3.73.25 $\int \frac{128x^8+\log (24)}{x\log (24)}dx$

Optimal. Leaf size=13 $$1+\frac{16x^8}{\log (24)}+\log (x)$$

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Rubi [A]  time = 0.01, antiderivative size = 12, normalized size of antiderivative = 0.92, number of steps used = 3, number of rules used = 2, integrand size = 16, $\frac{\text{number of rules}}{\text{integrand size}}$ = 0.125, Rules used = {12, 14} $$\begin{array}{c}\frac{16x^8}{\log (24)}+\log (x)\end{array}$$

Antiderivative was successfully verified.

[In]

Int[(128*x^8 + Log[24])/(x*Log[24]),x]

[Out]

(16*x^8)/Log[24] + Log[x]

Rule 12

Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] &&  !MatchQ[u, (b_)*(v_) /; FreeQ[b, x]]

Rule 14

Int[(u_)*((c_.)*(x_))^(m_.), x_Symbol] :> Int[ExpandIntegrand[(c*x)^m*u, x], x] /; FreeQ[{c, m}, x] && SumQ[u]
&&  !LinearQ[u, x] &&  !MatchQ[u, (a_) + (b_.)*(v_) /; FreeQ[{a, b}, x] && InverseFunctionQ[v]]

Rubi steps

$$\begin{array}{c}\begin{array}{rl}\text{integral}& =\frac{\int \frac{128x^8+\log (24)}{x}dx}{\log (24)}\\ & =\frac{\int (128x^7+\frac{\log (24)}{x})dx}{\log (24)}\\ & =\frac{16x^8}{\log (24)}+\log (x)\end{array}\end{array}$$

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Mathematica [A]  time = 0.00, size = 12, normalized size = 0.92 $$\begin{array}{c}\frac{16x^8}{\log (24)}+\log (x)\end{array}$$

Antiderivative was successfully verified.

[In]

Integrate[(128*x^8 + Log[24])/(x*Log[24]),x]

[Out]

(16*x^8)/Log[24] + Log[x]

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fricas [A]  time = 1.07, size = 16, normalized size = 1.23 $$\begin{array}{c}\frac{16x^8+\log \left(24\right)\log (x)}{\log \left(24\right)}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((log(24)+128*x^8)/x/log(24),x, algorithm="fricas")

[Out]

(16*x^8 + log(24)*log(x))/log(24)

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giac [A]  time = 0.14, size = 19, normalized size = 1.46 $$\begin{array}{c}\frac{128x^8+\log \left(24\right)\log \left(x^8\right)}{8\log \left(24\right)}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((log(24)+128*x^8)/x/log(24),x, algorithm="giac")

[Out]

1/8*(128*x^8 + log(24)*log(x^8))/log(24)

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maple [A]  time = 0.04, size = 13, normalized size = 1.00

method	result	size
norman	$\frac{16x^8}{\ln \left(24\right)}+\ln (x)$	$13$
default	$\frac{16x^8+\ln \left(24\right)\ln (x)}{\ln \left(24\right)}$	$17$
risch	$\frac{16x^8}{3\ln (2)+\ln (3)}+\ln (x)$	$18$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((ln(24)+128*x^8)/x/ln(24),x,method=_RETURNVERBOSE)

[Out]

16*x^8/ln(24)+ln(x)

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maxima [A]  time = 0.36, size = 19, normalized size = 1.46 $$\begin{array}{c}\frac{128x^8+\log \left(24\right)\log \left(x^8\right)}{8\log \left(24\right)}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((log(24)+128*x^8)/x/log(24),x, algorithm="maxima")

[Out]

1/8*(128*x^8 + log(24)*log(x^8))/log(24)

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mupad [B]  time = 0.03, size = 12, normalized size = 0.92 $$\begin{array}{c}\ln (x)+\frac{16x^8}{\ln \left(24\right)}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((log(24) + 128*x^8)/(x*log(24)),x)

[Out]

log(x) + (16*x^8)/log(24)

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sympy [A]  time = 0.10, size = 14, normalized size = 1.08 $$\begin{array}{c}\frac{16x^8+\log \left(24\right)\log (x)}{\log \left(24\right)}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((ln(24)+128*x**8)/x/ln(24),x)

[Out]

(16*x**8 + log(24)*log(x))/log(24)

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