3.1892 \(\int (-x^3+x^4) \, dx\)

Optimal. Leaf size=15 \[ \frac{x^5}{5}-\frac{x^4}{4} \]

[Out]

-x^4/4 + x^5/5

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Rubi [A]  time = 0.0019756, antiderivative size = 15, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 0, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., Rules used = {} \[ \frac{x^5}{5}-\frac{x^4}{4} \]

Antiderivative was successfully verified.

[In]

Int[-x^3 + x^4,x]

[Out]

-x^4/4 + x^5/5

Rubi steps

\begin{align*} \int \left (-x^3+x^4\right ) \, dx &=-\frac{x^4}{4}+\frac{x^5}{5}\\ \end{align*}

Mathematica [A]  time = 0.0000316, size = 15, normalized size = 1. \[ \frac{x^5}{5}-\frac{x^4}{4} \]

Antiderivative was successfully verified.

[In]

Integrate[-x^3 + x^4,x]

[Out]

-x^4/4 + x^5/5

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Maple [A]  time = 0.002, size = 12, normalized size = 0.8 \begin{align*} -{\frac{{x}^{4}}{4}}+{\frac{{x}^{5}}{5}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(x^4-x^3,x)

[Out]

-1/4*x^4+1/5*x^5

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Maxima [A]  time = 0.971731, size = 15, normalized size = 1. \begin{align*} \frac{1}{5} \, x^{5} - \frac{1}{4} \, x^{4} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x^4-x^3,x, algorithm="maxima")

[Out]

1/5*x^5 - 1/4*x^4

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Fricas [A]  time = 1.75352, size = 26, normalized size = 1.73 \begin{align*} \frac{1}{5} x^{5} - \frac{1}{4} x^{4} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x^4-x^3,x, algorithm="fricas")

[Out]

1/5*x^5 - 1/4*x^4

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Sympy [A]  time = 0.050116, size = 8, normalized size = 0.53 \begin{align*} \frac{x^{5}}{5} - \frac{x^{4}}{4} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x**4-x**3,x)

[Out]

x**5/5 - x**4/4

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Giac [A]  time = 1.06505, size = 15, normalized size = 1. \begin{align*} \frac{1}{5} \, x^{5} - \frac{1}{4} \, x^{4} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x^4-x^3,x, algorithm="giac")

[Out]

1/5*x^5 - 1/4*x^4