Important note:  In this document  log(x) means natural logarithm.  For other bases, a subscript is used to indicate the base, for example logarithm base 10 of x is denoted  (Subscript[log, 10])(x).

∫(3 (x^2) + 2 x + 
            1) \[DifferentialD]x

∫((2/(x^(3/4))) + 
            (1/(Sqrt[x]))) \[DifferentialD]x

∫(((9 t + 
                11))^4) \[DifferentialD]t

∫3 cos(
            5 t) \[DifferentialD]t

∫(cos(
              3 x) + (E^(7 x))) \[DifferentialD]x

∫sin(x) cos(
            x) \[DifferentialD]x

\(∫\((\@x\%7 + 3\ x\^13 + 
                  1\/\@x\%7)\) \[DifferentialD]x\)

Mathematica doesn't give the following integral in the expected form!  I took the difference with the expected answer, and found a constant.

\(TraditionalForm\`∫\(\(\(sin\^3\)(x)\)\ \(cos(
            x)\)\) \(\(\[DifferentialD]\)\(x\)\(
\)\)\)

TrigExpand[% - (((sin^4)(x))/4)]

\(TraditionalForm\`\(\(
\)\(∫\(sin(
          x\^3)\)\ \(x\^2\) \[DifferentialD]x\)\)\)

∫6 x (Sqrt[(x^2) + 1]) \[DifferentialD]x;
Factor[%]

\(TraditionalForm\`\(\(
\)\(∫\(\(4  
              x\)\/\@\(x\^2 + 1\)\) \[DifferentialD]x\)\)\)

∫tan(x) \[DifferentialD]x

∫cot(x) \[DifferentialD]x

∫((3 x)/((x^2) + 
              1)) \[DifferentialD]x

∫(E^(5 x)) \[DifferentialD]x

∫(E^(5 x^2))  4  
        x \[DifferentialD]x

∫((log(
              x))/x) \[DifferentialD]x

∫(Sqrt[(E^x) + 1]) (E^x) \[DifferentialD]x;
Factor[%]

\(TraditionalForm\`
\(∫\((E\^\(-x\) + E\^x)\)\^5\ \ \((E\^\(-x\) - E\^x)\)\ \[DifferentialD]x;\)\)
Simplify[%]

∫((sin(2 x))/(cos(2 x) + 
              4)) \[DifferentialD]x

Make the substitution u = (t^(2/3)) + 1.

\(TraditionalForm\`\(∫\(1\/\@t\%3\ \@\(t\^\(2/3\) + 1\)\) \[DifferentialD]t;\)\)
Factor[%]

In the following, make the substitution u = x+ 3.

∫((x^2)/(Sqrt[x + 3])) \[DifferentialD]x