Optimal. Leaf size=10 \[ -2 \cos \left (\sqrt {x-7}\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.02, antiderivative size = 10, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 3, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.188, Rules used = {3431, 15, 2638} \[ -2 \cos \left (\sqrt {x-7}\right ) \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 15
Rule 2638
Rule 3431
Rubi steps
\begin {align*} \int \frac {\sin \left (\sqrt {-7+x}\right )}{\sqrt {-7+x}} \, dx &=2 \operatorname {Subst}\left (\int \frac {x \sin (x)}{\sqrt {x^2}} \, dx,x,\sqrt {-7+x}\right )\\ &=2 \operatorname {Subst}\left (\int \sin (x) \, dx,x,\sqrt {-7+x}\right )\\ &=-2 \cos \left (\sqrt {-7+x}\right )\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.02, size = 10, normalized size = 1.00 \[ -2 \cos \left (\sqrt {x-7}\right ) \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.59, size = 8, normalized size = 0.80 \[ -2 \, \cos \left (\sqrt {x - 7}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.12, size = 8, normalized size = 0.80 \[ -2 \, \cos \left (\sqrt {x - 7}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.01, size = 9, normalized size = 0.90 \[ -2 \cos \left (\sqrt {-7+x}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.31, size = 8, normalized size = 0.80 \[ -2 \, \cos \left (\sqrt {x - 7}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 2.42, size = 8, normalized size = 0.80 \[ -2\,\cos \left (\sqrt {x-7}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.26, size = 10, normalized size = 1.00 \[ - 2 \cos {\left (\sqrt {x - 7} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________