Trig Integrals without immediate answers

Question 1

If the power of cos is odd…

Answer 1

factor out 1 cosx
replace remaining even powered cosx ‘s with cos^2(x)=1-sin^2(x)
u substitution where u=sinx

Question 2

If the power of sin is odd…

Answer 2

factor out 1 sinx
replace remaining even powered sinx ‘s with sin^2(x)=1-cos^2(x)
u substitution were u=cosx

Question 3

If the power of sinx or/and cosx is/are even…

Answer 3

use 1/2 angle formulas:

sin^2(x)=(1/2)(1-cos(2x))
cos^2(x)=(1/2)(1+cos(2x))
sinxcosx=(1/2)(sin(2x))

Question 4

If power of tanx is odd (and secantx is present)…

Answer 4

factor out secxtanx
replace remaining even powered tanx ‘s with tan^2(x)=sec^2(x)-1
u substitution where u=secx du=secxtanx

Question 5

If power of sec is even…

Answer 5

factor out sec^2(x)
replace with sec^2(x)=tan^2(x) +1
use u substitution where u=tanx and du=sec^2(x)