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