Question 1

Find ∫e^(4x) dx.

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Question 2

Find ∫cos(2x) dx.

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Question 3

Find ∫(3x + 2)⁴ dx.

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Question 4

Find ∫x(x² + 3)⁵ dx using u = x² + 3.

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Question 5

Find ∫(2x)/(x² + 4) dx.

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Question 6

Find ∫6x(x² + 1)² dx.

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Question 7

Find ∫(x²)/(x³ + 2) dx.

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Question 8

Find ∫3x²(x³ + 5)⁴ dx using a substitution.

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Question 9

Find ∫x²(x³ − 1)⁴ dx using a suitable substitution.

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Question 10

Find ∫x√(x² + 9) dx using u = x² + 9.

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Question 11

Find ∫1/(3x − 1) dx.

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Question 12

Find ∫(6x + 4)(3x² + 4x − 1)³ dx, noticing the bracket's derivative.

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Question 13

Find ∫cos x · sin³x dx using u = sin x.

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Question 14

Evaluate ∫₁² (2x)/(x² + 3) dx using u = x² + 3.

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Question 15

Evaluate ∫₀² 2x(x² + 1)² dx using u = x² + 1.

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Question 16

Find ∫sin(5x) dx and hence evaluate ∫₀^(π/5) sin(5x) dx.

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Topic 5.10: Integration by Substitution Questions

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