Chapter 6: Trig Integrals and Substitutions

Question 1

∫tan(x) dx

Answer 1

ln |sec(x)| + C

Question 2

∫sec(x) dx

Answer 2

ln|sec(x) + tan(x)| + C

Question 3

What is the secant reduction formula?

Answer 3

∫secⁿ(x) dx =

(1/(n-1))*sec^n-2(x)*tan(x) + ((n-2)/(n-1))*∫sec^n-2(x) dx

Question 4

What is the trigonometric substitution for the expression

sqrt(x²-a²)

Answer 4

x = a sec(θ)

Question 5

What is the trigonometric substitution for the expression

sqrt(a²+x²)

Answer 5

x = a tan(θ)

Question 6

What is the trigonometric substitution for the expression

sqrt(a²-x²)

Answer 6

x = a sin(θ)