\[ y'(x)=\frac {\cos (y(x)) \left (x^3 \cos (y(x))-x-1\right )}{(x+1) (x \sin (y(x))-1)} \] ✓ Mathematica : cpu = 0.242643 (sec), leaf count = 849
\[\left \{\left \{y(x)\to \tan ^{-1}\left (\frac {6 \left (2 x^4-3 x^3+6 x^2+6 c_1 x-6 \log (x+1) x+\sqrt {4 x^6-12 x^5+33 x^4+12 (2 c_1-3) x^3-36 c_1 x^2+72 c_1 x+36 \log ^2(x+1)+36 \left (c_1{}^2+1\right )-12 \left (2 x^3-3 x^2+6 x+6 c_1\right ) \log (x+1)}\right )}{4 x^6-12 x^5+33 x^4+12 (2 c_1-3) x^3-36 (c_1-1) x^2+72 c_1 x+36 \log ^2(x+1)+36 \left (c_1{}^2+1\right )-12 \left (2 x^3-3 x^2+6 x+6 c_1\right ) \log (x+1)},x-\frac {\left (2 x^3-3 x^2+6 x+6 c_1-6 \log (x+1)\right ) \left (2 x^4-3 x^3+6 x^2+6 c_1 x-6 \log (x+1) x+\sqrt {4 x^6-12 x^5+33 x^4+12 (2 c_1-3) x^3-36 c_1 x^2+72 c_1 x+36 \log ^2(x+1)+36 \left (c_1{}^2+1\right )-12 \left (2 x^3-3 x^2+6 x+6 c_1\right ) \log (x+1)}\right )}{4 x^6-12 x^5+33 x^4+12 (2 c_1-3) x^3-36 (c_1-1) x^2+72 c_1 x+36 \log ^2(x+1)+36 \left (c_1{}^2+1\right )-12 \left (2 x^3-3 x^2+6 x+6 c_1\right ) \log (x+1)}\right )\right \},\left \{y(x)\to \tan ^{-1}\left (-\frac {6 \left (-2 x^4+3 x^3-6 x^2-6 c_1 x+6 \log (x+1) x+\sqrt {4 x^6-12 x^5+33 x^4+12 (2 c_1-3) x^3-36 c_1 x^2+72 c_1 x+36 \log ^2(x+1)+36 \left (c_1{}^2+1\right )-12 \left (2 x^3-3 x^2+6 x+6 c_1\right ) \log (x+1)}\right )}{4 x^6-12 x^5+33 x^4+12 (2 c_1-3) x^3-36 (c_1-1) x^2+72 c_1 x+36 \log ^2(x+1)+36 \left (c_1{}^2+1\right )-12 \left (2 x^3-3 x^2+6 x+6 c_1\right ) \log (x+1)},x-\frac {\left (2 x^3-3 x^2+6 x+6 c_1-6 \log (x+1)\right ) \left (2 x^4-3 x^3+6 x^2+6 c_1 x-6 \log (x+1) x-\sqrt {4 x^6-12 x^5+33 x^4+12 (2 c_1-3) x^3-36 c_1 x^2+72 c_1 x+36 \log ^2(x+1)+36 \left (c_1{}^2+1\right )-12 \left (2 x^3-3 x^2+6 x+6 c_1\right ) \log (x+1)}\right )}{4 x^6-12 x^5+33 x^4+12 (2 c_1-3) x^3-36 (c_1-1) x^2+72 c_1 x+36 \log ^2(x+1)+36 \left (c_1{}^2+1\right )-12 \left (2 x^3-3 x^2+6 x+6 c_1\right ) \log (x+1)}\right )\right \}\right \}\] ✓ Maple : cpu = 1.611 (sec), leaf count = 723
\[\left \{y \left (x \right ) = \arctan \left (\frac {36 x +\left (-2 x^{3}+3 x^{2}-6 c_{1}-6 x +6 \ln \left (x +1\right )\right ) \sqrt {4 x^{6}-12 x^{5}+33 x^{4}-36 c_{1} x^{2}+\left (24 c_{1}-36\right ) x^{3}+36 c_{1}^{2}+72 c_{1} x +36 \ln \left (x +1\right )^{2}+\left (-24 x^{3}+36 x^{2}-72 x -72 c_{1}\right ) \ln \left (x +1\right )+36}}{4 x^{6}-12 x^{5}+33 x^{4}+\left (24 c_{1}-36\right ) x^{3}+36 c_{1}^{2}+72 c_{1} x +\left (-36 c_{1}+36\right ) x^{2}+36 \ln \left (x +1\right )^{2}+\left (-24 x^{3}+36 x^{2}-72 x -72 c_{1}\right ) \ln \left (x +1\right )+36}, \frac {12 x^{4}-18 x^{3}+36 c_{1} x +36 x^{2}-36 x \ln \left (x +1\right )+6 \sqrt {4 x^{6}-12 x^{5}+33 x^{4}-36 c_{1} x^{2}+\left (24 c_{1}-36\right ) x^{3}+36 c_{1}^{2}+72 c_{1} x +36 \ln \left (x +1\right )^{2}+\left (-24 x^{3}+36 x^{2}-72 x -72 c_{1}\right ) \ln \left (x +1\right )+36}}{4 x^{6}-12 x^{5}+33 x^{4}+\left (24 c_{1}-36\right ) x^{3}+36 c_{1}^{2}+72 c_{1} x +\left (-36 c_{1}+36\right ) x^{2}+36 \ln \left (x +1\right )^{2}+\left (-24 x^{3}+36 x^{2}-72 x -72 c_{1}\right ) \ln \left (x +1\right )+36}\right ), y \left (x \right ) = \arctan \left (\frac {36 x +\left (2 x^{3}-3 x^{2}+6 c_{1}+6 x -6 \ln \left (x +1\right )\right ) \sqrt {4 x^{6}-12 x^{5}+33 x^{4}-36 c_{1} x^{2}+\left (24 c_{1}-36\right ) x^{3}+36 c_{1}^{2}+72 c_{1} x +36 \ln \left (x +1\right )^{2}+\left (-24 x^{3}+36 x^{2}-72 x -72 c_{1}\right ) \ln \left (x +1\right )+36}}{4 x^{6}-12 x^{5}+33 x^{4}+\left (24 c_{1}-36\right ) x^{3}+36 c_{1}^{2}+72 c_{1} x +\left (-36 c_{1}+36\right ) x^{2}+36 \ln \left (x +1\right )^{2}+\left (-24 x^{3}+36 x^{2}-72 x -72 c_{1}\right ) \ln \left (x +1\right )+36}, \frac {12 x^{4}-18 x^{3}+36 c_{1} x +36 x^{2}-36 x \ln \left (x +1\right )-6 \sqrt {4 x^{6}-12 x^{5}+33 x^{4}-36 c_{1} x^{2}+\left (24 c_{1}-36\right ) x^{3}+36 c_{1}^{2}+72 c_{1} x +36 \ln \left (x +1\right )^{2}+\left (-24 x^{3}+36 x^{2}-72 x -72 c_{1}\right ) \ln \left (x +1\right )+36}}{4 x^{6}-12 x^{5}+33 x^{4}+\left (24 c_{1}-36\right ) x^{3}+36 c_{1}^{2}+72 c_{1} x +\left (-36 c_{1}+36\right ) x^{2}+36 \ln \left (x +1\right )^{2}+\left (-24 x^{3}+36 x^{2}-72 x -72 c_{1}\right ) \ln \left (x +1\right )+36}\right )\right \}\]