3.20.66 \(\int \frac {15}{11+15 x} \, dx\)

Optimal. Leaf size=22 \[ 4+\log \left (1+2 x+4 \left (2+3 x+\frac {2+x}{4}\right )\right ) \]

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Rubi [A]  time = 0.00, antiderivative size = 6, normalized size of antiderivative = 0.27, number of steps used = 2, number of rules used = 2, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.222, Rules used = {12, 31} \begin {gather*} \log (15 x+11) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[15/(11 + 15*x),x]

[Out]

Log[11 + 15*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 31

Int[((a_) + (b_.)*(x_))^(-1), x_Symbol] :> Simp[Log[RemoveContent[a + b*x, x]]/b, x] /; FreeQ[{a, b}, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=15 \int \frac {1}{11+15 x} \, dx\\ &=\log (11+15 x)\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 6, normalized size = 0.27 \begin {gather*} \log (11+15 x) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[15/(11 + 15*x),x]

[Out]

Log[11 + 15*x]

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fricas [A]  time = 0.51, size = 6, normalized size = 0.27 \begin {gather*} \log \left (15 \, x + 11\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(15/(15*x+11),x, algorithm="fricas")

[Out]

log(15*x + 11)

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giac [A]  time = 0.18, size = 7, normalized size = 0.32 \begin {gather*} \log \left ({\left | 15 \, x + 11 \right |}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(15/(15*x+11),x, algorithm="giac")

[Out]

log(abs(15*x + 11))

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maple [A]  time = 0.31, size = 7, normalized size = 0.32

method	result	size
default	\(\ln \left (15 x +11\right )\)	\(7\)
norman	\(\ln \left (15 x +11\right )\)	\(7\)
meijerg	\(\ln \left (1+\frac {15 x}{11}\right )\)	\(7\)
risch	\(\ln \left (15 x +11\right )\)	\(7\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(15/(15*x+11),x,method=_RETURNVERBOSE)

[Out]

ln(15*x+11)

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maxima [A]  time = 0.37, size = 6, normalized size = 0.27 \begin {gather*} \log \left (15 \, x + 11\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(15/(15*x+11),x, algorithm="maxima")

[Out]

log(15*x + 11)

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mupad [B]  time = 1.15, size = 4, normalized size = 0.18 \begin {gather*} \ln \left (x+\frac {11}{15}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(15/(15*x + 11),x)

[Out]

log(x + 11/15)

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sympy [A]  time = 0.05, size = 5, normalized size = 0.23 \begin {gather*} \log {\left (15 x + 11 \right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(15/(15*x+11),x)

[Out]

log(15*x + 11)

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