Integral calculus
      The indefinite integral
      Trigonometric integrals
        Integrals of the rational functions containing sine and cosine,   R (sin x, cos x) dx
Trigonometric integrals of the form
Integrals of rational functions containing sine and cosine,  R (sin x, cos x) dx
Integrals of the form
  R (sin x, cos x) dx
where R denotes a rational function of sin x and cos x, can be transformed to a rational function of the new variable t, using substitution  tan (x/2) = t. Then,
therefore, by substituting
In case the integrand expression does not change the sign when both the sine and the cosine functions change the sign, i.e., if 
R (- sin x- cos x or  R (sin x, cos x)
we can use the substitution tan x = t. Therefore,
Example:  101. Evaluate
Solution: 
Example:  102. Evaluate
By substituting,
Solution: 
The same integrals can be solved using another method, see examples 17. and 18.
Example:  103. Evaluate
By substituting,
Solution: 
Example:  104. Evaluate
By substituting,
Solution: 
Calculus contents F
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