7.2 U Substitution

MATH 151 SI
7.2 U Substitution
Name
7.2 U Substitution
Evaluate the following indefinite integrals using U substitution
1. ∫ 24(6π‘₯ + 7)3 𝑑π‘₯
2
2. ∫ 2π‘₯ βˆ— 𝑒 2π‘₯ 𝑑π‘₯
3π‘₯+7
3. ∫ 2
𝑑π‘₯
6π‘₯ +28π‘₯+7
2
4.
4π‘₯
∫ π‘₯2
𝑑π‘₯
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MATH 151 SI
5. ∫
1
βˆšπ‘ (9+βˆšπ‘ )
7.2 U Substitution
4/22/14
𝑑𝑠
6. ∫ π‘ž(π‘ž βˆ’ 5)4 π‘‘π‘ž
3π‘₯
7. ∫ 3π‘₯βˆ’7 𝑑π‘₯
√
Rule
Constant
Power
Definition
Example
∫ π‘˜π‘‘π‘₯ =
∫ 10𝑑π‘₯
∫ π‘₯ 𝑛 𝑑π‘₯ =
∫ π‘₯ 4 𝑑π‘₯ =
n β‰  βˆ’1
Exponential
∫ 𝑒 π‘˜π‘₯ 𝑑π‘₯ =
∫ 4βˆ’3π‘₯ 𝑑π‘₯ =
∫ π‘Žπ‘˜π‘₯ 𝑑π‘₯ =
Logarithmic
1
∫ 𝑑π‘₯ =
π‘₯
∫
1
𝑑π‘₯ =
2π‘₯
MATH 151 SI
7.2 U Substitution
4/22/14