Unit 5: Calculus

Topic 5.10: Integration by Substitution Questions

Practice 20 exam-style questions for IB Math AA SL Topic 5.10. Review the question stems below, then unlock the full Question Bank to access markschemes, model answers, and AI grading.

1Find2 marks

2026

Find ∫cos(2x) dx.

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2Choose1 mark

Find

\int sin (3 x) d x

, including the constant.

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3Choose1 mark

Work out

\int e^{5 x} d x

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4Find2 marks

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Find

\int cos (2 x) d x

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5Find2 marks

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Find ∫e^4x dx.

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6Find2 marks

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Find

\int e^{4 x} d x

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7Find2 marks

2026

Find

\int (3 x + 2)^{4} d x

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8Find2 marks

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Find ∫(3x + 2)⁴ dx.

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9Find3 marks

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Find

\int (6 x + 4) (3 x^{2} + 4 x - 1)^{3} d x

, noticing the bracket's derivative.

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10Find3 marks

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Find

\int cos x \cdot sin^{3} x d x

using

u = sin x

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11Find3 marks

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Find

\int x^{2} (x^{3} - 1)^{4} d x

using a suitable substitution.

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12Find2 marks

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Find ∫1/(3x − 1) dx.

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13Find3 marks

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

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14Find3 marks

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

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15Find3 marks

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

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16Choose1 mark

Integrate

\frac{1}{2 x + 7}

with respect to

x

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17Choose1 mark

Notice the numerator, then find

\int \frac{3 x ^{2}}{x ^{3} + 8} d x

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18Find3 marks

2026

Find

\int x (x^{2} + 3)^{5} d x

using

u = x^{2} + 3

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19Find2 marks

2026

Find ∫(2x)/(x² + 4) dx.

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20Find3 marks

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Find ∫6x(x² + 1)² dx.

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