3.1915 \(\int (-5 x^{3/2}+7 x^{5/2}) \, dx\)

Optimal. Leaf size=15 \[ 2 x^{7/2}-2 x^{5/2} \]

[Out]

-2*x^(5/2) + 2*x^(7/2)

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Rubi [A]  time = 0.0018477, antiderivative size = 15, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 0, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., Rules used = {} \[ 2 x^{7/2}-2 x^{5/2} \]

Antiderivative was successfully verified.

[In]

Int[-5*x^(3/2) + 7*x^(5/2),x]

[Out]

-2*x^(5/2) + 2*x^(7/2)

Rubi steps

\begin{align*} \int \left (-5 x^{3/2}+7 x^{5/2}\right ) \, dx &=-2 x^{5/2}+2 x^{7/2}\\ \end{align*}

Mathematica [A]  time = 0.0031643, size = 10, normalized size = 0.67 \[ 2 (x-1) x^{5/2} \]

Antiderivative was successfully verified.

[In]

Integrate[-5*x^(3/2) + 7*x^(5/2),x]

[Out]

2*(-1 + x)*x^(5/2)

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Maple [A]  time = 0.004, size = 9, normalized size = 0.6 \begin{align*} 2\,{x}^{5/2} \left ( -1+x \right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-5*x^(3/2)+7*x^(5/2),x)

[Out]

2*x^(5/2)*(-1+x)

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Maxima [A]  time = 0.973274, size = 15, normalized size = 1. \begin{align*} 2 \, x^{\frac{7}{2}} - 2 \, x^{\frac{5}{2}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-5*x^(3/2)+7*x^(5/2),x, algorithm="maxima")

[Out]

2*x^(7/2) - 2*x^(5/2)

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Fricas [A]  time = 2.20989, size = 31, normalized size = 2.07 \begin{align*} 2 \,{\left (x^{3} - x^{2}\right )} \sqrt{x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-5*x^(3/2)+7*x^(5/2),x, algorithm="fricas")

[Out]

2*(x^3 - x^2)*sqrt(x)

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Sympy [A]  time = 0.054393, size = 12, normalized size = 0.8 \begin{align*} 2 x^{\frac{7}{2}} - 2 x^{\frac{5}{2}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-5*x**(3/2)+7*x**(5/2),x)

[Out]

2*x**(7/2) - 2*x**(5/2)

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Giac [A]  time = 1.0534, size = 15, normalized size = 1. \begin{align*} 2 \, x^{\frac{7}{2}} - 2 \, x^{\frac{5}{2}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-5*x^(3/2)+7*x^(5/2),x, algorithm="giac")

[Out]

2*x^(7/2) - 2*x^(5/2)