3.568 \(\int \left (c+d x^{-1+n}\right ) \, dx\)

Optimal. Leaf size=12 \[ c x+\frac{d x^n}{n} \]

[Out]

c*x + (d*x^n)/n

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Rubi [A]  time = 0.0100353, antiderivative size = 12, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 0, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0. \[ c x+\frac{d x^n}{n} \]

Antiderivative was successfully verified.

[In]  Int[c + d*x^(-1 + n),x]

[Out]

c*x + (d*x^n)/n

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{d x^{n}}{n} + \int c\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(c+d*x**(-1+n),x)

[Out]

d*x**n/n + Integral(c, x)

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Mathematica [A]  time = 0.00267154, size = 12, normalized size = 1. \[ c x+\frac{d x^n}{n} \]

Antiderivative was successfully verified.

[In]  Integrate[c + d*x^(-1 + n),x]

[Out]

c*x + (d*x^n)/n

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Maple [A]  time = 0.002, size = 13, normalized size = 1.1 \[ cx+{\frac{d{x}^{n}}{n}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(c+d*x^(-1+n),x)

[Out]

c*x+d*x^n/n

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Maxima [F]  time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: ValueError} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(d*x^(n - 1) + c,x, algorithm="maxima")

[Out]

Exception raised: ValueError

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Fricas [A]  time = 0.226963, size = 23, normalized size = 1.92 \[ \frac{c n x + d x x^{n - 1}}{n} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(d*x^(n - 1) + c,x, algorithm="fricas")

[Out]

(c*n*x + d*x*x^(n - 1))/n

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Sympy [A]  time = 0.037488, size = 15, normalized size = 1.25 \[ c x + d \left (\begin{cases} \frac{x^{n}}{n} & \text{for}\: n - 1 \neq -1 \\\log{\left (x \right )} & \text{otherwise} \end{cases}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(c+d*x**(-1+n),x)

[Out]

c*x + d*Piecewise((x**n/n, Ne(n - 1, -1)), (log(x), True))

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GIAC/XCAS [A]  time = 0.213055, size = 16, normalized size = 1.33 \[ c x + \frac{d x^{n}}{n} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(d*x^(n - 1) + c,x, algorithm="giac")

[Out]

c*x + d*x^n/n