Integral calculus
The indefinite integral
Trigonometric integrals
 Trigonometric integrals of the form ∫ sinm x, cosn x dx
 Integrals of the rational functions containing sine and cosine, ∫ R (sin x, cos x) dx
Trigonometric integrals
Trigonometric integrals of the form
sinm x, cosn x dx
where m and  n are integers, we use the following substitutions;
1)   if  is a positive odd integer then,  cos x = t
2)   if  n  is a positive odd integer then,  sin x = t
3)   if  m + n  is a negative even integer then,
If  m and  n are positive even integers then the integrand expression can be transformed using the following
trigonometric identities,
In the following examples use appropriate substitutions and trigonometric identities given above.
 Example:  85. Evaluate
 Solution:
 Example:  86. Evaluate
 Solution:
 Example:  87. Evaluate
 Solution:
 Example:  88. Evaluate
 Solution:
 Example:  89. Evaluate
 Solution:
 Example:  90. Evaluate
 Solution:
This integral we can solve using the integration by parts formula, thus
 Example:  91. Evaluate
 Solution:
 Example:  92. Evaluate
 Solution:
Calculus contents F