3.16.99 \(\int (-\frac {1}{x^2}+\frac {10}{x}+6 \sqrt {x}) \, dx\)

Optimal. Leaf size=15 \[ 4 x^{3/2}+\frac {1}{x}+10 \log (x) \]

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Rubi [A]  time = 0.00, antiderivative size = 15, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 0, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} 4 x^{3/2}+\frac {1}{x}+10 \log (x) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-x^(-2) + 10/x + 6*Sqrt[x],x]

[Out]

x^(-1) + 4*x^(3/2) + 10*Log[x]

Rubi steps

\begin {align*} \int \left (-\frac {1}{x^2}+\frac {10}{x}+6 \sqrt {x}\right ) \, dx &=\frac {1}{x}+4 x^{3/2}+10 \log (x)\\ \end {align*}

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Mathematica [A]  time = 0.01, size = 15, normalized size = 1.00 \begin {gather*} 4 x^{3/2}+\frac {1}{x}+10 \log (x) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-x^(-2) + 10/x + 6*Sqrt[x],x]

[Out]

x^(-1) + 4*x^(3/2) + 10*Log[x]

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IntegrateAlgebraic [A]  time = 0.02, size = 22, normalized size = 1.47 \begin {gather*} \frac {4 x^{5/2}+1}{x}+20 \log \left (\sqrt {x}\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

IntegrateAlgebraic[-x^(-2) + 10/x + 6*Sqrt[x],x]

[Out]

(1 + 4*x^(5/2))/x + 20*Log[Sqrt[x]]

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fricas [A]  time = 1.25, size = 18, normalized size = 1.20 \begin {gather*} \frac {4 \, x^{\frac {5}{2}} + 20 \, x \log \left (\sqrt {x}\right ) + 1}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-1/x^2+10/x+6*x^(1/2),x, algorithm="fricas")

[Out]

(4*x^(5/2) + 20*x*log(sqrt(x)) + 1)/x

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giac [A]  time = 0.95, size = 14, normalized size = 0.93 \begin {gather*} 4 \, x^{\frac {3}{2}} + \frac {1}{x} + 10 \, \log \left ({\left | x \right |}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-1/x^2+10/x+6*x^(1/2),x, algorithm="giac")

[Out]

4*x^(3/2) + 1/x + 10*log(abs(x))

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maple [A]  time = 0.00, size = 14, normalized size = 0.93 \begin {gather*} 4 x^{\frac {3}{2}}+10 \ln \relax (x )+\frac {1}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-1/x^2+10/x+6*x^(1/2),x)

[Out]

1/x+4*x^(3/2)+10*ln(x)

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maxima [A]  time = 1.02, size = 13, normalized size = 0.87 \begin {gather*} 4 \, x^{\frac {3}{2}} + \frac {1}{x} + 10 \, \log \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-1/x^2+10/x+6*x^(1/2),x, algorithm="maxima")

[Out]

4*x^(3/2) + 1/x + 10*log(x)

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mupad [B]  time = 0.29, size = 15, normalized size = 1.00 \begin {gather*} 20\,\ln \left (\sqrt {x}\right )+\frac {1}{x}+4\,x^{3/2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(10/x - 1/x^2 + 6*x^(1/2),x)

[Out]

20*log(x^(1/2)) + 1/x + 4*x^(3/2)

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sympy [A]  time = 0.06, size = 14, normalized size = 0.93 \begin {gather*} 4 x^{\frac {3}{2}} + 10 \log {\relax (x )} + \frac {1}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-1/x**2+10/x+6*x**(1/2),x)

[Out]

4*x**(3/2) + 10*log(x) + 1/x

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