3.1311 \(\int (c+d x)^{10} \, dx\)

Optimal. Leaf size=14 \[ \frac{(c+d x)^{11}}{11 d} \]

[Out]

(c + d*x)^11/(11*d)

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Rubi [A]  time = 0.0017762, antiderivative size = 14, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 7, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.143, Rules used = {32} \[ \frac{(c+d x)^{11}}{11 d} \]

Antiderivative was successfully verified.

[In]

Int[(c + d*x)^10,x]

[Out]

(c + d*x)^11/(11*d)

Rule 32

Int[((a_.) + (b_.)*(x_))^(m_), x_Symbol] :> Simp[(a + b*x)^(m + 1)/(b*(m + 1)), x] /; FreeQ[{a, b, m}, x] && N
eQ[m, -1]

Rubi steps

\begin{align*} \int (c+d x)^{10} \, dx &=\frac{(c+d x)^{11}}{11 d}\\ \end{align*}

Mathematica [A]  time = 0.0010003, size = 14, normalized size = 1. \[ \frac{(c+d x)^{11}}{11 d} \]

Antiderivative was successfully verified.

[In]

Integrate[(c + d*x)^10,x]

[Out]

(c + d*x)^11/(11*d)

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Maple [A]  time = 0., size = 13, normalized size = 0.9 \begin{align*}{\frac{ \left ( dx+c \right ) ^{11}}{11\,d}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((d*x+c)^10,x)

[Out]

1/11*(d*x+c)^11/d

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Maxima [A]  time = 0.957012, size = 16, normalized size = 1.14 \begin{align*} \frac{{\left (d x + c\right )}^{11}}{11 \, d} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((d*x+c)^10,x, algorithm="maxima")

[Out]

1/11*(d*x + c)^11/d

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Fricas [B]  time = 1.59102, size = 230, normalized size = 16.43 \begin{align*} \frac{1}{11} x^{11} d^{10} + x^{10} d^{9} c + 5 x^{9} d^{8} c^{2} + 15 x^{8} d^{7} c^{3} + 30 x^{7} d^{6} c^{4} + 42 x^{6} d^{5} c^{5} + 42 x^{5} d^{4} c^{6} + 30 x^{4} d^{3} c^{7} + 15 x^{3} d^{2} c^{8} + 5 x^{2} d c^{9} + x c^{10} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((d*x+c)^10,x, algorithm="fricas")

[Out]

1/11*x^11*d^10 + x^10*d^9*c + 5*x^9*d^8*c^2 + 15*x^8*d^7*c^3 + 30*x^7*d^6*c^4 + 42*x^6*d^5*c^5 + 42*x^5*d^4*c^
6 + 30*x^4*d^3*c^7 + 15*x^3*d^2*c^8 + 5*x^2*d*c^9 + x*c^10

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Sympy [B]  time = 0.077456, size = 114, normalized size = 8.14 \begin{align*} c^{10} x + 5 c^{9} d x^{2} + 15 c^{8} d^{2} x^{3} + 30 c^{7} d^{3} x^{4} + 42 c^{6} d^{4} x^{5} + 42 c^{5} d^{5} x^{6} + 30 c^{4} d^{6} x^{7} + 15 c^{3} d^{7} x^{8} + 5 c^{2} d^{8} x^{9} + c d^{9} x^{10} + \frac{d^{10} x^{11}}{11} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((d*x+c)**10,x)

[Out]

c**10*x + 5*c**9*d*x**2 + 15*c**8*d**2*x**3 + 30*c**7*d**3*x**4 + 42*c**6*d**4*x**5 + 42*c**5*d**5*x**6 + 30*c
**4*d**6*x**7 + 15*c**3*d**7*x**8 + 5*c**2*d**8*x**9 + c*d**9*x**10 + d**10*x**11/11

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Giac [A]  time = 1.06738, size = 16, normalized size = 1.14 \begin{align*} \frac{{\left (d x + c\right )}^{11}}{11 \, d} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((d*x+c)^10,x, algorithm="giac")

[Out]

1/11*(d*x + c)^11/d