3.123 \(\int \frac{a c+b c x^2}{a+b x^2} \, dx\)

Optimal. Leaf size=3 \[ c x \]

[Out]

c*x

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Rubi [A]  time = 0.00466407, antiderivative size = 3, 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 \[ c x \]

Antiderivative was successfully verified.

[In]  Int[(a*c + b*c*x^2)/(a + b*x^2),x]

[Out]

c*x

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Rubi in Sympy [A]  time = 3.14877, size = 2, normalized size = 0.67 \[ c x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((b*c*x**2+a*c)/(b*x**2+a),x)

[Out]

c*x

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Mathematica [A]  time = 0.000350061, size = 3, normalized size = 1. \[ c x \]

Antiderivative was successfully verified.

[In]  Integrate[(a*c + b*c*x^2)/(a + b*x^2),x]

[Out]

c*x

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Maple [A]  time = 0., size = 4, normalized size = 1.3 \[ cx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((b*c*x^2+a*c)/(b*x^2+a),x)

[Out]

c*x

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Maxima [A]  time = 1.33213, size = 4, normalized size = 1.33 \[ c x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

c*x

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Fricas [A]  time = 0.219684, size = 4, normalized size = 1.33 \[ c x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

c*x

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Sympy [A]  time = 0.086926, size = 2, normalized size = 0.67 \[ c x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*c*x**2+a*c)/(b*x**2+a),x)

[Out]

c*x

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GIAC/XCAS [A]  time = 0.221594, size = 4, normalized size = 1.33 \[ c x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

c*x