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

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

[Out]

c*x+d*x^n/n

________________________________________________________________________________________

Rubi [A]  time = 0.00, antiderivative size = 12, 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 = {} \[ c x+\frac {d x^n}{n} \]

Antiderivative was successfully verified.

[In]

Int[c + d*x^(-1 + n),x]

[Out]

c*x + (d*x^n)/n

Rubi steps

\begin {align*} \int \left (c+d x^{-1+n}\right ) \, dx &=c x+\frac {d x^n}{n}\\ \end {align*}

________________________________________________________________________________________

Mathematica [A]  time = 0.00, size = 12, normalized size = 1.00 \[ c x+\frac {d x^n}{n} \]

Antiderivative was successfully verified.

[In]

Integrate[c + d*x^(-1 + n),x]

[Out]

c*x + (d*x^n)/n

________________________________________________________________________________________

fricas [A]  time = 0.44, size = 17, normalized size = 1.42 \[ \frac {c n x + d x x^{n - 1}}{n} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

(c*n*x + d*x*x^(n - 1))/n

________________________________________________________________________________________

giac [A]  time = 0.17, size = 12, normalized size = 1.00 \[ c x + \frac {d x^{n}}{n} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

c*x + d*x^n/n

________________________________________________________________________________________

maple [A]  time = 0.04, size = 13, normalized size = 1.08 \[ c x +\frac {d \,x^{n}}{n} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(c+d*x^(n-1),x)

[Out]

c*x+d*x^n/n

________________________________________________________________________________________

maxima [A]  time = 1.32, size = 12, normalized size = 1.00 \[ c x + \frac {d x^{n}}{n} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

c*x + d*x^n/n

________________________________________________________________________________________

mupad [B]  time = 5.01, size = 12, normalized size = 1.00 \[ c\,x+\frac {d\,x^n}{n} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(c + d*x^(n - 1),x)

[Out]

c*x + (d*x^n)/n

________________________________________________________________________________________

sympy [A]  time = 0.07, size = 15, normalized size = 1.25 \[ c x + d \left (\begin {cases} \frac {x^{n}}{n} & \text {for}\: n - 1 \neq -1 \\\log {\relax (x )} & \text {otherwise} \end {cases}\right ) \]

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))

________________________________________________________________________________________