3.54 \(\int (1+4 x+4 x^2+4 x^4) \, dx\)

Optimal. Leaf size=21 \[ \frac{4 x^5}{5}+\frac{4 x^3}{3}+2 x^2+x \]

[Out]

x + 2*x^2 + (4*x^3)/3 + (4*x^5)/5

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Rubi [A]  time = 0.0026362, antiderivative size = 21, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 0, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., Rules used = {} \[ \frac{4 x^5}{5}+\frac{4 x^3}{3}+2 x^2+x \]

Antiderivative was successfully verified.

[In]

Int[1 + 4*x + 4*x^2 + 4*x^4,x]

[Out]

x + 2*x^2 + (4*x^3)/3 + (4*x^5)/5

Rubi steps

\begin{align*} \int \left (1+4 x+4 x^2+4 x^4\right ) \, dx &=x+2 x^2+\frac{4 x^3}{3}+\frac{4 x^5}{5}\\ \end{align*}

Mathematica [A]  time = 0.0000427, size = 21, normalized size = 1. \[ \frac{4 x^5}{5}+\frac{4 x^3}{3}+2 x^2+x \]

Antiderivative was successfully verified.

[In]

Integrate[1 + 4*x + 4*x^2 + 4*x^4,x]

[Out]

x + 2*x^2 + (4*x^3)/3 + (4*x^5)/5

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Maple [A]  time = 0.001, size = 18, normalized size = 0.9 \begin{align*} x+2\,{x}^{2}+{\frac{4\,{x}^{3}}{3}}+{\frac{4\,{x}^{5}}{5}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(4*x^4+4*x^2+4*x+1,x)

[Out]

x+2*x^2+4/3*x^3+4/5*x^5

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Maxima [A]  time = 1.09257, size = 23, normalized size = 1.1 \begin{align*} \frac{4}{5} \, x^{5} + \frac{4}{3} \, x^{3} + 2 \, x^{2} + x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(4*x^4+4*x^2+4*x+1,x, algorithm="maxima")

[Out]

4/5*x^5 + 4/3*x^3 + 2*x^2 + x

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Fricas [A]  time = 1.09068, size = 42, normalized size = 2. \begin{align*} \frac{4}{5} x^{5} + \frac{4}{3} x^{3} + 2 x^{2} + x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(4*x^4+4*x^2+4*x+1,x, algorithm="fricas")

[Out]

4/5*x^5 + 4/3*x^3 + 2*x^2 + x

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Sympy [A]  time = 0.052716, size = 19, normalized size = 0.9 \begin{align*} \frac{4 x^{5}}{5} + \frac{4 x^{3}}{3} + 2 x^{2} + x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(4*x**4+4*x**2+4*x+1,x)

[Out]

4*x**5/5 + 4*x**3/3 + 2*x**2 + x

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Giac [A]  time = 1.14291, size = 23, normalized size = 1.1 \begin{align*} \frac{4}{5} \, x^{5} + \frac{4}{3} \, x^{3} + 2 \, x^{2} + x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(4*x^4+4*x^2+4*x+1,x, algorithm="giac")

[Out]

4/5*x^5 + 4/3*x^3 + 2*x^2 + x