3.1.60 \(\int (8+24 x+8 x^2-15 x^3+8 x^4) \, dx\) [60]

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

[Out]

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

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Rubi [A]
time = 0.00, antiderivative size = 30, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 0, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \frac {8 x^5}{5}-\frac {15 x^4}{4}+\frac {8 x^3}{3}+12 x^2+8 x \end {gather*}

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*}

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Mathematica [A]
time = 0.00, size = 30, normalized size = 1.00 \begin {gather*} 8 x+12 x^2+\frac {8 x^3}{3}-\frac {15 x^4}{4}+\frac {8 x^5}{5} \end {gather*}

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 = 0.01, size = 25, normalized size = 0.83

method	result	size
gosper	\(8 x +12 x^{2}+\frac {8}{3} x^{3}-\frac {15}{4} x^{4}+\frac {8}{5} x^{5}\)	\(25\)
default	\(8 x +12 x^{2}+\frac {8}{3} x^{3}-\frac {15}{4} x^{4}+\frac {8}{5} x^{5}\)	\(25\)
norman	\(8 x +12 x^{2}+\frac {8}{3} x^{3}-\frac {15}{4} x^{4}+\frac {8}{5} x^{5}\)	\(25\)
risch	\(8 x +12 x^{2}+\frac {8}{3} x^{3}-\frac {15}{4} x^{4}+\frac {8}{5} x^{5}\)	\(25\)

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,method=_RETURNVERBOSE)

[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 = 0.27, size = 24, normalized size = 0.80 \begin {gather*} \frac {8}{5} \, x^{5} - \frac {15}{4} \, x^{4} + \frac {8}{3} \, x^{3} + 12 \, x^{2} + 8 \, x \end {gather*}

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 = 0.39, size = 24, normalized size = 0.80 \begin {gather*} \frac {8}{5} \, x^{5} - \frac {15}{4} \, x^{4} + \frac {8}{3} \, x^{3} + 12 \, x^{2} + 8 \, x \end {gather*}

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 = 0.01, size = 27, normalized size = 0.90 \begin {gather*} \frac {8 x^{5}}{5} - \frac {15 x^{4}}{4} + \frac {8 x^{3}}{3} + 12 x^{2} + 8 x \end {gather*}

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 = 5.35, size = 24, normalized size = 0.80 \begin {gather*} \frac {8}{5} \, x^{5} - \frac {15}{4} \, x^{4} + \frac {8}{3} \, x^{3} + 12 \, x^{2} + 8 \, x \end {gather*}

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

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Mupad [B]
time = 0.02, size = 24, normalized size = 0.80 \begin {gather*} \frac {8\,x^5}{5}-\frac {15\,x^4}{4}+\frac {8\,x^3}{3}+12\,x^2+8\,x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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