{145924 \left (5+28 x+x^2\right )}+\frac {49077 x (5+14 x)}{145924 \left (5+28 x+x^2\right )}+\frac {2849 (210+397 x)}{36481 \left (5+28 x+x^2\right )}+\frac {x^2 (440+2569 x)}{145924 \left (5+28 x+x^2\right )}+\frac {5 (146364+5243 x)}{145924 \left (5+28 x+x^2\right )}-\frac {\int \frac {-209720-1167392 x}{5+28 x+x^2} \, dx}{1167392}+\frac {5 \int \left (\frac {1167392}{5 x}-\frac {8 (4059657+145924 x)}{5 \left (5+28 x+x^2\right )}\right ) \, dx}{1167392}-2 \frac {1575 \operatorname {Subst}\left (\int \frac {1}{764-x^2} \, dx,x,28+2 x\right )}{36481}+2 \frac {248535 \operatorname {Subst}\left (\int \frac {1}{764-x^2} \, dx,x,28+2 x\right )}{72962}+32 \int \left (\frac {56 e^{\frac {16 (28+x)^2}{\left (5+28 x+x^2\right )^2}}}{\left (5+28 x+x^2\right )^2}+\frac {e^{\frac {16 (28+x)^2}{\left (5+28 x+x^2\right )^2}} x}{\left (5+28 x+x^2\right )^2}\right ) \, dx-\frac {2262106 \operatorname {Subst}\left (\int \frac {1}{764-x^2} \, dx,x,28+2 x\right )}{36481}+64 \int \left (\frac {10766 e^{\frac {16 (28+x)^2}{\left (5+28 x+x^2\right )^2}}}{\left (5+28 x+x^2\right )^3}+\frac {387 e^{\frac {16 (28+x)^2}{\left (5+28 x+x^2\right )^2}} x}{\left (5+28 x+x^2\right )^3}\right ) \, dx\\ &=-\frac {5243 x}{145924}-\frac {525 (14+x)}{191 \left (5+28 x+x^2\right )^2}-\frac {2367 x^3 (14+x)}{764 \left (5+28 x+x^2\right )^2}+\frac {11835 (5+14 x)}{764 \left (5+28 x+x^2\right )^2}+\frac {5698 x (5+14 x)}{191 \left (5+28 x+x^2\right )^2}+\frac {21 x^3 (5+14 x)}{191 \left (5+28 x+x^2\right )^2}+\frac {x^4 (5+14 x)}{764 \left (5+28 x+x^2\right )^2}+\frac {25 (387+14 x)}{764 \left (5+28 x+x^2\right )^2}-\frac {245385 (14+x)}{145924 \left (5+28 x+x^2\right )}+\frac {49077 x (5+14 x)}{145924 \left (5+28 x+x^2\right )}+\frac {2849 (210+397 x)}{36481 \left (5+28 x+x^2\right )}+\frac {x^2 (440+2569 x)}{145924 \left (5+28 x+x^2\right )}+\frac {5 (146364+5243 x)}{145924 \left (5+28 x+x^2\right )}-\frac {2016721 \tanh ^{-1}\left (\frac {14+x}{\sqrt {191}}\right )}{72962 \sqrt {191}}+\log (x)-\frac {\int \frac {4059657+145924 x}{5+28 x+x^2} \, dx}{145924}+32 \int \frac {e^{\frac {16 (28+x)^2}{\left (5+28 x+x^2\right )^2}} x}{\left (5+28 x+x^2\right )^2} \, dx+1792 \int \frac {e^{\frac {16 (28+x)^2}{\left (5+28 x+x^2\right )^2}}}{\left (5+28 x+x^2\right )^2} \, dx+24768 \int \frac {e^{\frac {16 (28+x)^2}{\left (5+28 x+x^2\right )^2}} x}{\left (5+28 x+x^2\right )^3} \, dx+689024 \int \frac {e^{\frac {16 (28+x)^2}{\left (5+28 x+x^2\right )^2}}}{\left (5+28 x+x^2\right )^3} \, dx-\frac {\left (-27871484+2016721 \sqrt {191}\right ) \int \frac {1}{14-\sqrt {191}+x} \, dx}{55742968}+\frac {\left (27871484+2016721 \sqrt {191}\right ) \int \frac {1}{14+\sqrt {191}+x} \, dx}{55742968}\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.86, size = 24, normalized size = 1.04 \begin {gather*} -e^{\frac {16 (28+x)^2}{\left (5+28 x+x^2\right )^2}}+\log (x) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(125 + 2100*x + 11835*x^2 + 22792*x^3 + 2367*x^4 + 84*x^5 + x^6 + E^((12544 + 896*x + 16*x^2)/(25 +
280*x + 794*x^2 + 56*x^3 + x^4))*(697984*x + 75104*x^2 + 2688*x^3 + 32*x^4))/(125*x + 2100*x^2 + 11835*x^3 + 2
2792*x^4 + 2367*x^5 + 84*x^6 + x^7),x]

[Out]

-E^((16*(28 + x)^2)/(5 + 28*x + x^2)^2) + Log[x]

