3.64.15 \(\int \frac {-10-3 x^3+4 x^4+15 x^5}{x^3} \, dx\)

Optimal. Leaf size=22 \[ -9+\frac {5}{x^2}+4 x^3+(-1+x) x (3+x)+\log (2) \]

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Rubi [A]  time = 0.01, antiderivative size = 19, normalized size of antiderivative = 0.86, number of steps used = 2, number of rules used = 1, integrand size = 21, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.048, Rules used = {14} \begin {gather*} 5 x^3+2 x^2+\frac {5}{x^2}-3 x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-10 - 3*x^3 + 4*x^4 + 15*x^5)/x^3,x]

[Out]

5/x^2 - 3*x + 2*x^2 + 5*x^3

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} &=\int \left (-3-\frac {10}{x^3}+4 x+15 x^2\right ) \, dx\\ &=\frac {5}{x^2}-3 x+2 x^2+5 x^3\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 19, normalized size = 0.86 \begin {gather*} \frac {5}{x^2}-3 x+2 x^2+5 x^3 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-10 - 3*x^3 + 4*x^4 + 15*x^5)/x^3,x]

[Out]

5/x^2 - 3*x + 2*x^2 + 5*x^3

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fricas [A]  time = 0.65, size = 21, normalized size = 0.95 \begin {gather*} \frac {5 \, x^{5} + 2 \, x^{4} - 3 \, x^{3} + 5}{x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((15*x^5+4*x^4-3*x^3-10)/x^3,x, algorithm="fricas")

[Out]

(5*x^5 + 2*x^4 - 3*x^3 + 5)/x^2

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giac [A]  time = 0.22, size = 19, normalized size = 0.86 \begin {gather*} 5 \, x^{3} + 2 \, x^{2} - 3 \, x + \frac {5}{x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((15*x^5+4*x^4-3*x^3-10)/x^3,x, algorithm="giac")

[Out]

5*x^3 + 2*x^2 - 3*x + 5/x^2

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maple [A]  time = 0.03, size = 20, normalized size = 0.91

method	result	size
default	\(5 x^{3}+2 x^{2}-3 x +\frac {5}{x^{2}}\)	\(20\)
risch	\(5 x^{3}+2 x^{2}-3 x +\frac {5}{x^{2}}\)	\(20\)
gosper	\(\frac {5 x^{5}+2 x^{4}-3 x^{3}+5}{x^{2}}\)	\(22\)
norman	\(\frac {5 x^{5}+2 x^{4}-3 x^{3}+5}{x^{2}}\)	\(22\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((15*x^5+4*x^4-3*x^3-10)/x^3,x,method=_RETURNVERBOSE)

[Out]

5*x^3+2*x^2-3*x+5/x^2

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maxima [A]  time = 0.37, size = 19, normalized size = 0.86 \begin {gather*} 5 \, x^{3} + 2 \, x^{2} - 3 \, x + \frac {5}{x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((15*x^5+4*x^4-3*x^3-10)/x^3,x, algorithm="maxima")

[Out]

5*x^3 + 2*x^2 - 3*x + 5/x^2

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mupad [B]  time = 0.04, size = 19, normalized size = 0.86 \begin {gather*} \frac {5}{x^2}-3\,x+2\,x^2+5\,x^3 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(3*x^3 - 4*x^4 - 15*x^5 + 10)/x^3,x)

[Out]

5/x^2 - 3*x + 2*x^2 + 5*x^3

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sympy [A]  time = 0.06, size = 17, normalized size = 0.77 \begin {gather*} 5 x^{3} + 2 x^{2} - 3 x + \frac {5}{x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((15*x**5+4*x**4-3*x**3-10)/x**3,x)

[Out]

5*x**3 + 2*x**2 - 3*x + 5/x**2

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