3.17.7 $\int (36x+9x^2)dx$

Optimal. Leaf size=8 $$3x^2(6+x)$$

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Rubi [A]  time = 0.00, antiderivative size = 11, normalized size of antiderivative = 1.38, 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 = {} $$\begin{array}{c}3x^3+18x^2\end{array}$$

Antiderivative was successfully verified.

[In]

Int[36*x + 9*x^2,x]

[Out]

18*x^2 + 3*x^3

Rubi steps

$$\begin{array}{c}\begin{array}{rl}\text{integral}& =18x^2+3x^3\end{array}\end{array}$$

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Mathematica [A]  time = 0.00, size = 11, normalized size = 1.38 $$\begin{array}{c}18x^2+3x^3\end{array}$$

Antiderivative was successfully verified.

[In]

Integrate[36*x + 9*x^2,x]

[Out]

18*x^2 + 3*x^3

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fricas [A]  time = 0.49, size = 11, normalized size = 1.38 $$\begin{array}{c}3x^3+18x^2\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(9*x^2+36*x,x, algorithm="fricas")

[Out]

3*x^3 + 18*x^2

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giac [A]  time = 0.22, size = 11, normalized size = 1.38 $$\begin{array}{c}3x^3+18x^2\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(9*x^2+36*x,x, algorithm="giac")

[Out]

3*x^3 + 18*x^2

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maple [A]  time = 0.01, size = 9, normalized size = 1.12

method	result	size
gosper	$3x^2(x+6)$	$9$
default	$3x^3+18x^2$	$12$
norman	$3x^3+18x^2$	$12$
risch	$3x^3+18x^2$	$12$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(9*x^2+36*x,x,method=_RETURNVERBOSE)

[Out]

3*x^2*(x+6)

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maxima [A]  time = 0.43, size = 11, normalized size = 1.38 $$\begin{array}{c}3x^3+18x^2\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(9*x^2+36*x,x, algorithm="maxima")

[Out]

3*x^3 + 18*x^2

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mupad [B]  time = 0.02, size = 8, normalized size = 1.00 $$\begin{array}{c}3x^2(x+6)\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(36*x + 9*x^2,x)

[Out]

3*x^2*(x + 6)

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sympy [A]  time = 0.05, size = 8, normalized size = 1.00 $$\begin{array}{c}3x^3+18x^2\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(9*x**2+36*x,x)

[Out]

3*x**3 + 18*x**2

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