Optimal. Leaf size=23 \[ \frac{c \sqrt{c x^2} \log (a+b x)}{b x} \]
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Rubi [A] time = 0.0114327, antiderivative size = 23, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.1 \[ \frac{c \sqrt{c x^2} \log (a+b x)}{b x} \]
Antiderivative was successfully verified.
[In] Int[(c*x^2)^(3/2)/(x^3*(a + b*x)),x]
[Out]
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Rubi in Sympy [A] time = 13.0937, size = 19, normalized size = 0.83 \[ \frac{c \sqrt{c x^{2}} \log{\left (a + b x \right )}}{b x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((c*x**2)**(3/2)/x**3/(b*x+a),x)
[Out]
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Mathematica [A] time = 0.00525604, size = 22, normalized size = 0.96 \[ \frac{\left (c x^2\right )^{3/2} \log (a+b x)}{b x^3} \]
Antiderivative was successfully verified.
[In] Integrate[(c*x^2)^(3/2)/(x^3*(a + b*x)),x]
[Out]
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Maple [A] time = 0.005, size = 21, normalized size = 0.9 \[{\frac{\ln \left ( bx+a \right ) }{b{x}^{3}} \left ( c{x}^{2} \right ) ^{{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((c*x^2)^(3/2)/x^3/(b*x+a),x)
[Out]
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Maxima [A] time = 1.35739, size = 18, normalized size = 0.78 \[ \frac{c^{\frac{3}{2}} \log \left (b x + a\right )}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2)^(3/2)/((b*x + a)*x^3),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.211369, size = 28, normalized size = 1.22 \[ \frac{\sqrt{c x^{2}} c \log \left (b x + a\right )}{b x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2)^(3/2)/((b*x + a)*x^3),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\left (c x^{2}\right )^{\frac{3}{2}}}{x^{3} \left (a + b x\right )}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x**2)**(3/2)/x**3/(b*x+a),x)
[Out]
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GIAC/XCAS [A] time = 0.206746, size = 38, normalized size = 1.65 \[ c^{\frac{3}{2}}{\left (\frac{{\rm ln}\left ({\left | b x + a \right |}\right ){\rm sign}\left (x\right )}{b} - \frac{{\rm ln}\left ({\left | a \right |}\right ){\rm sign}\left (x\right )}{b}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2)^(3/2)/((b*x + a)*x^3),x, algorithm="giac")
[Out]