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The Substitution Rule- HW Problems
Evaluate the integrals using the substitution given.
1. ∫(sin4 (𝑥))(cos(𝑥 ))𝑑𝑥, 𝑢 = sin(𝑥 )
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2. ∫ 𝑥 7 (1 + 𝑥 8 )3 𝑑𝑥, 𝑢 = 1 + 𝑥8
Evaluate the indefinite integrals.
3. ∫ 2𝑥 (cos(𝑥 2 ))𝑑𝑥
4. ∫ 𝑥√1 + 𝑥 2 𝑑𝑥
𝑥
5. ∫ (1+𝑥 2 )4 𝑑𝑥
6𝑥 2
6. ∫ √1−𝑥 3 𝑑𝑥
3 sin(𝑥)
7. ∫ (1+cos(𝑥))3 𝑑𝑥
8. ∫(tan4 (𝑥)) (sec 2 (𝑥))𝑑𝑥
cos(√𝜃)
9. ∫ 𝑑𝜃
√𝜃
10. ∫ 𝑥 √𝑥 + 3𝑑𝑥
𝑥
11. ∫ √7−𝑥 𝑑𝑥
12. ∫(𝑡 + 1) sin(𝑡 2 + 2𝑡 − 4) 𝑑𝑡
The Substitution Rule- HW Problems
Evaluate the integrals using the substitution given.
1. ∫(sin4 (𝑥))(cos(𝑥 ))𝑑𝑥, 𝑢 = sin(𝑥 )
1
2. ∫ 𝑥 7 (1 + 𝑥 8 )3 𝑑𝑥, 𝑢 = 1 + 𝑥8
Evaluate the indefinite integrals.
3. ∫ 2𝑥 (cos(𝑥 2 ))𝑑𝑥
4. ∫ 𝑥√1 + 𝑥 2 𝑑𝑥
𝑥
5. ∫ (1+𝑥 2 )4 𝑑𝑥
6𝑥 2
6. ∫ √1−𝑥 3 𝑑𝑥
3 sin(𝑥)
7. ∫ (1+cos(𝑥))3 𝑑𝑥
8. ∫(tan4 (𝑥)) (sec 2 (𝑥))𝑑𝑥
cos(√𝜃)
9. ∫ 𝑑𝜃
√𝜃
10. ∫ 𝑥 √𝑥 + 3𝑑𝑥
𝑥
11. ∫ √7−𝑥 𝑑𝑥
12. ∫(𝑡 + 1) sin(𝑡 2 + 2𝑡 − 4) 𝑑𝑡
