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

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

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Rubi [A]  time = 0.00, antiderivative size = 15, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 0, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} 2 x^{7/2}-2 x^{5/2} \end {gather*}

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*}

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Mathematica [A]  time = 0.00, size = 10, normalized size = 0.67 \begin {gather*} 2 (x-1) x^{5/2} \end {gather*}

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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IntegrateAlgebraic [A]  time = 0.01, size = 10, normalized size = 0.67 \begin {gather*} 2 (x-1) x^{5/2} \end {gather*}

Antiderivative was successfully verified.

[In]

IntegrateAlgebraic[-5*x^(3/2) + 7*x^(5/2),x]

[Out]

2*(-1 + x)*x^(5/2)

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fricas [A]  time = 1.23, size = 14, normalized size = 0.93 \begin {gather*} 2 \, {\left (x^{3} - x^{2}\right )} \sqrt {x} \end {gather*}

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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giac [A]  time = 0.89, size = 11, normalized size = 0.73 \begin {gather*} 2 \, x^{\frac {7}{2}} - 2 \, x^{\frac {5}{2}} \end {gather*}

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)

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maple [A]  time = 0.00, size = 9, normalized size = 0.60 \begin {gather*} 2 \left (x -1\right ) x^{\frac {5}{2}} \end {gather*}

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)*(x-1)

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maxima [A]  time = 1.01, size = 11, normalized size = 0.73 \begin {gather*} 2 \, x^{\frac {7}{2}} - 2 \, x^{\frac {5}{2}} \end {gather*}

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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mupad [B]  time = 0.03, size = 8, normalized size = 0.53 \begin {gather*} 2\,x^{5/2}\,\left (x-1\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(7*x^(5/2) - 5*x^(3/2),x)

[Out]

2*x^(5/2)*(x - 1)

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sympy [A]  time = 0.06, size = 12, normalized size = 0.80 \begin {gather*} 2 x^{\frac {7}{2}} - 2 x^{\frac {5}{2}} \end {gather*}

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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