3.30 \(\int \frac{\left (b x^2\right )^{5/2}}{x^6} \, dx\)

Optimal. Leaf size=18 \[ \frac{b^2 \sqrt{b x^2} \log (x)}{x} \]

[Out]

(b^2*Sqrt[b*x^2]*Log[x])/x

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Rubi [A]  time = 0.00749944, antiderivative size = 18, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154 \[ \frac{b^2 \sqrt{b x^2} \log (x)}{x} \]

Antiderivative was successfully verified.

[In]  Int[(b*x^2)^(5/2)/x^6,x]

[Out]

(b^2*Sqrt[b*x^2]*Log[x])/x

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Rubi in Sympy [A]  time = 2.31369, size = 15, normalized size = 0.83 \[ \frac{b^{2} \sqrt{b x^{2}} \log{\left (x \right )}}{x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((b*x**2)**(5/2)/x**6,x)

[Out]

b**2*sqrt(b*x**2)*log(x)/x

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Mathematica [A]  time = 0.00357357, size = 15, normalized size = 0.83 \[ \frac{\left (b x^2\right )^{5/2} \log (x)}{x^5} \]

Antiderivative was successfully verified.

[In]  Integrate[(b*x^2)^(5/2)/x^6,x]

[Out]

((b*x^2)^(5/2)*Log[x])/x^5

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Maple [A]  time = 0.004, size = 14, normalized size = 0.8 \[{\frac{\ln \left ( x \right ) }{{x}^{5}} \left ( b{x}^{2} \right ) ^{{\frac{5}{2}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((b*x^2)^(5/2)/x^6,x)

[Out]

(b*x^2)^(5/2)/x^5*ln(x)

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Maxima [F]  time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: RuntimeError} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^2)^(5/2)/x^6,x, algorithm="maxima")

[Out]

Exception raised: RuntimeError

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Fricas [A]  time = 0.273451, size = 22, normalized size = 1.22 \[ \frac{\sqrt{b x^{2}} b^{2} \log \left (x\right )}{x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^2)^(5/2)/x^6,x, algorithm="fricas")

[Out]

sqrt(b*x^2)*b^2*log(x)/x

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Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \int \frac{\left (b x^{2}\right )^{\frac{5}{2}}}{x^{6}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x**2)**(5/2)/x**6,x)

[Out]

Integral((b*x**2)**(5/2)/x**6, x)

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GIAC/XCAS [A]  time = 0.212495, size = 12, normalized size = 0.67 \[ b^{\frac{5}{2}}{\rm ln}\left ({\left | x \right |}\right ){\rm sign}\left (x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^2)^(5/2)/x^6,x, algorithm="giac")

[Out]

b^(5/2)*ln(abs(x))*sign(x)