Optimal. Leaf size=10 \[ -2 \cos \left (\sqrt {1+x}\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.01, 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 = {3512, 15, 2718}
\begin {gather*} -2 \cos \left (\sqrt {x+1}\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 15
Rule 2718
Rule 3512
Rubi steps
\begin {align*} \int \frac {\sin \left (\sqrt {1+x}\right )}{\sqrt {1+x}} \, dx &=2 \text {Subst}\left (\int \frac {x \sin (x)}{\sqrt {x^2}} \, dx,x,\sqrt {1+x}\right )\\ &=2 \text {Subst}\left (\int \sin (x) \, dx,x,\sqrt {1+x}\right )\\ &=-2 \cos \left (\sqrt {1+x}\right )\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.02, size = 10, normalized size = 1.00 \begin {gather*} -2 \cos \left (\sqrt {1+x}\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Mathics [A]
time = 1.67, size = 8, normalized size = 0.80 \begin {gather*} -2 \text {Cos}\left [\sqrt {1+x}\right ] \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.06, size = 9, normalized size = 0.90
method | result | size |
derivativedivides | \(-2 \cos \left (\sqrt {1+x}\right )\) | \(9\) |
default | \(-2 \cos \left (\sqrt {1+x}\right )\) | \(9\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.29, size = 8, normalized size = 0.80 \begin {gather*} -2 \, \cos \left (\sqrt {x + 1}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.33, size = 8, normalized size = 0.80 \begin {gather*} -2 \, \cos \left (\sqrt {x + 1}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.12, size = 10, normalized size = 1.00 \begin {gather*} - 2 \cos {\left (\sqrt {x + 1} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.00, size = 11, normalized size = 1.10 \begin {gather*} -2 \cos \left (\sqrt {x+1}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.17, size = 8, normalized size = 0.80 \begin {gather*} -2\,\cos \left (\sqrt {x+1}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________