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

Optimal result

Integrand size = 18, antiderivative size = 15 \[ \int \left (-\frac {1}{x^2}+\frac {10}{x}+6 \sqrt {x}\right ) \, dx=\frac {1}{x}+4 x^{3/2}+10 \log (x) \]

[Out]

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

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 15, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \left (-\frac {1}{x^2}+\frac {10}{x}+6 \sqrt {x}\right ) \, dx=4 x^{3/2}+\frac {1}{x}+10 \log (x) \]

[In]

Int[-x^(-2) + 10/x + 6*Sqrt[x],x]

[Out]

x^(-1) + 4*x^(3/2) + 10*Log[x]

Rubi steps \begin{align*} \text {integral}& = \frac {1}{x}+4 x^{3/2}+10 \log (x) \\ \end{align*}

Mathematica [A] (verified)

Time = 0.02 (sec) , antiderivative size = 15, normalized size of antiderivative = 1.00 \[ \int \left (-\frac {1}{x^2}+\frac {10}{x}+6 \sqrt {x}\right ) \, dx=\frac {1}{x}+4 x^{3/2}+10 \log (x) \]

[In]

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

[Out]

x^(-1) + 4*x^(3/2) + 10*Log[x]

Maple [A] (verified)

Time = 0.06 (sec) , antiderivative size = 14, normalized size of antiderivative = 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	\(-\frac {-1+x}{x}+4 x^{\frac {3}{2}}-10 \ln \left (\frac {1}{x}\right )\)	\(21\)

[In]

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

[Out]

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

Fricas [A] (verification not implemented)

none

Time = 0.22 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.20 \[ \int \left (-\frac {1}{x^2}+\frac {10}{x}+6 \sqrt {x}\right ) \, dx=\frac {4 \, x^{\frac {5}{2}} + 20 \, x \log \left (\sqrt {x}\right ) + 1}{x} \]

[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

Sympy [A] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.93 \[ \int \left (-\frac {1}{x^2}+\frac {10}{x}+6 \sqrt {x}\right ) \, dx=4 x^{\frac {3}{2}} + 10 \log {\left (x \right )} + \frac {1}{x} \]

[In]

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

[Out]

4*x**(3/2) + 10*log(x) + 1/x

Maxima [A] (verification not implemented)

none

Time = 0.21 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.87 \[ \int \left (-\frac {1}{x^2}+\frac {10}{x}+6 \sqrt {x}\right ) \, dx=4 \, x^{\frac {3}{2}} + \frac {1}{x} + 10 \, \log \left (x\right ) \]

[In]

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

[Out]

4*x^(3/2) + 1/x + 10*log(x)

Giac [A] (verification not implemented)

none

Time = 0.27 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.93 \[ \int \left (-\frac {1}{x^2}+\frac {10}{x}+6 \sqrt {x}\right ) \, dx=4 \, x^{\frac {3}{2}} + \frac {1}{x} + 10 \, \log \left ({\left | x \right |}\right ) \]

[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))

Mupad [B] (verification not implemented)

Time = 0.35 (sec) , antiderivative size = 15, normalized size of antiderivative = 1.00 \[ \int \left (-\frac {1}{x^2}+\frac {10}{x}+6 \sqrt {x}\right ) \, dx=20\,\ln \left (\sqrt {x}\right )+\frac {1}{x}+4\,x^{3/2} \]

[In]

int(10/x - 1/x^2 + 6*x^(1/2),x)

[Out]

20*log(x^(1/2)) + 1/x + 4*x^(3/2)