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fricas [A]  time = 0.59, size = 36, normalized size = 1.57 \begin {gather*} -e^{\left (\frac {16 \, {\left (x^{2} + 56 \, x + 784\right )}}{x^{4} + 56 \, x^{3} + 794 \, x^{2} + 280 \, x + 25}\right )} + \log \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((32*x^4+2688*x^3+75104*x^2+697984*x)*exp((16*x^2+896*x+12544)/(x^4+56*x^3+794*x^2+280*x+25))+x^6+84
*x^5+2367*x^4+22792*x^3+11835*x^2+2100*x+125)/(x^7+84*x^6+2367*x^5+22792*x^4+11835*x^3+2100*x^2+125*x),x, algo
rithm="fricas")

[Out]

-e^(16*(x^2 + 56*x + 784)/(x^4 + 56*x^3 + 794*x^2 + 280*x + 25)) + log(x)

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giac [B]  time = 0.36, size = 77, normalized size = 3.35 \begin {gather*} -e^{\left (\frac {16 \, x^{2}}{x^{4} + 56 \, x^{3} + 794 \, x^{2} + 280 \, x + 25} + \frac {896 \, x}{x^{4} + 56 \, x^{3} + 794 \, x^{2} + 280 \, x + 25} + \frac {12544}{x^{4} + 56 \, x^{3} + 794 \, x^{2} + 280 \, x + 25}\right )} + \log \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((32*x^4+2688*x^3+75104*x^2+697984*x)*exp((16*x^2+896*x+12544)/(x^4+56*x^3+794*x^2+280*x+25))+x^6+84
*x^5+2367*x^4+22792*x^3+11835*x^2+2100*x+125)/(x^7+84*x^6+2367*x^5+22792*x^4+11835*x^3+2100*x^2+125*x),x, algo
rithm="giac")

[Out]

-e^(16*x^2/(x^4 + 56*x^3 + 794*x^2 + 280*x + 25) + 896*x/(x^4 + 56*x^3 + 794*x^2 + 280*x + 25) + 12544/(x^4 +
56*x^3 + 794*x^2 + 280*x + 25)) + log(x)

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maple [A]  time = 1.17, size = 24, normalized size = 1.04

method	result	size
risch	\(\ln \relax (x )-{\mathrm e}^{\frac {16 \left (x +28\right )^{2}}{\left (x^{2}+28 x +5\right )^{2}}}\)	\(24\)
norman	\(\frac {-280 x \,{\mathrm e}^{\frac {16 x^{2}+896 x +12544}{x^{4}+56 x^{3}+794 x^{2}+280 x +25}}-794 x^{2} {\mathrm e}^{\frac {16 x^{2}+896 x +12544}{x^{4}+56 x^{3}+794 x^{2}+280 x +25}}-56 x^{3} {\mathrm e}^{\frac {16 x^{2}+896 x +12544}{x^{4}+56 x^{3}+794 x^{2}+280 x +25}}-x^{4} {\mathrm e}^{\frac {16 x^{2}+896 x +12544}{x^{4}+56 x^{3}+794 x^{2}+280 x +25}}-25 \,{\mathrm e}^{\frac {16 x^{2}+896 x +12544}{x^{4}+56 x^{3}+794 x^{2}+280 x +25}}}{\left (x^{2}+28 x +5\right )^{2}}+\ln \relax (x )\)	\(196\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((32*x^4+2688*x^3+75104*x^2+697984*x)*exp((16*x^2+896*x+12544)/(x^4+56*x^3+794*x^2+280*x+25))+x^6+84*x^5+2
367*x^4+22792*x^3+11835*x^2+2100*x+125)/(x^7+84*x^6+2367*x^5+22792*x^4+11835*x^3+2100*x^2+125*x),x,method=_RET
URNVERBOSE)

[Out]

ln(x)-exp(16*(x+28)^2/(x^2+28*x+5)^2)

