3.25.22 \(\int (1+2 x) \, dx\)

Optimal. Leaf size=16 \[ 2-\frac {16}{e^8}-e^5+x+x^2 \]

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Rubi [A]  time = 0.00, antiderivative size = 5, normalized size of antiderivative = 0.31, number of steps used = 1, number of rules used = 0, integrand size = 5, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} x^2+x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[1 + 2*x,x]

[Out]

x + x^2

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=x+x^2\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 5, normalized size = 0.31 \begin {gather*} x+x^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[1 + 2*x,x]

[Out]

x + x^2

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fricas [A]  time = 0.58, size = 5, normalized size = 0.31 \begin {gather*} x^{2} + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

x^2 + x

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giac [A]  time = 0.21, size = 5, normalized size = 0.31 \begin {gather*} x^{2} + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2*x+1,x, algorithm="giac")

[Out]

x^2 + x

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maple [A]  time = 0.01, size = 6, normalized size = 0.38

method	result	size
gosper	\(x^{2}+x\)	\(6\)
default	\(x^{2}+x\)	\(6\)
norman	\(x^{2}+x\)	\(6\)
risch	\(x^{2}+x\)	\(6\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(2*x+1,x,method=_RETURNVERBOSE)

[Out]

x^2+x

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maxima [A]  time = 0.39, size = 5, normalized size = 0.31 \begin {gather*} x^{2} + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

x^2 + x

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mupad [B]  time = 0.04, size = 5, normalized size = 0.31 \begin {gather*} x\,\left (x+1\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(2*x + 1,x)

[Out]

x*(x + 1)

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sympy [A]  time = 0.05, size = 3, normalized size = 0.19 \begin {gather*} x^{2} + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2*x+1,x)

[Out]

x**2 + x

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