Integrals for Exponential sin and cos

Question 1

What do you do if n and m are both odd numbers for the following function:

Answer 1

Pick to use either n or m as odd and solve.

Question 2

What do you do if only n is an odd number for the following function:

Answer 2

Strip one sin out and convert the rest to cos using

sin²x=1-cos²x

then use u-substitution using

u=cosx

Question 3

What do you do if only m is an odd number for the following function:

Answer 3

Strip one cos out and convert the rest to sin using:

cos²x=1-sin²x

Then solve using u-substitution using;

u=sinx

Question 4

What do you do if both n and m are even numbers for the following function:

Answer 4

Use double- or half-angle formulas to reduce the integral.

Question 5

What do you do if n is even and m is odd for the following function;

Answer 5

Deal with each individual integral separately.

Question 6

What do you do if n is odd for the following function:

Answer 6

Strip out one tan and one sec and convert the rest to sec using tan²x=sec²x-1

Then solve using u-substitution using

u=secx

Question 7

What do you do if m is even for the following function:

Answer 7

Strip out two sec and convert the rest to tan using

sec²x=1+tan²x

then u-substitution using

u=tanx

Question 8

What do you do if n is odd and m is even for the following function:

Answer 8

Pick to use rules based on m or n.