3.1913 \(\int (-\frac{1}{x^2}+\frac{10}{x}+6 \sqrt{x}) \, dx\)

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

[Out]

x^(-1) + 4*x^(3/2) + 10*Log[x]

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Rubi [A]  time = 0.002104, antiderivative size = 15, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 0, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., Rules used = {} \[ 4 x^{3/2}+\frac{1}{x}+10 \log (x) \]

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*}

Mathematica [A]  time = 0.0091254, size = 15, normalized size = 1. \[ 4 x^{3/2}+\frac{1}{x}+10 \log (x) \]

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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Maple [A]  time = 0.001, size = 14, normalized size = 0.9 \begin{align*}{x}^{-1}+4\,{x}^{3/2}+10\,\ln \left ( x \right ) \end{align*}

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 = 0.960703, size = 18, normalized size = 1.2 \begin{align*} 4 \, x^{\frac{3}{2}} + \frac{1}{x} + 10 \, \log \left (x\right ) \end{align*}

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 = 2.36892, size = 53, normalized size = 3.53 \begin{align*} \frac{4 \, x^{\frac{5}{2}} + 20 \, x \log \left (\sqrt{x}\right ) + 1}{x} \end{align*}

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 = 0.056319, size = 14, normalized size = 0.93 \begin{align*} 4 x^{\frac{3}{2}} + 10 \log{\left (x \right )} + \frac{1}{x} \end{align*}

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 = 1.05302, size = 19, normalized size = 1.27 \begin{align*} 4 \, x^{\frac{3}{2}} + \frac{1}{x} + 10 \, \log \left ({\left | x \right |}\right ) \end{align*}

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))