3.76.10 \(\int (225+45 \log (2)) \, dx\) [7510]

Optimal. Leaf size=11 \[ 5 (2+9 x) (5+\log (2)) \]

[Out]

5*(ln(2)+5)*(9*x+2)

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Rubi [A]
time = 0.00, antiderivative size = 7, normalized size of antiderivative = 0.64, number of steps used = 1, number of rules used = 1, integrand size = 6, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.167, Rules used = {8} \begin {gather*} 45 x (5+\log (2)) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[225 + 45*Log[2],x]

[Out]

45*x*(5 + Log[2])

Rule 8

Int[a_, x_Symbol] :> Simp[a*x, x] /; FreeQ[a, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=45 x (5+\log (2))\\ \end {aligned} \end {gather*}

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Mathematica [A]
time = 0.00, size = 9, normalized size = 0.82 \begin {gather*} 225 x+45 x \log (2) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[225 + 45*Log[2],x]

[Out]

225*x + 45*x*Log[2]

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Maple [A]
time = 0.18, size = 9, normalized size = 0.82

method	result	size
default	\(x \left (45 \ln \left (2\right )+225\right )\)	\(9\)
norman	\(x \left (45 \ln \left (2\right )+225\right )\)	\(9\)
risch	\(45 x \ln \left (2\right )+225 x\)	\(10\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(45*ln(2)+225,x,method=_RETURNVERBOSE)

[Out]

x*(45*ln(2)+225)

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Maxima [A]
time = 0.27, size = 7, normalized size = 0.64 \begin {gather*} 45 \, x {\left (\log \left (2\right ) + 5\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(45*log(2)+225,x, algorithm="maxima")

[Out]

45*x*(log(2) + 5)

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Fricas [A]
time = 0.37, size = 9, normalized size = 0.82 \begin {gather*} 45 \, x \log \left (2\right ) + 225 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(45*log(2)+225,x, algorithm="fricas")

[Out]

45*x*log(2) + 225*x

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Sympy [A]
time = 0.00, size = 7, normalized size = 0.64 \begin {gather*} x \left (45 \log {\left (2 \right )} + 225\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(45*ln(2)+225,x)

[Out]

x*(45*log(2) + 225)

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Giac [A]
time = 0.41, size = 7, normalized size = 0.64 \begin {gather*} 45 \, x {\left (\log \left (2\right ) + 5\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(45*log(2)+225,x, algorithm="giac")

[Out]

45*x*(log(2) + 5)

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Mupad [B]
time = 0.00, size = 8, normalized size = 0.73 \begin {gather*} x\,\left (45\,\ln \left (2\right )+225\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(45*log(2) + 225,x)

[Out]

x*(45*log(2) + 225)

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