Optimal. Leaf size=29 \[ \text {Int}\left (\frac {1}{\text {F0}(x)+x^2},x\right )-\text {Int}\left (\frac {x^2}{\left (\text {F0}(x)+x^2\right )^2},x\right ) \]
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Rubi [A] time = 0.08, 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 = {} \[ \int \frac {\text {F0}(x)}{\left (x^2+\text {F0}(x)\right )^2} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {\text {F0}(x)}{\left (x^2+\text {F0}(x)\right )^2} \, dx &=\int \left (-\frac {x^2}{\left (x^2+\text {F0}(x)\right )^2}+\frac {1}{x^2+\text {F0}(x)}\right ) \, dx\\ &=-\int \frac {x^2}{\left (x^2+\text {F0}(x)\right )^2} \, dx+\int \frac {1}{x^2+\text {F0}(x)} \, dx\\ \end {align*}
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Mathematica [A] time = 0.02, size = 0, normalized size = 0.00 \[ \int \frac {\text {F0}(x)}{\left (x^2+\text {F0}(x)\right )^2} \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 0.38, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {F_{0}\relax (x)}{x^{4} + 2 \, x^{2} F_{0}\relax (x) + F_{0}\relax (x)^{2}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {F_{0}\relax (x)}{{\left (x^{2} + F_{0}\relax (x)\right )}^{2}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 0, normalized size = 0.00 \[ \int \frac {\mathit {F0} \relax (x )}{\left (x^{2}+\mathit {F0} \relax (x )\right )^{2}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {F_{0}\relax (x)}{{\left (x^{2} + F_{0}\relax (x)\right )}^{2}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [A] time = 0.00, size = -1, normalized size = -0.03 \[ \int \frac {F_{0}\relax (x)}{{\left (F_{0}\relax (x)+x^2\right )}^2} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\operatorname {F_{0}}{\relax (x )}}{\left (x^{2} + \operatorname {F_{0}}{\relax (x )}\right )^{2}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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