3.60 \(\int (8+24 x+8 x^2-15 x^3+8 x^4) \, dx\)

Optimal. Leaf size=30 \[ \frac{8 x^5}{5}-\frac{15 x^4}{4}+\frac{8 x^3}{3}+12 x^2+8 x \]

[Out]

8*x + 12*x^2 + (8*x^3)/3 - (15*x^4)/4 + (8*x^5)/5

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Rubi [A]  time = 0.0038845, antiderivative size = 30, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 0, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., Rules used = {} \[ \frac{8 x^5}{5}-\frac{15 x^4}{4}+\frac{8 x^3}{3}+12 x^2+8 x \]

Antiderivative was successfully verified.

[In]

Int[8 + 24*x + 8*x^2 - 15*x^3 + 8*x^4,x]

[Out]

8*x + 12*x^2 + (8*x^3)/3 - (15*x^4)/4 + (8*x^5)/5

Rubi steps

\begin{align*} \int \left (8+24 x+8 x^2-15 x^3+8 x^4\right ) \, dx &=8 x+12 x^2+\frac{8 x^3}{3}-\frac{15 x^4}{4}+\frac{8 x^5}{5}\\ \end{align*}

Mathematica [A]  time = 0.0000704, size = 30, normalized size = 1. \[ \frac{8 x^5}{5}-\frac{15 x^4}{4}+\frac{8 x^3}{3}+12 x^2+8 x \]

Antiderivative was successfully verified.

[In]

Integrate[8 + 24*x + 8*x^2 - 15*x^3 + 8*x^4,x]

[Out]

8*x + 12*x^2 + (8*x^3)/3 - (15*x^4)/4 + (8*x^5)/5

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Maple [A]  time = 0.002, size = 25, normalized size = 0.8 \begin{align*} 8\,x+12\,{x}^{2}+{\frac{8\,{x}^{3}}{3}}-{\frac{15\,{x}^{4}}{4}}+{\frac{8\,{x}^{5}}{5}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(8*x^4-15*x^3+8*x^2+24*x+8,x)

[Out]

8*x+12*x^2+8/3*x^3-15/4*x^4+8/5*x^5

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Maxima [A]  time = 1.19578, size = 32, normalized size = 1.07 \begin{align*} \frac{8}{5} \, x^{5} - \frac{15}{4} \, x^{4} + \frac{8}{3} \, x^{3} + 12 \, x^{2} + 8 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(8*x^4-15*x^3+8*x^2+24*x+8,x, algorithm="maxima")

[Out]

8/5*x^5 - 15/4*x^4 + 8/3*x^3 + 12*x^2 + 8*x

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Fricas [A]  time = 1.2414, size = 61, normalized size = 2.03 \begin{align*} \frac{8}{5} x^{5} - \frac{15}{4} x^{4} + \frac{8}{3} x^{3} + 12 x^{2} + 8 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(8*x^4-15*x^3+8*x^2+24*x+8,x, algorithm="fricas")

[Out]

8/5*x^5 - 15/4*x^4 + 8/3*x^3 + 12*x^2 + 8*x

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Sympy [A]  time = 0.052436, size = 27, normalized size = 0.9 \begin{align*} \frac{8 x^{5}}{5} - \frac{15 x^{4}}{4} + \frac{8 x^{3}}{3} + 12 x^{2} + 8 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(8*x**4-15*x**3+8*x**2+24*x+8,x)

[Out]

8*x**5/5 - 15*x**4/4 + 8*x**3/3 + 12*x**2 + 8*x

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Giac [A]  time = 1.12765, size = 32, normalized size = 1.07 \begin{align*} \frac{8}{5} \, x^{5} - \frac{15}{4} \, x^{4} + \frac{8}{3} \, x^{3} + 12 \, x^{2} + 8 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(8*x^4-15*x^3+8*x^2+24*x+8,x, algorithm="giac")

[Out]

8/5*x^5 - 15/4*x^4 + 8/3*x^3 + 12*x^2 + 8*x