3.65.13 \(\int \frac {-15-24 x^6}{32 x^6} \, dx\)

Optimal. Leaf size=19 \[ -2+5 e^4+\frac {3}{32 x^5}-\frac {3 x}{4} \]

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Rubi [A]  time = 0.00, antiderivative size = 13, normalized size of antiderivative = 0.68, number of steps used = 3, number of rules used = 2, integrand size = 14, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {12, 14} \begin {gather*} \frac {3}{32 x^5}-\frac {3 x}{4} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-15 - 24*x^6)/(32*x^6),x]

[Out]

3/(32*x^5) - (3*x)/4

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 {gather*} \begin {aligned} \text {integral} &=\frac {1}{32} \int \frac {-15-24 x^6}{x^6} \, dx\\ &=\frac {1}{32} \int \left (-24-\frac {15}{x^6}\right ) \, dx\\ &=\frac {3}{32 x^5}-\frac {3 x}{4}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 11, normalized size = 0.58 \begin {gather*} \frac {3}{32} \left (\frac {1}{x^5}-8 x\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-15 - 24*x^6)/(32*x^6),x]

[Out]

(3*(x^(-5) - 8*x))/32

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fricas [A]  time = 0.69, size = 12, normalized size = 0.63 \begin {gather*} -\frac {3 \, {\left (8 \, x^{6} - 1\right )}}{32 \, x^{5}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/32*(-24*x^6-15)/x^6,x, algorithm="fricas")

[Out]

-3/32*(8*x^6 - 1)/x^5

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giac [A]  time = 0.18, size = 9, normalized size = 0.47 \begin {gather*} -\frac {3}{4} \, x + \frac {3}{32 \, x^{5}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/32*(-24*x^6-15)/x^6,x, algorithm="giac")

[Out]

-3/4*x + 3/32/x^5

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maple [A]  time = 0.04, size = 10, normalized size = 0.53

method	result	size
default	\(-\frac {3 x}{4}+\frac {3}{32 x^{5}}\)	\(10\)
risch	\(-\frac {3 x}{4}+\frac {3}{32 x^{5}}\)	\(10\)
norman	\(\frac {\frac {3}{32}-\frac {3 x^{6}}{4}}{x^{5}}\)	\(12\)
gosper	\(-\frac {3 \left (8 x^{6}-1\right )}{32 x^{5}}\)	\(13\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/32*(-24*x^6-15)/x^6,x,method=_RETURNVERBOSE)

[Out]

-3/4*x+3/32/x^5

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maxima [A]  time = 0.36, size = 9, normalized size = 0.47 \begin {gather*} -\frac {3}{4} \, x + \frac {3}{32 \, x^{5}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/32*(-24*x^6-15)/x^6,x, algorithm="maxima")

[Out]

-3/4*x + 3/32/x^5

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mupad [B]  time = 0.02, size = 9, normalized size = 0.47 \begin {gather*} \frac {3}{32\,x^5}-\frac {3\,x}{4} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-((3*x^6)/4 + 15/32)/x^6,x)

[Out]

3/(32*x^5) - (3*x)/4

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sympy [A]  time = 0.08, size = 10, normalized size = 0.53 \begin {gather*} - \frac {3 x}{4} + \frac {3}{32 x^{5}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/32*(-24*x**6-15)/x**6,x)

[Out]

-3*x/4 + 3/(32*x**5)

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