Trig Integration

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8 Terms

1
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√(a2  - x2 )

x = asin(θ)

1 - sin2 (θ) = cos2 (θ)

2
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√(a2 + x2 )

x = atan(θ)

1 + tan2 (θ) = sec2 (θ)

3
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√(x2  - a2 )

x = asec(θ)

sec2 (θ) -1 = tan2 (θ)

4
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∫ sin(x)cos(x)

sin(x) is odd

u = cos(x), du = -sin(x)dx

Use sin(x) = 1 - cos2 (x) = 1 - u2 

5
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∫ sin(x)cos(x)

cos(x) is odd

u = sin(x), du = cos(x)dx

Use cos(x) = 1- sin2 (x) = 1 - u2 

6
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∫ sin(x)cos(x)

Both are even

sin2 (x) = ½ (1 - cos(2x))

cos2 (x) = ½ (1 + cos(2x))

7
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∫ sec(x)tan(x)

tan(x) is odd

u = sec(x), du = sec(x)tan(x)dx

Use tan2 (x) = sec2 (x) - 1 = (u2  - 1)

8
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∫ sec(x)tan(x)

sec(x) is odd

u = tan(x), du = sec2 (x)

Use sec2 (x) = 1 + tan2 (x)