Optimal. Leaf size=11 \[ -\frac {1}{2} \log \left (\cos \left (x^2+1\right )\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.01, antiderivative size = 11, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 8, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.250, Rules used = {3747, 3475} \[ -\frac {1}{2} \log \left (\cos \left (x^2+1\right )\right ) \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 3475
Rule 3747
Rubi steps
\begin {align*} \int x \tan \left (1+x^2\right ) \, dx &=\frac {1}{2} \operatorname {Subst}\left (\int \tan (1+x) \, dx,x,x^2\right )\\ &=-\frac {1}{2} \log \left (\cos \left (1+x^2\right )\right )\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.02, size = 11, normalized size = 1.00 \[ -\frac {1}{2} \log \left (\cos \left (x^2+1\right )\right ) \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.79, size = 15, normalized size = 1.36 \[ -\frac {1}{4} \, \log \left (\frac {1}{\tan \left (x^{2} + 1\right )^{2} + 1}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.17, size = 10, normalized size = 0.91 \[ -\frac {1}{2} \, \log \left ({\left | \cos \left (x^{2} + 1\right ) \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.00, size = 10, normalized size = 0.91 \[ -\frac {\ln \left (\cos \left (x^{2}+1\right )\right )}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.33, size = 9, normalized size = 0.82 \[ \frac {1}{2} \, \log \left (\sec \left (x^{2} + 1\right )\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.28, size = 13, normalized size = 1.18 \[ \frac {\ln \left ({\mathrm {tan}\left (x^2+1\right )}^2+1\right )}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.12, size = 12, normalized size = 1.09 \[ \frac {\log {\left (\tan ^{2}{\left (x^{2} + 1 \right )} + 1 \right )}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________