3.2289 \(\int (a+b \sqrt [3]{x}) \, dx\)

Optimal. Leaf size=14 \[ a x+\frac {3}{4} b x^{4/3} \]

[Out]

a*x+3/4*b*x^(4/3)

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Rubi [A]  time = 0.00, antiderivative size = 14, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 0, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ a x+\frac {3}{4} b x^{4/3} \]

Antiderivative was successfully verified.

[In]

Int[a + b*x^(1/3),x]

[Out]

a*x + (3*b*x^(4/3))/4

Rubi steps

\begin {align*} \int \left (a+b \sqrt [3]{x}\right ) \, dx &=a x+\frac {3}{4} b x^{4/3}\\ \end {align*}

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Mathematica [A]  time = 0.00, size = 14, normalized size = 1.00 \[ a x+\frac {3}{4} b x^{4/3} \]

Antiderivative was successfully verified.

[In]

Integrate[a + b*x^(1/3),x]

[Out]

a*x + (3*b*x^(4/3))/4

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fricas [A]  time = 0.62, size = 10, normalized size = 0.71 \[ \frac {3}{4} \, b x^{\frac {4}{3}} + a x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(a+b*x^(1/3),x, algorithm="fricas")

[Out]

3/4*b*x^(4/3) + a*x

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giac [A]  time = 0.16, size = 10, normalized size = 0.71 \[ \frac {3}{4} \, b x^{\frac {4}{3}} + a x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(a+b*x^(1/3),x, algorithm="giac")

[Out]

3/4*b*x^(4/3) + a*x

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maple [A]  time = 0.00, size = 11, normalized size = 0.79 \[ \frac {3 b \,x^{\frac {4}{3}}}{4}+a x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(a+b*x^(1/3),x)

[Out]

a*x+3/4*b*x^(4/3)

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maxima [A]  time = 0.87, size = 10, normalized size = 0.71 \[ \frac {3}{4} \, b x^{\frac {4}{3}} + a x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(a+b*x^(1/3),x, algorithm="maxima")

[Out]

3/4*b*x^(4/3) + a*x

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mupad [B]  time = 0.03, size = 10, normalized size = 0.71 \[ a\,x+\frac {3\,b\,x^{4/3}}{4} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(a + b*x^(1/3),x)

[Out]

a*x + (3*b*x^(4/3))/4

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sympy [A]  time = 0.06, size = 12, normalized size = 0.86 \[ a x + \frac {3 b x^{\frac {4}{3}}}{4} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(a+b*x**(1/3),x)

[Out]

a*x + 3*b*x**(4/3)/4

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