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Limits

Limits by direct substitutionLimits by factoring (0/0 forms)Limits at infinityOne-sided limits and continuity

Derivatives

Derivatives with the power ruleThe product and quotient rulesThe chain ruleDerivatives of trigonometric, exponential and logarithmic functionsEquations of tangent lines

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Critical points, extrema and increasing intervalsPosition, velocity and accelerationOptimization problemsRelated ratesConcavity and inflection points

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Indefinite integrals (antiderivatives)Definite integralsIntegration by substitutionArea between curvesRiemann sums and the trapezoidal rule

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Differential equations: initial value problemsExponential growth and decay models (dy/dt = ky)

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1. Integration by substitution

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Planned: 12 / 60 questions

12 questionsSign in to download PDFsSettingsShow answers

Name ______________________Date ____________Score ____ / 12

Integration by substitution practice

Integration by substitution · 1–12

Integrate using substitution.

Medium

1.∫2x(x² − 8)³ dx

Medium

2.∫2x(x² − 9)⁵ dx

Medium

3.∫2x(x² + 9)³ dx

Medium

4.∫2x(x² + 1)⁵ dx

Medium

5.∫2x(x² + 2)⁴ dx

Medium

6.∫2x(x² − 6)⁵ dx

Medium

7.∫2x(x² + 3)² dx

Medium

8.∫2x(x² + 5)⁴ dx

Medium

9.∫2x(x² + 6)⁵ dx

Medium

10.∫2x(x² + 1)³ dx

Medium

11.∫2x(x² + 6)³ dx

Medium

12.∫2x(x² − 8)⁴ dx

Answer key — Integration by substitution practice

Integration by substitution

1.14(x² − 8)⁴ + C

2.16(x² − 9)⁶ + C

3.14(x² + 9)⁴ + C

4.16(x² + 1)⁶ + C

5.15(x² + 2)⁵ + C

6.16(x² − 6)⁶ + C

7.13(x² + 3)³ + C

8.15(x² + 5)⁵ + C

9.16(x² + 6)⁶ + C

10.14(x² + 1)⁴ + C

11.14(x² + 6)⁴ + C

12.15(x² − 8)⁵ + C

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