Examples for Section 7.5
Integration in Mathematica

Selecting Palettes/Basic Input from the File menu brings up a window of buttons you can press to enter symbols, exponents, fractions, square roots, etc. After filling in the boxes, you press the enter key (or shift-return) to evaluate the expression. For an indefinte integral use:

∫\[Placeholder] \[DifferentialD]\[Placeholder]

and for a definite integral use:

(∫_\[Placeholder]^\[Placeholder]) \[Placeholder] 
        \[DifferentialD]\[Placeholder]

Any symbolic expression in Mathematica can also be entered using a function name. For an indefinite integral the syntax is:

Integrate[ f[x],  x]

For a definite integral from a to b it is:

Integrate[ f[x],  {x, a, b} ]

p. 591

7.

∫((Sqrt[9 - 4  x])/(x^2)) \[DifferentialD]x

(∫_1^2)((Sqrt[ 9 - 4  x])/(x^2)) \[DifferentialD]x

These could also be entered as follows:

Integrate[ Sqrt[9  -  4  x]/x^2,  x]

Integrate[ Sqrt[9  -  4  x]/x^2,  {x, 1, 2}]

N[%]

19.

∫\[DifferentialD](θ/(5 + 4  Sin[2  θ]))

(∫_0
        ^(2  π))\[DifferentialD](θ/(5 + 
          4  Sin[2  θ]))

21.

∫(E^(2  t)) Cos[3  t] \[DifferentialD]t

(∫_0^(2  π))(E^(2  t)) Cos[3  t] 
        \[DifferentialD]t

31.

∫(x^2) ArcTan[x] \[DifferentialD]x

(∫_(-1)^2) (x^2) ArcTan[x] \[DifferentialD]x  // 
      Simplify

33.

∫Sin[3  x] Cos[2  x] \[DifferentialD]x

(∫_0^π) Sin[3  x] Cos[2  x] \[DifferentialD]x

52.

∫ArcTan[(Sqrt[y])] \[DifferentialD]y

(∫_0^100) ArcTan[(Sqrt[y])] \[DifferentialD]y

53.

∫Sin[2  x]^5 \[DifferentialD]x

(∫_0^(π/2))Sin[2  x]^5 \[DifferentialD]x

79.

∫x (π^x) \[DifferentialD]x

(∫_0^4) x (π^x) \[DifferentialD]x