05 - Integration Substitution Log Exp - Kuta Software

Kuta Software - Infinite Calculus

Name___________________________________

Integration by Substitution

Date________________ Period____

Evaluate each indefinite integral. Use the provided substitution. 1)

∫

20 x 4 dx; u = 4 x 5 + 3 4x5 + 3

3)

∫

80 x 3 ⋅ 3 5 x

4

−2

dx; u = 5 x 4 − 2

2)

∫

36 x 2 e

4)

∫

2 dx; u = −1 + ln 4 x x(−1 + ln 4 x )

6)

∫

20e

4 x3 + 3

dx; u = 4 x 3 + 3

Evaluate each indefinite integral. 5)

7)

∫

12 x 2 dx x3 + 2

∫ 10sin −2x ⋅ e

cos −2 x

dx

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8)

∫

e

5x

5e

5x

dx

+3

−3 + ln 3 x

dx x

Worksheet by Kuta Software LLC

Kuta Software - Infinite Calculus

Name___________________________________

Integration by Substitution

Date________________ Period____

Evaluate each indefinite integral. Use the provided substitution. 1)

∫

20 x 4 dx; u = 4 x 5 + 3 4x5 + 3

2)

∫

ln 4 x 5 + 3 + C

3)

∫

80 x 3 ⋅ 3 5 x

4

−2

3e

dx; u = 5 x 4 − 2

4)

∫

5x4 − 2

4⋅3 ln 3

36 x 2 e

4 x3 + 3

4x3 + 3

dx; u = 4 x 3 + 3

+C

2 dx; u = −1 + ln 4 x x(−1 + ln 4 x ) 2 ln −1 + ln 4 x + C

+C

Evaluate each indefinite integral. 5)

∫

12 x 2 dx x3 + 2

6)

∫

4 ln 2 x 3 + 4 + C

7)

∫ 10sin −2x ⋅ e 5e

cos −2 x

cos −2 x

20e e

5x

5x

dx

+3

4 ln e 5 x + 3 + C

dx

+C

8)

∫

5e

−3 + ln 3 x

dx x

5e

−3 + ln 3 x

+C

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Worksheet by Kuta Software LLC