3.73.24 $\int (2+4x+2\log (x))dx$

Optimal. Leaf size=16 $$3+2x(-\frac{5}{7x}+x+\log (x))$$

________________________________________________________________________________________

Rubi [A]  time = 0.00, antiderivative size = 11, normalized size of antiderivative = 0.69, number of steps used = 2, number of rules used = 1, integrand size = 9, $\frac{\text{number of rules}}{\text{integrand size}}$ = 0.111, Rules used = {2295} $$\begin{array}{c}2x^2+2x\log (x)\end{array}$$

Antiderivative was successfully verified.

[In]

Int[2 + 4*x + 2*Log[x],x]

[Out]

2*x^2 + 2*x*Log[x]

Rule 2295

Int[Log[(c_.)*(x_)^(n_.)], x_Symbol] :> Simp[x*Log[c*x^n], x] - Simp[n*x, x] /; FreeQ[{c, n}, x]

Rubi steps

$$\begin{array}{c}\begin{array}{rl}\text{integral}& =2x+2x^2+2\int \log (x)dx\\ & =2x^2+2x\log (x)\end{array}\end{array}$$

________________________________________________________________________________________

Mathematica [A]  time = 0.00, size = 11, normalized size = 0.69 $$\begin{array}{c}2x^2+2x\log (x)\end{array}$$

Antiderivative was successfully verified.

[In]

Integrate[2 + 4*x + 2*Log[x],x]

[Out]

2*x^2 + 2*x*Log[x]

________________________________________________________________________________________

fricas [A]  time = 0.57, size = 11, normalized size = 0.69 $$\begin{array}{c}2x^2+2x\log (x)\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2*log(x)+4*x+2,x, algorithm="fricas")

[Out]

2*x^2 + 2*x*log(x)

________________________________________________________________________________________

giac [A]  time = 0.11, size = 11, normalized size = 0.69 $$\begin{array}{c}2x^2+2x\log (x)\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2*log(x)+4*x+2,x, algorithm="giac")

[Out]

2*x^2 + 2*x*log(x)

________________________________________________________________________________________

maple [A]  time = 0.01, size = 12, normalized size = 0.75

method	result	size
default	$2x\ln (x)+2x^2$	$12$
norman	$2x\ln (x)+2x^2$	$12$
risch	$2x\ln (x)+2x^2$	$12$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(2*ln(x)+4*x+2,x,method=_RETURNVERBOSE)

[Out]

2*x*ln(x)+2*x^2

________________________________________________________________________________________

maxima [A]  time = 0.36, size = 11, normalized size = 0.69 $$\begin{array}{c}2x^2+2x\log (x)\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2*log(x)+4*x+2,x, algorithm="maxima")

[Out]

2*x^2 + 2*x*log(x)

________________________________________________________________________________________

mupad [B]  time = 4.29, size = 7, normalized size = 0.44 $$\begin{array}{c}2x(x+\ln (x))\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(4*x + 2*log(x) + 2,x)

[Out]

2*x*(x + log(x))

________________________________________________________________________________________

sympy [A]  time = 0.13, size = 10, normalized size = 0.62 $$\begin{array}{c}2x^2+2x\log (x)\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2*ln(x)+4*x+2,x)

[Out]

2*x**2 + 2*x*log(x)

________________________________________________________________________________________