3.17.18 $\int \frac{1}{3}(15-4\log (176))dx$

Optimal. Leaf size=12 $$-1+5x-\frac{4}{3}x\log (176)$$

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Rubi [A]  time = 0.00, antiderivative size = 11, normalized size of antiderivative = 0.92, number of steps used = 1, number of rules used = 1, integrand size = 10, $\frac{\text{number of rules}}{\text{integrand size}}$ = 0.100, Rules used = {8} $$\begin{array}{c}\frac{1}{3}x(15-4\log (176))\end{array}$$

Antiderivative was successfully verified.

[In]

Int[(15 - 4*Log[176])/3,x]

[Out]

(x*(15 - 4*Log[176]))/3

Rule 8

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

Rubi steps

$$\begin{array}{c}\begin{array}{rl}\text{integral}& =\frac{1}{3}x(15-4\log (176))\end{array}\end{array}$$

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Mathematica [A]  time = 0.00, size = 11, normalized size = 0.92 $$\begin{array}{c}5x-\frac{4}{3}x\log (176)\end{array}$$

Antiderivative was successfully verified.

[In]

Integrate[(15 - 4*Log[176])/3,x]

[Out]

5*x - (4*x*Log[176])/3

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fricas [A]  time = 0.65, size = 9, normalized size = 0.75 $$\begin{array}{c}-\frac{4}{3}x\log \left(176\right)+5x\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-4/3*log(176)+5,x, algorithm="fricas")

[Out]

-4/3*x*log(176) + 5*x

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giac [A]  time = 0.22, size = 9, normalized size = 0.75 $$\begin{array}{c}-\frac{1}{3}x(4\log \left(176\right)-15)\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-4/3*log(176)+5,x, algorithm="giac")

[Out]

-1/3*x*(4*log(176) - 15)

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maple [A]  time = 0.02, size = 9, normalized size = 0.75

method	result	size
default	$(-\frac{4\ln \left(176\right)}{3}+5)x$	$9$
norman	$(-\frac{4\ln \left(176\right)}{3}+5)x$	$9$
risch	$-\frac{16x\ln (2)}{3}-\frac{4x\ln \left(11\right)}{3}+5x$	$15$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-4/3*ln(176)+5,x,method=_RETURNVERBOSE)

[Out]

(-4/3*ln(176)+5)*x

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maxima [A]  time = 0.37, size = 9, normalized size = 0.75 $$\begin{array}{c}-\frac{1}{3}x(4\log \left(176\right)-15)\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-4/3*log(176)+5,x, algorithm="maxima")

[Out]

-1/3*x*(4*log(176) - 15)

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mupad [B]  time = 0.00, size = 9, normalized size = 0.75 $$\begin{array}{c}-x(\frac{4\ln \left(176\right)}{3}-5)\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(5 - (4*log(176))/3,x)

[Out]

-x*((4*log(176))/3 - 5)

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sympy [A]  time = 0.05, size = 8, normalized size = 0.67 $$\begin{array}{c}x(5-\frac{4\log \left(176\right)}{3})\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-4/3*ln(176)+5,x)

[Out]

x*(5 - 4*log(176)/3)

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