Methods of Integration

Question 1

Integration by substitution

Answer 1

u=

du/dx =

Question 2

Integration by parts

Answer 2

The integral of uv’ = uv - integral of u’v

Log Algebra Trig Exponential

Question 3

Integrals of sin(ax)cos(bx)

Answer 3

Use formulas for sin(a+/-b) and cos(a+/- b)

Question 4

Integrals of sin^n(x)cos^n(x)

Answer 4

If one or both powers are odd use substitution/inspection - sin^2 + cos^2 =1

If both powers are even, us the double angle formulas

Question 5

Trigonometric Substitution

Answer 5

Sin if minus, tan if +
use sin^2 + cos^2=1 and Sec^2 =tan^2 +1
x = a/btanU
Draw right angle triangle