3.29.61 \(\int \frac {1}{5} (1+10 x) \, dx\)

Optimal. Leaf size=23 \[ 4+\frac {1}{5} \left (-2+5 x^2\right )+\frac {1}{5} (x-\log (5)) \]

________________________________________________________________________________________

Rubi [A]  time = 0.00, antiderivative size = 11, normalized size of antiderivative = 0.48, number of steps used = 1, number of rules used = 1, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {9} \begin {gather*} \frac {1}{100} (10 x+1)^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(1 + 10*x)/5,x]

[Out]

(1 + 10*x)^2/100

Rule 9

Int[(a_)*((b_) + (c_.)*(x_)), x_Symbol] :> Simp[(a*(b + c*x)^2)/(2*c), x] /; FreeQ[{a, b, c}, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{100} (1+10 x)^2\\ \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [A]  time = 0.00, size = 9, normalized size = 0.39 \begin {gather*} \frac {x}{5}+x^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(1 + 10*x)/5,x]

[Out]

x/5 + x^2

________________________________________________________________________________________

fricas [A]  time = 0.44, size = 7, normalized size = 0.30 \begin {gather*} x^{2} + \frac {1}{5} \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2*x+1/5,x, algorithm="fricas")

[Out]

x^2 + 1/5*x

________________________________________________________________________________________

giac [A]  time = 0.16, size = 7, normalized size = 0.30 \begin {gather*} x^{2} + \frac {1}{5} \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2*x+1/5,x, algorithm="giac")

[Out]

x^2 + 1/5*x

________________________________________________________________________________________

maple [A]  time = 0.02, size = 8, normalized size = 0.35

method	result	size
default	\(x^{2}+\frac {1}{5} x\)	\(8\)
norman	\(x^{2}+\frac {1}{5} x\)	\(8\)
risch	\(x^{2}+\frac {1}{5} x\)	\(8\)
gosper	\(\frac {\left (1+5 x \right ) x}{5}\)	\(9\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(2*x+1/5,x,method=_RETURNVERBOSE)

[Out]

x^2+1/5*x

________________________________________________________________________________________

maxima [A]  time = 0.48, size = 7, normalized size = 0.30 \begin {gather*} x^{2} + \frac {1}{5} \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2*x+1/5,x, algorithm="maxima")

[Out]

x^2 + 1/5*x

________________________________________________________________________________________

mupad [B]  time = 0.03, size = 8, normalized size = 0.35 \begin {gather*} \frac {x\,\left (5\,x+1\right )}{5} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(2*x + 1/5,x)

[Out]

(x*(5*x + 1))/5

________________________________________________________________________________________

sympy [A]  time = 0.04, size = 5, normalized size = 0.22 \begin {gather*} x^{2} + \frac {x}{5} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2*x+1/5,x)

[Out]

x**2 + x/5

________________________________________________________________________________________