In[]:=
Integrate
Log
2
π
4
+
2
Log[y]

1+
2
y
,{y,0,1},
π
2
Log[2]
Out[]=

1
∫
0
Log
2
π
4
+
2
Log[y]

1+
2
y
y,
1
2
πLog[2]
In[]:=
Plot
Log
2
π
4
+
2
Log[y]

1+
2
y
,{y,0,1}
Out[]=
0.2
0.4
0.6
0.8
1.0
1.0
1.5
2.0
2.5
3.0
In[]:=
NIntegrate
Log
2
π
4
+
2
Log[y]

1+
2
y
,{y,0,1},N
π
2
Log[2]
Out[]=
{1.08879,1.08879}
In[]:=
Integrate
Log
2
π
4
+
2
Log[y]

1+
2
y
,{y,0,1}//FullSimplify
Out[]=
1
∫
0
Log
2
π
4
+
2
Log[y]

1+
2
y
y
In[]:=
N
π
2
Log[2]
Out[]=
1.08879