3.3.50 \(\int \frac {a+b x}{x^{10}} \, dx\) [250]

Optimal. Leaf size=17 \[ -\frac {a}{9 x^9}-\frac {b}{8 x^8} \]

[Out]

-1/9*a/x^9-1/8*b/x^8

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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 = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {45} \begin {gather*} -\frac {a}{9 x^9}-\frac {b}{8 x^8} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(a + b*x)/x^10,x]

[Out]

-1/9*a/x^9 - b/(8*x^8)

Rule 45

Int[((a_.) + (b_.)*(x_))^(m_.)*((c_.) + (d_.)*(x_))^(n_.), x_Symbol] :> Int[ExpandIntegrand[(a + b*x)^m*(c + d
*x)^n, x], x] /; FreeQ[{a, b, c, d, n}, x] && NeQ[b*c - a*d, 0] && IGtQ[m, 0] && ( !IntegerQ[n] || (EqQ[c, 0]
&& LeQ[7*m + 4*n + 4, 0]) || LtQ[9*m + 5*(n + 1), 0] || GtQ[m + n + 2, 0])

Rubi steps

\begin {align*} \int \frac {a+b x}{x^{10}} \, dx &=\int \left (\frac {a}{x^{10}}+\frac {b}{x^9}\right ) \, dx\\ &=-\frac {a}{9 x^9}-\frac {b}{8 x^8}\\ \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}{8 x^8} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(a + b*x)/x^10,x]

[Out]

-1/9*a/x^9 - b/(8*x^8)

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Mathics [A]
time = 1.64, size = 12, normalized size = 0.71 \begin {gather*} \frac {-\frac {a}{9}-\frac {b x}{8}}{x^9} \end {gather*}

Antiderivative was successfully verified.

[In]

mathics('Integrate[(a + b*x)^1/x^10,x]')

[Out]

(-a / 9 - b x / 8) / x ^ 9

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Maple [A]
time = 0.01, size = 14, normalized size = 0.82

method	result	size
norman	\(\frac {-\frac {b x}{8}-\frac {a}{9}}{x^{9}}\)	\(13\)
risch	\(\frac {-\frac {b x}{8}-\frac {a}{9}}{x^{9}}\)	\(13\)
gosper	\(-\frac {9 b x +8 a}{72 x^{9}}\)	\(14\)
default	\(-\frac {a}{9 x^{9}}-\frac {b}{8 x^{8}}\)	\(14\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-1/9*a/x^9-1/8*b/x^8

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Maxima [A]
time = 0.24, size = 13, normalized size = 0.76 \begin {gather*} -\frac {9 \, b x + 8 \, a}{72 \, x^{9}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-1/72*(9*b*x + 8*a)/x^9

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Fricas [A]
time = 0.30, size = 13, normalized size = 0.76 \begin {gather*} -\frac {9 \, b x + 8 \, a}{72 \, x^{9}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-1/72*(9*b*x + 8*a)/x^9

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Sympy [A]
time = 0.08, size = 14, normalized size = 0.82 \begin {gather*} \frac {- 8 a - 9 b x}{72 x^{9}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

(-8*a - 9*b*x)/(72*x**9)

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Giac [A]
time = 0.00, size = 17, normalized size = 1.00 \begin {gather*} \frac {-9 x b-8 a}{72 x^{9}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-1/72*(9*b*x + 8*a)/x^9

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Mupad [B]
time = 0.03, size = 13, normalized size = 0.76 \begin {gather*} -\frac {8\,a+9\,b\,x}{72\,x^9} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((a + b*x)/x^10,x)

[Out]

-(8*a + 9*b*x)/(72*x^9)

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