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maxima [B]  time = 3.06, size = 323, normalized size = 14.04 \begin {gather*} \frac {8197959 \, x^{3} + 173437274 \, x^{2} + 61547605 \, x + 5507025}{145924 \, {\left (x^{4} + 56 \, x^{3} + 794 \, x^{2} + 280 \, x + 25\right )}} - \frac {21 \, {\left (291773 \, x^{3} + 4082722 \, x^{2} + 1439015 \, x + 128450\right )}}{72962 \, {\left (x^{4} + 56 \, x^{3} + 794 \, x^{2} + 280 \, x + 25\right )}} + \frac {5 \, {\left (5243 \, x^{3} + 293168 \, x^{2} + 4137777 \, x + 1101405\right )}}{145924 \, {\left (x^{4} + 56 \, x^{3} + 794 \, x^{2} + 280 \, x + 25\right )}} + \frac {2849 \, {\left (397 \, x^{3} + 16674 \, x^{2} + 9775 \, x + 1050\right )}}{36481 \, {\left (x^{4} + 56 \, x^{3} + 794 \, x^{2} + 280 \, x + 25\right )}} - \frac {2367 \, {\left (105 \, x^{3} + 77372 \, x^{2} + 28315 \, x + 2575\right )}}{145924 \, {\left (x^{4} + 56 \, x^{3} + 794 \, x^{2} + 280 \, x + 25\right )}} - \frac {11835 \, {\left (21 \, x^{3} + 882 \, x^{2} + 5663 \, x + 515\right )}}{145924 \, {\left (x^{4} + 56 \, x^{3} + 794 \, x^{2} + 280 \, x + 25\right )}} + \frac {525 \, {\left (3 \, x^{3} + 126 \, x^{2} + 809 \, x - 5138\right )}}{72962 \, {\left (x^{4} + 56 \, x^{3} + 794 \, x^{2} + 280 \, x + 25\right )}} - e^{\left (\frac {448 \, x}{x^{4} + 56 \, x^{3} + 794 \, x^{2} + 280 \, x + 25} + \frac {12464}{x^{4} + 56 \, x^{3} + 794 \, x^{2} + 280 \, x + 25} + \frac {16}{x^{2} + 28 \, x + 5}\right )} + \log \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((32*x^4+2688*x^3+75104*x^2+697984*x)*exp((16*x^2+896*x+12544)/(x^4+56*x^3+794*x^2+280*x+25))+x^6+84
*x^5+2367*x^4+22792*x^3+11835*x^2+2100*x+125)/(x^7+84*x^6+2367*x^5+22792*x^4+11835*x^3+2100*x^2+125*x),x, algo
rithm="maxima")

[Out]

1/145924*(8197959*x^3 + 173437274*x^2 + 61547605*x + 5507025)/(x^4 + 56*x^3 + 794*x^2 + 280*x + 25) - 21/72962
*(291773*x^3 + 4082722*x^2 + 1439015*x + 128450)/(x^4 + 56*x^3 + 794*x^2 + 280*x + 25) + 5/145924*(5243*x^3 +
293168*x^2 + 4137777*x + 1101405)/(x^4 + 56*x^3 + 794*x^2 + 280*x + 25) + 2849/36481*(397*x^3 + 16674*x^2 + 97
75*x + 1050)/(x^4 + 56*x^3 + 794*x^2 + 280*x + 25) - 2367/145924*(105*x^3 + 77372*x^2 + 28315*x + 2575)/(x^4 +
56*x^3 + 794*x^2 + 280*x + 25) - 11835/145924*(21*x^3 + 882*x^2 + 5663*x + 515)/(x^4 + 56*x^3 + 794*x^2 + 280
*x + 25) + 525/72962*(3*x^3 + 126*x^2 + 809*x - 5138)/(x^4 + 56*x^3 + 794*x^2 + 280*x + 25) - e^(448*x/(x^4 +
56*x^3 + 794*x^2 + 280*x + 25) + 12464/(x^4 + 56*x^3 + 794*x^2 + 280*x + 25) + 16/(x^2 + 28*x + 5)) + log(x)

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mupad [B]  time = 4.79, size = 78, normalized size = 3.39 \begin {gather*} \ln \relax (x)-{\mathrm {e}}^{\frac {896\,x}{x^4+56\,x^3+794\,x^2+280\,x+25}}\,{\mathrm {e}}^{\frac {16\,x^2}{x^4+56\,x^3+794\,x^2+280\,x+25}}\,{\mathrm {e}}^{\frac {12544}{x^4+56\,x^3+794\,x^2+280\,x+25}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((2100*x + exp((896*x + 16*x^2 + 12544)/(280*x + 794*x^2 + 56*x^3 + x^4 + 25))*(697984*x + 75104*x^2 + 2688
*x^3 + 32*x^4) + 11835*x^2 + 22792*x^3 + 2367*x^4 + 84*x^5 + x^6 + 125)/(125*x + 2100*x^2 + 11835*x^3 + 22792*
x^4 + 2367*x^5 + 84*x^6 + x^7),x)

[Out]

log(x) - exp((896*x)/(280*x + 794*x^2 + 56*x^3 + x^4 + 25))*exp((16*x^2)/(280*x + 794*x^2 + 56*x^3 + x^4 + 25)
)*exp(12544/(280*x + 794*x^2 + 56*x^3 + x^4 + 25))

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sympy [A]  time = 0.30, size = 32, normalized size = 1.39 \begin {gather*} - e^{\frac {16 x^{2} + 896 x + 12544}{x^{4} + 56 x^{3} + 794 x^{2} + 280 x + 25}} + \log {\relax (x )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((32*x**4+2688*x**3+75104*x**2+697984*x)*exp((16*x**2+896*x+12544)/(x**4+56*x**3+794*x**2+280*x+25))
+x**6+84*x**5+2367*x**4+22792*x**3+11835*x**2+2100*x+125)/(x**7+84*x**6+2367*x**5+22792*x**4+11835*x**3+2100*x
**2+125*x),x)

[Out]

-exp((16*x**2 + 896*x + 12544)/(x**4 + 56*x**3 + 794*x**2 + 280*x + 25)) + log(x)

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