3.73 \(\int \frac{\left (b x^2\right )^p}{x} \, dx\)

Optimal. Leaf size=14 \[ \frac{\left (b x^2\right )^p}{2 p} \]

[Out]

(b*x^2)^p/(2*p)

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Rubi [A]  time = 0.00984844, antiderivative size = 14, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.182 \[ \frac{\left (b x^2\right )^p}{2 p} \]

Antiderivative was successfully verified.

[In]  Int[(b*x^2)^p/x,x]

[Out]

(b*x^2)^p/(2*p)

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Rubi in Sympy [A]  time = 2.73557, size = 8, normalized size = 0.57 \[ \frac{\left (b x^{2}\right )^{p}}{2 p} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((b*x**2)**p/x,x)

[Out]

(b*x**2)**p/(2*p)

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Mathematica [A]  time = 0.0019327, size = 14, normalized size = 1. \[ \frac{\left (b x^2\right )^p}{2 p} \]

Antiderivative was successfully verified.

[In]  Integrate[(b*x^2)^p/x,x]

[Out]

(b*x^2)^p/(2*p)

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Maple [A]  time = 0.002, size = 13, normalized size = 0.9 \[{\frac{ \left ( b{x}^{2} \right ) ^{p}}{2\,p}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((b*x^2)^p/x,x)

[Out]

1/2*(b*x^2)^p/p

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Maxima [A]  time = 1.43914, size = 18, normalized size = 1.29 \[ \frac{b^{p}{\left (x^{2}\right )}^{p}}{2 \, p} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/2*b^p*(x^2)^p/p

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Fricas [A]  time = 0.26879, size = 16, normalized size = 1.14 \[ \frac{\left (b x^{2}\right )^{p}}{2 \, p} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/2*(b*x^2)^p/p

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Sympy [A]  time = 0.463908, size = 14, normalized size = 1. \[ \begin{cases} \frac{b^{p} \left (x^{2}\right )^{p}}{2 p} & \text{for}\: p \neq 0 \\\log{\left (x \right )} & \text{otherwise} \end{cases} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x**2)**p/x,x)

[Out]

Piecewise((b**p*(x**2)**p/(2*p), Ne(p, 0)), (log(x), True))

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GIAC/XCAS [F]  time = 0., size = 0, normalized size = 0. \[ \int \frac{\left (b x^{2}\right )^{p}}{x}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

integrate((b*x^2)^p/x, x)