In [1]: 2*x/(x**2+y**2)+cos(x)
Out[1]:
  2⋅x
─────── + cos(x)
 2    2
x  + y

In [2]: 2*(x**2+y**2+y)/(x**2+y**2)
Out[2]:
   2      2
2⋅x  + 2⋅y  + 2⋅y
─────────────────
      2    2
     x  + y

In [3]: exp(2*t)*cos(t)
Out[3]:
 2⋅t
ℯ   ⋅cos(t)

In [4]: t*exp(3*t**2)
Out[4]:
      2
   3⋅t
t⋅ℯ

In [5]: _1.subs({x:_3,y:_4})*_2.diff(t)
Out[5]: 0

In [6]: _1.subs({x:_3,y:_4})*_3.diff(t)
Out[6]:
                                ⎛                           2⋅t            ⎞
⎛   2⋅t             2⋅t       ⎞ ⎜   ⎛ 2⋅t       ⎞        2⋅ℯ   ⋅cos(t)     ⎟
⎝- ℯ   ⋅sin(t) + 2⋅ℯ   ⋅cos(t)⎠⋅⎜cos⎝ℯ   ⋅cos(t)⎠ + ───────────────────────⎟
                                ⎜                          2               ⎟
                                ⎜                    2  6⋅t     4⋅t    2   ⎟
                                ⎝                   t ⋅ℯ     + ℯ   ⋅cos (t)⎠

In [7]: _2.subs({x:_3,y:_4})*_4.diff(t)
Out[7]:
⎛         2       2⎞ ⎛         2           2                 ⎞
⎜   2  3⋅t     3⋅t ⎟ ⎜   2  6⋅t         3⋅t       4⋅t    2   ⎟
⎝6⋅t ⋅ℯ     + ℯ    ⎠⋅⎝2⋅t ⋅ℯ     + 2⋅t⋅ℯ     + 2⋅ℯ   ⋅cos (t)⎠
──────────────────────────────────────────────────────────────
                          2
                    2  6⋅t     4⋅t    2
                   t ⋅ℯ     + ℯ   ⋅cos (t)

In [8]: integrate(
KeyboardInterrupt

In [8]: simplify(_6+_7)
Out[8]:
⎛         2       2⎞ ⎛         2           2                 ⎞
⎜   2  3⋅t     3⋅t ⎟ ⎜   2  6⋅t         3⋅t       4⋅t    2   ⎟                                   ⎛                           2⋅t
⎝6⋅t ⋅ℯ     + ℯ    ⎠⋅⎝2⋅t ⋅ℯ     + 2⋅t⋅ℯ     + 2⋅ℯ   ⋅cos (t)⎠   ⎛   2⋅t             2⋅t       ⎞ ⎜   ⎛ 2⋅t       ⎞        2⋅ℯ   ⋅cos(t)
────────────────────────────────────────────────────────────── + ⎝- ℯ   ⋅sin(t) + 2⋅ℯ   ⋅cos(t)⎠⋅⎜cos⎝ℯ   ⋅cos(t)⎠ + ───────────────────
                          2                                                                      ⎜                          2
                    2  6⋅t     4⋅t    2                                                          ⎜                    2  6⋅t     4⋅t
                   t ⋅ℯ     + ℯ   ⋅cos (t)                                                       ⎝                   t ⋅ℯ     + ℯ   ⋅cos


    ⎞
    ⎟
────⎟
    ⎟
2   ⎟
 (t)⎠


In [9]: Integral(_8, (t,0,1)).n()
Out[9]: 44.6165874413244


In [13]: log(cos(1)**2+exp(2))+4+sin(exp(2)*cos(1)) + 2*exp(3)-sin(1)
Out[13]:
             ⎛ 2       ⎞      ⎛   2       2⎞          3
-sin(1) + sin⎝ℯ ⋅cos(1)⎠ + log⎝cos (1) + ℯ ⎠ + 4 + 2⋅ℯ

In [14]: _.n()
Out[14]: 44.6165874413244