Optimal. Leaf size=24 \[ -\frac{a}{2 x^2}-\frac{b x^{n-2}}{2-n} \]
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Rubi [A] time = 0.0282935, antiderivative size = 24, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ -\frac{a}{2 x^2}-\frac{b x^{n-2}}{2-n} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^n)/x^3,x]
[Out]
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Rubi in Sympy [A] time = 3.71605, size = 17, normalized size = 0.71 \[ - \frac{a}{2 x^{2}} - \frac{b x^{n - 2}}{- n + 2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b*x**n)/x**3,x)
[Out]
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Mathematica [A] time = 0.0199218, size = 21, normalized size = 0.88 \[ \frac{b x^{n-2}}{n-2}-\frac{a}{2 x^2} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^n)/x^3,x]
[Out]
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Maple [A] time = 0.014, size = 21, normalized size = 0.9 \[{\frac{1}{{x}^{2}} \left ({\frac{b{{\rm e}^{n\ln \left ( x \right ) }}}{-2+n}}-{\frac{a}{2}} \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b*x^n)/x^3,x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: ValueError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^n + a)/x^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.237072, size = 31, normalized size = 1.29 \[ -\frac{a n - 2 \, b x^{n} - 2 \, a}{2 \,{\left (n - 2\right )} x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^n + a)/x^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.99042, size = 60, normalized size = 2.5 \[ \begin{cases} - \frac{a n}{2 n x^{2} - 4 x^{2}} + \frac{2 a}{2 n x^{2} - 4 x^{2}} + \frac{2 b x^{n}}{2 n x^{2} - 4 x^{2}} & \text{for}\: n \neq 2 \\- \frac{a}{2 x^{2}} + b \log{\left (x \right )} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b*x**n)/x**3,x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{b x^{n} + a}{x^{3}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^n + a)/x^3,x, algorithm="giac")
[Out]