Trig Integration Formula Memorization

sin²x (pythagorean)

1 - cos²x

cos²x (pythagorean)

1 - sin²x

sec²x

tan²x + 1

tan²x

sec²x - 1

sin2x

2 sinx cosx

cos2x identity 1

cos²x - sin²x

cos2x identity 2

2 cos²x - 1

cos2x identity 3

1 - 2 sin²x

tan2x

2 tanx / 1-tan²x

sin²x (half-angle)

½ (1 - cos(2x))

cos²x (half-angle)

½ (1 + cos(2x))

∫tanx dx

ln |secx| + C

∫secx dx

ln |secx + tanx| + C

sin A cos B

½ [ sin(A + B) + sin(A − B) ]

sin A sin B

½ [ cos(A − B) − cos(A + B) ]

cos A cos B

½ [ cos(A - B) + cos(A + B) ]

√a² - x²

asinθ

√x²+a²

atanθ

√x²-a²

asecθ

∫sin^m cos^1 or ∫cos^n sin^1

U-sub the larger power

Odd power of sin or cos

Split odd power, save a factor of the other, sub sin^2 + cos^2 = 1

Even power of sin AND cos

Split into squares, use half-angle formulas

Even power of sec

Split the even power, save a factor of sec^2, sub sec^2 = tan^2 + 1

Odd power of tan

Split everything, save a factor of sec tan, sub tan^2 = sec^2 - 1