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

Optimal. Leaf size=19 \[ -\frac{\left (b x^2\right )^p}{(1-2 p) x} \]

[Out]

-((b*x^2)^p/((1 - 2*p)*x))

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Rubi [A]  time = 0.0160033, antiderivative size = 19, 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 \[ -\frac{\left (b x^2\right )^p}{(1-2 p) x} \]

Antiderivative was successfully verified.

[In]  Int[(b*x^2)^p/x^2,x]

[Out]

-((b*x^2)^p/((1 - 2*p)*x))

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Rubi in Sympy [A]  time = 2.90858, size = 24, normalized size = 1.26 \[ - \frac{x^{- 2 p} x^{2 p - 1} \left (b x^{2}\right )^{p}}{- 2 p + 1} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-x**(-2*p)*x**(2*p - 1)*(b*x**2)**p/(-2*p + 1)

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Mathematica [A]  time = 0.00583361, size = 18, normalized size = 0.95 \[ \frac{\left (b x^2\right )^p}{(2 p-1) x} \]

Antiderivative was successfully verified.

[In]  Integrate[(b*x^2)^p/x^2,x]

[Out]

(b*x^2)^p/((-1 + 2*p)*x)

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Maple [A]  time = 0.002, size = 19, normalized size = 1. \[{\frac{ \left ( b{x}^{2} \right ) ^{p}}{x \left ( 2\,p-1 \right ) }} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((b*x^2)^p/x^2,x)

[Out]

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

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Maxima [A]  time = 1.4446, size = 26, normalized size = 1.37 \[ \frac{b^{p} x^{2 \, p}}{{\left (2 \, p - 1\right )} x} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

b^p*x^(2*p)/((2*p - 1)*x)

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Fricas [A]  time = 0.243604, size = 24, normalized size = 1.26 \[ \frac{\left (b x^{2}\right )^{p}}{{\left (2 \, p - 1\right )} x} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

(b*x^2)^p/((2*p - 1)*x)

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Sympy [F(-2)]  time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: TypeError} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x**2)**p/x**2,x)

[Out]

Exception raised: TypeError

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

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

integrate((b*x^2)^p/x^2, x)