3.20.13 \(\int (-\frac {1}{x^2}+\frac {10}{x}+6 \sqrt {x}) \, dx\) [1913]

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

[Out]

1/x+4*x^(3/2)+10*ln(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*} \frac {1}{x}+4 x^{3/2}+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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Mathics [A]
time = 1.64, size = 13, normalized size = 0.87 \begin {gather*} \frac {1}{x}+4 x^{\frac {3}{2}}+10 \text {Log}\left [x\right ] \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

1 / x + 4 x ^ (3 / 2) + 10 Log[x]

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Maple [A]
time = 0.05, size = 14, normalized size = 0.93

method	result	size
derivativedivides	\(\frac {1}{x}+4 x^{\frac {3}{2}}+10 \ln \left (x \right )\)	\(14\)
default	\(\frac {1}{x}+4 x^{\frac {3}{2}}+10 \ln \left (x \right )\)	\(14\)
risch	\(\frac {1}{x}+4 x^{\frac {3}{2}}+10 \ln \left (x \right )\)	\(14\)
trager	\(-\frac {-1+x}{x}+4 x^{\frac {3}{2}}-10 \ln \left (\frac {1}{x}\right )\)	\(21\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Maxima [A]
time = 0.26, size = 13, normalized size = 0.87 \begin {gather*} 4 \, x^{\frac {3}{2}} + \frac {1}{x} + 10 \, \log \left (x\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="maxima")

[Out]

4*x^(3/2) + 1/x + 10*log(x)

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Fricas [A]
time = 0.29, 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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Sympy [A]
time = 0.03, size = 14, normalized size = 0.93 \begin {gather*} 4 x^{\frac {3}{2}} + 10 \log {\left (x \right )} + \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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Giac [A]
time = 0.00, size = 19, normalized size = 1.27 \begin {gather*} \frac 1{x}+10 \ln \left |x\right |+\frac {2}{3}\cdot 6 \sqrt {x} 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) + 1/x + 10*log(abs(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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