3.16.82 \(\int (2 x+5 x^2) \, dx\)

Optimal. Leaf size=11 \[ \frac {5 x^3}{3}+x^2 \]

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Rubi [A]  time = 0.00, antiderivative size = 11, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 0, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \frac {5 x^3}{3}+x^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Int[2*x + 5*x^2,x]

[Out]

x^2 + (5*x^3)/3

Rubi steps

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

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Mathematica [A]  time = 0.00, size = 11, normalized size = 1.00 \begin {gather*} \frac {5 x^3}{3}+x^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[2*x + 5*x^2,x]

[Out]

x^2 + (5*x^3)/3

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IntegrateAlgebraic [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \left (2 x+5 x^2\right ) \, dx \end {gather*}

Verification is not applicable to the result.

[In]

IntegrateAlgebraic[2*x + 5*x^2,x]

[Out]

IntegrateAlgebraic[2*x + 5*x^2, x]

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fricas [A]  time = 0.72, size = 9, normalized size = 0.82 \begin {gather*} \frac {5}{3} x^{3} + x^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(5*x^2+2*x,x, algorithm="fricas")

[Out]

5/3*x^3 + x^2

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giac [A]  time = 1.10, size = 9, normalized size = 0.82 \begin {gather*} \frac {5}{3} \, x^{3} + x^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(5*x^2+2*x,x, algorithm="giac")

[Out]

5/3*x^3 + x^2

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maple [A]  time = 0.00, size = 10, normalized size = 0.91 \begin {gather*} \frac {5}{3} x^{3}+x^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(5*x^2+2*x,x)

[Out]

x^2+5/3*x^3

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maxima [A]  time = 1.10, size = 9, normalized size = 0.82 \begin {gather*} \frac {5}{3} \, x^{3} + x^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(5*x^2+2*x,x, algorithm="maxima")

[Out]

5/3*x^3 + x^2

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mupad [B]  time = 0.02, size = 10, normalized size = 0.91 \begin {gather*} \frac {x^2\,\left (5\,x+3\right )}{3} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(2*x + 5*x^2,x)

[Out]

(x^2*(5*x + 3))/3

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sympy [A]  time = 0.05, size = 8, normalized size = 0.73 \begin {gather*} \frac {5 x^{3}}{3} + x^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(5*x**2+2*x,x)

[Out]

5*x**3/3 + x**2

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