### 3.6 $$\int \cos (x) \, dx$$

Optimal. Leaf size=2 $\sin (x)$

[Out]

Sin[x]

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Rubi [A]  time = 0.0018374, antiderivative size = 2, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 2, $$\frac{\text{number of rules}}{\text{integrand size}}$$ = 0.5, Rules used = {2637} $\sin (x)$

Antiderivative was successfully veriﬁed.

[In]

Int[Cos[x],x]

[Out]

Sin[x]

Rule 2637

Int[sin[Pi/2 + (c_.) + (d_.)*(x_)], x_Symbol] :> Simp[Sin[c + d*x]/d, x] /; FreeQ[{c, d}, x]

Rubi steps

\begin{align*} \int \cos (x) \, dx &=\sin (x)\\ \end{align*}

Mathematica [A]  time = 0.0008872, size = 2, normalized size = 1. $\sin (x)$

Antiderivative was successfully veriﬁed.

[In]

Integrate[Cos[x],x]

[Out]

Sin[x]

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Maple [A]  time = 0.001, size = 3, normalized size = 1.5 \begin{align*} \sin \left ( x \right ) \end{align*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int(cos(x),x)

[Out]

sin(x)

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Maxima [A]  time = 0.928332, size = 3, normalized size = 1.5 \begin{align*} \sin \left (x\right ) \end{align*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(cos(x),x, algorithm="maxima")

[Out]

sin(x)

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Fricas [A]  time = 1.98609, size = 11, normalized size = 5.5 \begin{align*} \sin \left (x\right ) \end{align*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(cos(x),x, algorithm="fricas")

[Out]

sin(x)

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Sympy [A]  time = 0.052728, size = 2, normalized size = 1. \begin{align*} \sin{\left (x \right )} \end{align*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(cos(x),x)

[Out]

sin(x)

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Giac [A]  time = 1.05768, size = 3, normalized size = 1.5 \begin{align*} \sin \left (x\right ) \end{align*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(cos(x),x, algorithm="giac")

[Out]

sin(x)