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

Optimal result

Integrand size = 20, antiderivative size = 30 \[ \int \left (8+24 x+8 x^2-15 x^3+8 x^4\right ) \, dx=8 x+12 x^2+\frac {8 x^3}{3}-\frac {15 x^4}{4}+\frac {8 x^5}{5} \]

[Out]

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

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \left (8+24 x+8 x^2-15 x^3+8 x^4\right ) \, dx=\frac {8 x^5}{5}-\frac {15 x^4}{4}+\frac {8 x^3}{3}+12 x^2+8 x \]

[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*} \text {integral}& = 8 x+12 x^2+\frac {8 x^3}{3}-\frac {15 x^4}{4}+\frac {8 x^5}{5} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.00 \[ \int \left (8+24 x+8 x^2-15 x^3+8 x^4\right ) \, dx=8 x+12 x^2+\frac {8 x^3}{3}-\frac {15 x^4}{4}+\frac {8 x^5}{5} \]

[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

Maple [A] (verified)

Time = 0.02 (sec) , antiderivative size = 25, normalized size of antiderivative = 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	\(8 x +12 x^{2}+\frac {8}{3} x^{3}-\frac {15}{4} x^{4}+\frac {8}{5} x^{5}\)	\(25\)
parallelrisch	\(8 x +12 x^{2}+\frac {8}{3} x^{3}-\frac {15}{4} x^{4}+\frac {8}{5} x^{5}\)	\(25\)
parts	\(8 x +12 x^{2}+\frac {8}{3} x^{3}-\frac {15}{4} x^{4}+\frac {8}{5} x^{5}\)	\(25\)

[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

Fricas [A] (verification not implemented)

none

Time = 0.27 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.80 \[ \int \left (8+24 x+8 x^2-15 x^3+8 x^4\right ) \, dx=\frac {8}{5} \, x^{5} - \frac {15}{4} \, x^{4} + \frac {8}{3} \, x^{3} + 12 \, x^{2} + 8 \, x \]

[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

Sympy [A] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 27, normalized size of antiderivative = 0.90 \[ \int \left (8+24 x+8 x^2-15 x^3+8 x^4\right ) \, dx=\frac {8 x^{5}}{5} - \frac {15 x^{4}}{4} + \frac {8 x^{3}}{3} + 12 x^{2} + 8 x \]

[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

Maxima [A] (verification not implemented)

none

Time = 0.20 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.80 \[ \int \left (8+24 x+8 x^2-15 x^3+8 x^4\right ) \, dx=\frac {8}{5} \, x^{5} - \frac {15}{4} \, x^{4} + \frac {8}{3} \, x^{3} + 12 \, x^{2} + 8 \, x \]

[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

Giac [A] (verification not implemented)

none

Time = 0.29 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.80 \[ \int \left (8+24 x+8 x^2-15 x^3+8 x^4\right ) \, dx=\frac {8}{5} \, x^{5} - \frac {15}{4} \, x^{4} + \frac {8}{3} \, x^{3} + 12 \, x^{2} + 8 \, x \]

[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

Mupad [B] (verification not implemented)

Time = 0.01 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.80 \[ \int \left (8+24 x+8 x^2-15 x^3+8 x^4\right ) \, dx=\frac {8\,x^5}{5}-\frac {15\,x^4}{4}+\frac {8\,x^3}{3}+12\,x^2+8\,x \]

[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