3.7.19 \(\int \frac {a+b x^4}{x^{10}} \, dx\) [619]

Optimal. Leaf size=17 \[ -\frac {a}{9 x^9}-\frac {b}{5 x^5} \]

[Out]

-1/9*a/x^9-1/5*b/x^5

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Rubi [A]
time = 0.00, antiderivative size = 17, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {14} \begin {gather*} -\frac {a}{9 x^9}-\frac {b}{5 x^5} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(a + b*x^4)/x^10,x]

[Out]

-1/9*a/x^9 - b/(5*x^5)

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 {align*} \int \frac {a+b x^4}{x^{10}} \, dx &=\int \left (\frac {a}{x^{10}}+\frac {b}{x^6}\right ) \, dx\\ &=-\frac {a}{9 x^9}-\frac {b}{5 x^5}\\ \end {align*}

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Mathematica [A]
time = 0.00, size = 17, normalized size = 1.00 \begin {gather*} -\frac {a}{9 x^9}-\frac {b}{5 x^5} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(a + b*x^4)/x^10,x]

[Out]

-1/9*a/x^9 - b/(5*x^5)

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Maple [A]
time = 0.02, size = 14, normalized size = 0.82

method	result	size
default	\(-\frac {a}{9 x^{9}}-\frac {b}{5 x^{5}}\)	\(14\)
norman	\(\frac {-\frac {b \,x^{4}}{5}-\frac {a}{9}}{x^{9}}\)	\(15\)
risch	\(\frac {-\frac {b \,x^{4}}{5}-\frac {a}{9}}{x^{9}}\)	\(15\)
gosper	\(-\frac {9 b \,x^{4}+5 a}{45 x^{9}}\)	\(16\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((b*x^4+a)/x^10,x,method=_RETURNVERBOSE)

[Out]

-1/9*a/x^9-1/5*b/x^5

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Maxima [A]
time = 0.29, size = 15, normalized size = 0.88 \begin {gather*} -\frac {9 \, b x^{4} + 5 \, a}{45 \, x^{9}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((b*x^4+a)/x^10,x, algorithm="maxima")

[Out]

-1/45*(9*b*x^4 + 5*a)/x^9

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Fricas [A]
time = 0.35, size = 15, normalized size = 0.88 \begin {gather*} -\frac {9 \, b x^{4} + 5 \, a}{45 \, x^{9}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((b*x^4+a)/x^10,x, algorithm="fricas")

[Out]

-1/45*(9*b*x^4 + 5*a)/x^9

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Sympy [A]
time = 0.06, size = 15, normalized size = 0.88 \begin {gather*} \frac {- 5 a - 9 b x^{4}}{45 x^{9}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((b*x**4+a)/x**10,x)

[Out]

(-5*a - 9*b*x**4)/(45*x**9)

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Giac [A]
time = 1.14, size = 15, normalized size = 0.88 \begin {gather*} -\frac {9 \, b x^{4} + 5 \, a}{45 \, x^{9}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((b*x^4+a)/x^10,x, algorithm="giac")

[Out]

-1/45*(9*b*x^4 + 5*a)/x^9

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Mupad [B]
time = 0.03, size = 15, normalized size = 0.88 \begin {gather*} -\frac {9\,b\,x^4+5\,a}{45\,x^9} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((a + b*x^4)/x^10,x)

[Out]

-(5*a + 9*b*x^4)/(45*x^9)

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